Gamma_0(11) Weight 2 ------------------------------------------------------- J_0(11), dim = 1 ------------------------------------------------------- 11A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 5 Torsion Bound = 5 |L(1)/Omega| = 1/5 Sha Bound = 5 ANALYTIC INVARIANTS: Omega+ = 1.2692093042795534217 + 0.3059862835737342116e-39i Omega- = 0.13729835100889706111e-38 + -2.9176332338769904587i L(1) = 0.25384186085591068434 w1 = -0.63460465213977671084 + -1.4588166169384952293i w2 = -1.2692093042795534217 + -0.3059862835737342116e-39i c4 = 495.99999999999527567 + -0.30608752059884439992e-36i c6 = 20008.000000008749296 + -0.37493358120158091857e-34i j = -757.67263785907241536 + -0.20669731864407559281e-35i HECKE EIGENFORM: f(q) = q + -2*q^2 + -1*q^3 + 2*q^4 + 1*q^5 + 2*q^6 + -2*q^7 + -2*q^9 + -2*q^10 + 1*q^11 + -2*q^12 + 4*q^13 + 4*q^14 + -1*q^15 + -4*q^16 + -2*q^17 + 4*q^18 + 2*q^20 + 2*q^21 + -2*q^22 + -1*q^23 + -4*q^25 + -8*q^26 + 5*q^27 + -4*q^28 + 2*q^30 + 7*q^31 + 8*q^32 + -1*q^33 + 4*q^34 + -2*q^35 + -4*q^36 + 3*q^37 + -4*q^39 + -8*q^41 + -4*q^42 + -6*q^43 + 2*q^44 + -2*q^45 + 2*q^46 + 8*q^47 + 4*q^48 + -3*q^49 + 8*q^50 + 2*q^51 + 8*q^52 + -6*q^53 + -10*q^54 + 1*q^55 + 5*q^59 + -2*q^60 + 12*q^61 + -14*q^62 + 4*q^63 + -8*q^64 + 4*q^65 + 2*q^66 + -7*q^67 + -4*q^68 + 1*q^69 + 4*q^70 + -3*q^71 + 4*q^73 + -6*q^74 + 4*q^75 + -2*q^77 + 8*q^78 + -10*q^79 + -4*q^80 + 1*q^81 + 16*q^82 + -6*q^83 + 4*q^84 + -2*q^85 + 12*q^86 + 15*q^89 + 4*q^90 + -8*q^91 + -2*q^92 + -7*q^93 + -16*q^94 + -8*q^96 + -7*q^97 + 6*q^98 + -2*q^99 + -8*q^100 + 2*q^101 + -4*q^102 + -16*q^103 + 2*q^105 + 12*q^106 + 18*q^107 + 10*q^108 + 10*q^109 + -2*q^110 + -3*q^111 + 8*q^112 + 9*q^113 + -1*q^115 + -8*q^117 + -10*q^118 + 4*q^119 + 1*q^121 + -24*q^122 + 8*q^123 + 14*q^124 + -9*q^125 + -8*q^126 + 8*q^127 + 6*q^129 + -8*q^130 + -18*q^131 + -2*q^132 + 14*q^134 + 5*q^135 + -7*q^137 + -2*q^138 + 10*q^139 + -4*q^140 + -8*q^141 + 6*q^142 + 4*q^143 + 8*q^144 + -8*q^146 + 3*q^147 + 6*q^148 + -10*q^149 + -8*q^150 + 2*q^151 + 4*q^153 + 4*q^154 + 7*q^155 + -8*q^156 + -7*q^157 + 20*q^158 + 6*q^159 + 8*q^160 + 2*q^161 + -2*q^162 + 4*q^163 + -16*q^164 + -1*q^165 + 12*q^166 + -12*q^167 + 3*q^169 + 4*q^170 + -12*q^172 + -6*q^173 + 8*q^175 + -4*q^176 + -5*q^177 + -30*q^178 + -15*q^179 + -4*q^180 + 7*q^181 + 16*q^182 + -12*q^183 + 3*q^185 + 14*q^186 + -2*q^187 + 16*q^188 + -10*q^189 + 17*q^191 + 8*q^192 + 4*q^193 + 14*q^194 + -4*q^195 + -6*q^196 + -2*q^197 + 4*q^198 + ... ------------------------------------------------------- Gamma_0(14) Weight 2 ------------------------------------------------------- J_0(14), dim = 1 ------------------------------------------------------- 14A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 2*3 Torsion Bound = 2*3 |L(1)/Omega| = 1/2*3 Sha Bound = 2*3 ANALYTIC INVARIANTS: Omega+ = 1.9813419560668832342 + -0.57966734777994701199e-45i Omega- = -2.6509824793649734287i L(1) = 0.33022365934448053903 w1 = 0.99067097803344161708 + 1.3254912396824867143i w2 = 0.99067097803344161708 + -1.3254912396824867143i c4 = -214.99999999999363375 + 0.51627365772238651979e-11i c6 = 5291.000000010010186 + -0.68978662053619098087e-8i j = 452.73209730191306582 + 0.84710694491255540172e-9i HECKE EIGENFORM: f(q) = q + -1*q^2 + -2*q^3 + 1*q^4 + 2*q^6 + 1*q^7 + -1*q^8 + 1*q^9 + -2*q^12 + -4*q^13 + -1*q^14 + 1*q^16 + 6*q^17 + -1*q^18 + 2*q^19 + -2*q^21 + 2*q^24 + -5*q^25 + 4*q^26 + 4*q^27 + 1*q^28 + -6*q^29 + -4*q^31 + -1*q^32 + -6*q^34 + 1*q^36 + 2*q^37 + -2*q^38 + 8*q^39 + 6*q^41 + 2*q^42 + 8*q^43 + -12*q^47 + -2*q^48 + 1*q^49 + 5*q^50 + -12*q^51 + -4*q^52 + 6*q^53 + -4*q^54 + -1*q^56 + -4*q^57 + 6*q^58 + -6*q^59 + 8*q^61 + 4*q^62 + 1*q^63 + 1*q^64 + -4*q^67 + 6*q^68 + -1*q^72 + 2*q^73 + -2*q^74 + 10*q^75 + 2*q^76 + -8*q^78 + 8*q^79 + -11*q^81 + -6*q^82 + -6*q^83 + -2*q^84 + -8*q^86 + 12*q^87 + -6*q^89 + -4*q^91 + 8*q^93 + 12*q^94 + 2*q^96 + -10*q^97 + -1*q^98 + -5*q^100 + 12*q^102 + -4*q^103 + 4*q^104 + -6*q^106 + 12*q^107 + 4*q^108 + 2*q^109 + -4*q^111 + 1*q^112 + 6*q^113 + 4*q^114 + -6*q^116 + -4*q^117 + 6*q^118 + 6*q^119 + -11*q^121 + -8*q^122 + -12*q^123 + -4*q^124 + -1*q^126 + -16*q^127 + -1*q^128 + -16*q^129 + 18*q^131 + 2*q^133 + 4*q^134 + -6*q^136 + 18*q^137 + 14*q^139 + 24*q^141 + 1*q^144 + -2*q^146 + -2*q^147 + 2*q^148 + -18*q^149 + -10*q^150 + 8*q^151 + -2*q^152 + 6*q^153 + 8*q^156 + -4*q^157 + -8*q^158 + -12*q^159 + 11*q^162 + -16*q^163 + 6*q^164 + 6*q^166 + -12*q^167 + 2*q^168 + 3*q^169 + 2*q^171 + 8*q^172 + -12*q^173 + -12*q^174 + -5*q^175 + 12*q^177 + 6*q^178 + -12*q^179 + 20*q^181 + 4*q^182 + -16*q^183 + -8*q^186 + -12*q^188 + 4*q^189 + 24*q^191 + -2*q^192 + 14*q^193 + 10*q^194 + 1*q^196 + -18*q^197 + 20*q^199 + 5*q^200 + ... ------------------------------------------------------- Gamma_0(15) Weight 2 ------------------------------------------------------- J_0(15), dim = 1 ------------------------------------------------------- 15A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2^2 Torsion Bound = 2^3 |L(1)/Omega| = 1/2^3 Sha Bound = 2^3 ANALYTIC INVARIANTS: Omega+ = 1.4006030423326020232 + 0.11271976031056334584e-37i Omega- = 1.5962422221317835101i L(1) = 0.1750753802915752529 w1 = 1.5962422221317835101i w2 = 1.4006030423326020232 + 0.11271976031056334584e-37i c4 = 480.99999999999539535 + -0.11074053372419936509e-34i c6 = 4879.0000000070087591 + -0.42890069723239564355e-33i j = 2198.2151308659332645 + -0.63852060580473614594e-34i HECKE EIGENFORM: f(q) = q + -1*q^2 + -1*q^3 + -1*q^4 + 1*q^5 + 1*q^6 + 3*q^8 + 1*q^9 + -1*q^10 + -4*q^11 + 1*q^12 + -2*q^13 + -1*q^15 + -1*q^16 + 2*q^17 + -1*q^18 + 4*q^19 + -1*q^20 + 4*q^22 + -3*q^24 + 1*q^25 + 2*q^26 + -1*q^27 + -2*q^29 + 1*q^30 + -5*q^32 + 4*q^33 + -2*q^34 + -1*q^36 + -10*q^37 + -4*q^38 + 2*q^39 + 3*q^40 + 10*q^41 + 4*q^43 + 4*q^44 + 1*q^45 + 8*q^47 + 1*q^48 + -7*q^49 + -1*q^50 + -2*q^51 + 2*q^52 + -10*q^53 + 1*q^54 + -4*q^55 + -4*q^57 + 2*q^58 + -4*q^59 + 1*q^60 + -2*q^61 + 7*q^64 + -2*q^65 + -4*q^66 + 12*q^67 + -2*q^68 + -8*q^71 + 3*q^72 + 10*q^73 + 10*q^74 + -1*q^75 + -4*q^76 + -2*q^78 + -1*q^80 + 1*q^81 + -10*q^82 + 12*q^83 + 2*q^85 + -4*q^86 + 2*q^87 + -12*q^88 + -6*q^89 + -1*q^90 + -8*q^94 + 4*q^95 + 5*q^96 + 2*q^97 + 7*q^98 + -4*q^99 + -1*q^100 + 6*q^101 + 2*q^102 + -16*q^103 + -6*q^104 + 10*q^106 + -12*q^107 + 1*q^108 + 14*q^109 + 4*q^110 + 10*q^111 + 2*q^113 + 4*q^114 + 2*q^116 + -2*q^117 + 4*q^118 + -3*q^120 + 5*q^121 + 2*q^122 + -10*q^123 + 1*q^125 + -8*q^127 + 3*q^128 + -4*q^129 + 2*q^130 + -12*q^131 + -4*q^132 + -12*q^134 + -1*q^135 + 6*q^136 + -6*q^137 + -4*q^139 + -8*q^141 + 8*q^142 + 8*q^143 + -1*q^144 + -2*q^145 + -10*q^146 + 7*q^147 + 10*q^148 + 22*q^149 + 1*q^150 + -8*q^151 + 12*q^152 + 2*q^153 + -2*q^156 + 14*q^157 + 10*q^159 + -5*q^160 + -1*q^162 + -4*q^163 + -10*q^164 + 4*q^165 + -12*q^166 + -9*q^169 + -2*q^170 + 4*q^171 + -4*q^172 + -18*q^173 + -2*q^174 + 4*q^176 + 4*q^177 + 6*q^178 + 20*q^179 + -1*q^180 + -10*q^181 + 2*q^183 + -10*q^185 + -8*q^187 + -8*q^188 + -4*q^190 + 16*q^191 + -7*q^192 + 2*q^193 + -2*q^194 + 2*q^195 + 7*q^196 + 6*q^197 + 4*q^198 + -8*q^199 + 3*q^200 + ... ------------------------------------------------------- Gamma_0(17) Weight 2 ------------------------------------------------------- J_0(17), dim = 1 ------------------------------------------------------- 17A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 2^2 Torsion Bound = 2^2 |L(1)/Omega| = 1/2^2 Sha Bound = 2^2 ANALYTIC INVARIANTS: Omega+ = 1.5470797535511201732 + -0.43447841757997306343e-33i Omega- = 0.33964661020505034238e-33 + 2.745739118089753672i L(1) = 0.3867699383877800433 w1 = -0.7735398767755600866 + -1.372869559044876836i w2 = -1.5470797535511201732 + 0.43447841757997306343e-33i c4 = 33.000000000249671654 + 0.23930515977994133707e-30i c6 = 12014.999999576970406 + 0.14537826379428910875e-28i j = -0.43027502069356309261 + -0.83214684979929813881e-32i HECKE EIGENFORM: f(q) = q + -1*q^2 + -1*q^4 + -2*q^5 + 4*q^7 + 3*q^8 + -3*q^9 + 2*q^10 + -2*q^13 + -4*q^14 + -1*q^16 + 1*q^17 + 3*q^18 + -4*q^19 + 2*q^20 + 4*q^23 + -1*q^25 + 2*q^26 + -4*q^28 + 6*q^29 + 4*q^31 + -5*q^32 + -1*q^34 + -8*q^35 + 3*q^36 + -2*q^37 + 4*q^38 + -6*q^40 + -6*q^41 + 4*q^43 + 6*q^45 + -4*q^46 + 9*q^49 + 1*q^50 + 2*q^52 + 6*q^53 + 12*q^56 + -6*q^58 + -12*q^59 + -10*q^61 + -4*q^62 + -12*q^63 + 7*q^64 + 4*q^65 + 4*q^67 + -1*q^68 + 8*q^70 + -4*q^71 + -9*q^72 + -6*q^73 + 2*q^74 + 4*q^76 + 12*q^79 + 2*q^80 + 9*q^81 + 6*q^82 + -4*q^83 + -2*q^85 + -4*q^86 + 10*q^89 + -6*q^90 + -8*q^91 + -4*q^92 + 8*q^95 + 2*q^97 + -9*q^98 + 1*q^100 + -10*q^101 + 8*q^103 + -6*q^104 + -6*q^106 + 8*q^107 + 6*q^109 + -4*q^112 + -14*q^113 + -8*q^115 + -6*q^116 + 6*q^117 + 12*q^118 + 4*q^119 + -11*q^121 + 10*q^122 + -4*q^124 + 12*q^125 + 12*q^126 + 8*q^127 + 3*q^128 + -4*q^130 + 16*q^131 + -16*q^133 + -4*q^134 + 3*q^136 + -6*q^137 + -8*q^139 + 8*q^140 + 4*q^142 + 3*q^144 + -12*q^145 + 6*q^146 + 2*q^148 + -10*q^149 + -16*q^151 + -12*q^152 + -3*q^153 + -8*q^155 + -2*q^157 + -12*q^158 + 10*q^160 + 16*q^161 + -9*q^162 + 24*q^163 + 6*q^164 + 4*q^166 + -4*q^167 + -9*q^169 + 2*q^170 + 12*q^171 + -4*q^172 + 22*q^173 + -4*q^175 + -10*q^178 + 12*q^179 + -6*q^180 + -2*q^181 + 8*q^182 + 12*q^184 + 4*q^185 + -8*q^190 + -16*q^191 + 2*q^193 + -2*q^194 + -9*q^196 + -18*q^197 + -20*q^199 + -3*q^200 + ... ------------------------------------------------------- Gamma_0(19) Weight 2 ------------------------------------------------------- J_0(19), dim = 1 ------------------------------------------------------- 19A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 1.3597597334883108107 + 0.89357968985713309066e-31i Omega- = 0.29757051331387211599e-29 + -4.1270923917172404647i L(1) = 0.45325324449610360358 w1 = -0.67987986674415540537 + -2.0635461958586202323i w2 = -1.3597597334883108107 + -0.89357968985713309066e-31i c4 = 447.99999999980911037 + -0.68424641734672241246e-28i c6 = 10088.000000136937544 + -0.61822617395497506154e-26i j = -13109.110945918256219 + -0.86384903441062371352e-25i HECKE EIGENFORM: f(q) = q + -2*q^3 + -2*q^4 + 3*q^5 + -1*q^7 + 1*q^9 + 3*q^11 + 4*q^12 + -4*q^13 + -6*q^15 + 4*q^16 + -3*q^17 + 1*q^19 + -6*q^20 + 2*q^21 + 4*q^25 + 4*q^27 + 2*q^28 + 6*q^29 + -4*q^31 + -6*q^33 + -3*q^35 + -2*q^36 + 2*q^37 + 8*q^39 + -6*q^41 + -1*q^43 + -6*q^44 + 3*q^45 + -3*q^47 + -8*q^48 + -6*q^49 + 6*q^51 + 8*q^52 + 12*q^53 + 9*q^55 + -2*q^57 + -6*q^59 + 12*q^60 + -1*q^61 + -1*q^63 + -8*q^64 + -12*q^65 + -4*q^67 + 6*q^68 + 6*q^71 + -7*q^73 + -8*q^75 + -2*q^76 + -3*q^77 + 8*q^79 + 12*q^80 + -11*q^81 + 12*q^83 + -4*q^84 + -9*q^85 + -12*q^87 + 12*q^89 + 4*q^91 + 8*q^93 + 3*q^95 + 8*q^97 + 3*q^99 + -8*q^100 + 6*q^101 + 14*q^103 + 6*q^105 + -18*q^107 + -8*q^108 + -16*q^109 + -4*q^111 + -4*q^112 + 6*q^113 + -12*q^116 + -4*q^117 + 3*q^119 + -2*q^121 + 12*q^123 + 8*q^124 + -3*q^125 + 2*q^127 + 2*q^129 + -15*q^131 + 12*q^132 + -1*q^133 + 12*q^135 + -3*q^137 + -13*q^139 + 6*q^140 + 6*q^141 + -12*q^143 + 4*q^144 + 18*q^145 + 12*q^147 + -4*q^148 + 21*q^149 + -10*q^151 + -3*q^153 + -12*q^155 + -16*q^156 + 14*q^157 + -24*q^159 + 20*q^163 + 12*q^164 + -18*q^165 + -18*q^167 + 3*q^169 + 1*q^171 + 2*q^172 + -18*q^173 + -4*q^175 + 12*q^176 + 12*q^177 + -18*q^179 + -6*q^180 + 2*q^181 + 2*q^183 + 6*q^185 + -9*q^187 + 6*q^188 + -4*q^189 + 3*q^191 + 16*q^192 + -4*q^193 + 24*q^195 + 12*q^196 + 18*q^197 + 11*q^199 + ... ------------------------------------------------------- Gamma_0(20) Weight 2 ------------------------------------------------------- J_0(20), dim = 1 ------------------------------------------------------- 20A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 2*3 Torsion Bound = 2*3 |L(1)/Omega| = 1/2*3 Sha Bound = 2*3 ANALYTIC INVARIANTS: Omega+ = 2.8243751419591137995 + -0.60650242879223896752e-45i Omega- = -2.2741651990410812607i L(1) = 0.47072919032651896658 w1 = 1.4121875709795568997 + -1.1370825995205406303i w2 = -1.4121875709795568997 + -1.1370825995205406303i c4 = -176.00000000000231173 + -0.11690435302745935616e-11i c6 = -2367.9999999979810162 + -0.24853222347605818446e-8i j = 851.84000000075352974 + -0.89802043514728136522e-9i HECKE EIGENFORM: f(q) = q + -2*q^3 + -1*q^5 + 2*q^7 + 1*q^9 + 2*q^13 + 2*q^15 + -6*q^17 + -4*q^19 + -4*q^21 + 6*q^23 + 1*q^25 + 4*q^27 + 6*q^29 + -4*q^31 + -2*q^35 + 2*q^37 + -4*q^39 + 6*q^41 + -10*q^43 + -1*q^45 + -6*q^47 + -3*q^49 + 12*q^51 + -6*q^53 + 8*q^57 + 12*q^59 + 2*q^61 + 2*q^63 + -2*q^65 + 2*q^67 + -12*q^69 + -12*q^71 + 2*q^73 + -2*q^75 + 8*q^79 + -11*q^81 + 6*q^83 + 6*q^85 + -12*q^87 + -6*q^89 + 4*q^91 + 8*q^93 + 4*q^95 + 2*q^97 + 6*q^101 + 14*q^103 + 4*q^105 + -6*q^107 + 2*q^109 + -4*q^111 + -6*q^113 + -6*q^115 + 2*q^117 + -12*q^119 + -11*q^121 + -12*q^123 + -1*q^125 + 2*q^127 + 20*q^129 + -8*q^133 + -4*q^135 + 18*q^137 + -4*q^139 + 12*q^141 + -6*q^145 + 6*q^147 + -6*q^149 + 20*q^151 + -6*q^153 + 4*q^155 + -22*q^157 + 12*q^159 + 12*q^161 + -10*q^163 + 18*q^167 + -9*q^169 + -4*q^171 + -6*q^173 + 2*q^175 + -24*q^177 + -12*q^179 + -10*q^181 + -4*q^183 + -2*q^185 + 8*q^189 + -12*q^191 + 26*q^193 + 4*q^195 + 18*q^197 + 8*q^199 + ... ------------------------------------------------------- Gamma_0(21) Weight 2 ------------------------------------------------------- J_0(21), dim = 1 ------------------------------------------------------- 21A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2^2 Torsion Bound = 2^3 |L(1)/Omega| = 1/2^3 Sha Bound = 2^3 ANALYTIC INVARIANTS: Omega+ = 1.8044616215539682224 + 0.29472810292846279258e-27i Omega- = -1.9109897807518291966i L(1) = 0.2255577026942460278 w1 = -1.9109897807518291966i w2 = -1.8044616215539682224 + -0.29472810292846279258e-27i c4 = 192.99999999996502162 + -0.75525051905516522399e-25i c6 = 575.00000003208539274 + -0.19302279967477339266e-23i j = 1811.3018392640124426 + -0.48372820272688486517e-24i HECKE EIGENFORM: f(q) = q + -1*q^2 + 1*q^3 + -1*q^4 + -2*q^5 + -1*q^6 + -1*q^7 + 3*q^8 + 1*q^9 + 2*q^10 + 4*q^11 + -1*q^12 + -2*q^13 + 1*q^14 + -2*q^15 + -1*q^16 + -6*q^17 + -1*q^18 + 4*q^19 + 2*q^20 + -1*q^21 + -4*q^22 + 3*q^24 + -1*q^25 + 2*q^26 + 1*q^27 + 1*q^28 + -2*q^29 + 2*q^30 + -5*q^32 + 4*q^33 + 6*q^34 + 2*q^35 + -1*q^36 + 6*q^37 + -4*q^38 + -2*q^39 + -6*q^40 + 2*q^41 + 1*q^42 + -4*q^43 + -4*q^44 + -2*q^45 + -1*q^48 + 1*q^49 + 1*q^50 + -6*q^51 + 2*q^52 + 6*q^53 + -1*q^54 + -8*q^55 + -3*q^56 + 4*q^57 + 2*q^58 + 12*q^59 + 2*q^60 + -2*q^61 + -1*q^63 + 7*q^64 + 4*q^65 + -4*q^66 + 4*q^67 + 6*q^68 + -2*q^70 + 3*q^72 + -6*q^73 + -6*q^74 + -1*q^75 + -4*q^76 + -4*q^77 + 2*q^78 + -16*q^79 + 2*q^80 + 1*q^81 + -2*q^82 + -12*q^83 + 1*q^84 + 12*q^85 + 4*q^86 + -2*q^87 + 12*q^88 + -14*q^89 + 2*q^90 + 2*q^91 + -8*q^95 + -5*q^96 + 18*q^97 + -1*q^98 + 4*q^99 + 1*q^100 + 14*q^101 + 6*q^102 + 8*q^103 + -6*q^104 + 2*q^105 + -6*q^106 + 4*q^107 + -1*q^108 + -18*q^109 + 8*q^110 + 6*q^111 + 1*q^112 + -14*q^113 + -4*q^114 + 2*q^116 + -2*q^117 + -12*q^118 + 6*q^119 + -6*q^120 + 5*q^121 + 2*q^122 + 2*q^123 + 12*q^125 + 1*q^126 + 3*q^128 + -4*q^129 + -4*q^130 + 4*q^131 + -4*q^132 + -4*q^133 + -4*q^134 + -2*q^135 + -18*q^136 + -6*q^137 + 12*q^139 + -2*q^140 + -8*q^143 + -1*q^144 + 4*q^145 + 6*q^146 + 1*q^147 + -6*q^148 + 6*q^149 + 1*q^150 + 8*q^151 + 12*q^152 + -6*q^153 + 4*q^154 + 2*q^156 + -2*q^157 + 16*q^158 + 6*q^159 + 10*q^160 + -1*q^162 + 4*q^163 + -2*q^164 + -8*q^165 + 12*q^166 + -8*q^167 + -3*q^168 + -9*q^169 + -12*q^170 + 4*q^171 + 4*q^172 + -10*q^173 + 2*q^174 + 1*q^175 + -4*q^176 + 12*q^177 + 14*q^178 + -4*q^179 + 2*q^180 + -26*q^181 + -2*q^182 + -2*q^183 + -12*q^185 + -24*q^187 + -1*q^189 + 8*q^190 + -8*q^191 + 7*q^192 + 2*q^193 + -18*q^194 + 4*q^195 + -1*q^196 + 22*q^197 + -4*q^198 + 24*q^199 + -3*q^200 + ... ------------------------------------------------------- Gamma_0(22) Weight 2 ------------------------------------------------------- J_0(22), dim = 2 ------------------------------------------------------- 22A (old = 11A), dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ------------------------------------------------------- Gamma_0(23) Weight 2 ------------------------------------------------------- J_0(23), dim = 2 ------------------------------------------------------- 23A (new) , dim = 2 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 5 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 11 Torsion Bound = 11 |L(1)/Omega| = 1/11 Sha Bound = 11 ANALYTIC INVARIANTS: Omega+ = 2.7327505324965964933 + 0.11649388849290241305e-24i Omega- = 5.8575268484637719828 + -0.81849091729712220778e-24i L(1) = 0.24843186659059968121 HECKE EIGENFORM: a^2+a-1 = 0, f(q) = q + a*q^2 + (-2*a-1)*q^3 + (-a-1)*q^4 + 2*a*q^5 + (a-2)*q^6 + (2*a+2)*q^7 + (-2*a-1)*q^8 + 2*q^9 + (-2*a+2)*q^10 + (-2*a-4)*q^11 + (a+3)*q^12 + 3*q^13 + 2*q^14 + (2*a-4)*q^15 + 3*a*q^16 + (-2*a+2)*q^17 + 2*a*q^18 + -2*q^19 + -2*q^20 + (-2*a-6)*q^21 + (-2*a-2)*q^22 + 1*q^23 + 5*q^24 + (-4*a-1)*q^25 + 3*a*q^26 + (2*a+1)*q^27 + (-2*a-4)*q^28 + -3*q^29 + (-6*a+2)*q^30 + (6*a+3)*q^31 + (a+5)*q^32 + (6*a+8)*q^33 + (4*a-2)*q^34 + 4*q^35 + (-2*a-2)*q^36 + -2*a*q^37 + -2*a*q^38 + (-6*a-3)*q^39 + (2*a-4)*q^40 + (-4*a-1)*q^41 + (-4*a-2)*q^42 + (4*a+6)*q^44 + 4*a*q^45 + a*q^46 + (-2*a-1)*q^47 + (3*a-6)*q^48 + (4*a+1)*q^49 + (3*a-4)*q^50 + (-6*a+2)*q^51 + (-3*a-3)*q^52 + (4*a-2)*q^53 + (-a+2)*q^54 + (-4*a-4)*q^55 + (-2*a-6)*q^56 + (4*a+2)*q^57 + -3*a*q^58 + (4*a+4)*q^59 + (4*a+2)*q^60 + (-8*a-2)*q^61 + (-3*a+6)*q^62 + (4*a+4)*q^63 + (-2*a+1)*q^64 + 6*a*q^65 + (2*a+6)*q^66 + (2*a-4)*q^67 + -2*a*q^68 + (-2*a-1)*q^69 + 4*a*q^70 + (2*a+11)*q^71 + (-4*a-2)*q^72 + (-4*a+9)*q^73 + (2*a-2)*q^74 + (-2*a+9)*q^75 + (2*a+2)*q^76 + (-8*a-12)*q^77 + (3*a-6)*q^78 + (-8*a-6)*q^79 + (-6*a+6)*q^80 + -11*q^81 + (3*a-4)*q^82 + (2*a-10)*q^83 + (6*a+8)*q^84 + (8*a-4)*q^85 + (6*a+3)*q^87 + (6*a+8)*q^88 + (-4*a-8)*q^89 + (-4*a+4)*q^90 + (6*a+6)*q^91 + (-a-1)*q^92 + -15*q^93 + (a-2)*q^94 + -4*a*q^95 + (-9*a-7)*q^96 + (6*a+14)*q^97 + (-3*a+4)*q^98 + (-4*a-8)*q^99 + (a+5)*q^100 + (4*a+2)*q^101 + (8*a-6)*q^102 + (-10*a+2)*q^103 + (-6*a-3)*q^104 + (-8*a-4)*q^105 + (-6*a+4)*q^106 + (12*a+6)*q^107 + (-a-3)*q^108 + -4*q^110 + (-2*a+4)*q^111 + 6*q^112 + (-2*a+10)*q^113 + (-2*a+4)*q^114 + 2*a*q^115 + (3*a+3)*q^116 + 6*q^117 + 4*q^118 + 4*a*q^119 + 10*a*q^120 + (12*a+9)*q^121 + (6*a-8)*q^122 + (-2*a+9)*q^123 + (-3*a-9)*q^124 + (-4*a-8)*q^125 + 4*q^126 + (6*a-11)*q^127 + (a-12)*q^128 + (-6*a+6)*q^130 + (6*a+15)*q^131 + (-8*a-14)*q^132 + (-4*a-4)*q^133 + (-6*a+2)*q^134 + (-2*a+4)*q^135 + (-6*a+2)*q^136 + (-16*a-12)*q^137 + (a-2)*q^138 + (-6*a-7)*q^139 + (-4*a-4)*q^140 + 5*q^141 + (9*a+2)*q^142 + (-6*a-12)*q^143 + 6*a*q^144 + -6*a*q^145 + (13*a-4)*q^146 + (2*a-9)*q^147 + 2*q^148 + (16*a+14)*q^149 + (11*a-2)*q^150 + (2*a+3)*q^151 + (4*a+2)*q^152 + (-4*a+4)*q^153 + (-4*a-8)*q^154 + (-6*a+12)*q^155 + (3*a+9)*q^156 + (-12*a-4)*q^157 + (2*a-8)*q^158 + (8*a-6)*q^159 + (8*a+2)*q^160 + (2*a+2)*q^161 + -11*a*q^162 + (2*a-7)*q^163 + (a+5)*q^164 + (4*a+12)*q^165 + (-12*a+2)*q^166 + (-4*a+4)*q^167 + (10*a+10)*q^168 + -4*q^169 + (-12*a+8)*q^170 + -4*q^171 + (8*a+18)*q^173 + (-3*a+6)*q^174 + (-2*a-10)*q^175 + (-6*a-6)*q^176 + (-4*a-12)*q^177 + (-4*a-4)*q^178 + (6*a-3)*q^179 + -4*q^180 + (14*a+8)*q^181 + 6*q^182 + (-4*a+18)*q^183 + (-2*a-1)*q^184 + (4*a-4)*q^185 + -15*a*q^186 + -4*q^187 + (a+3)*q^188 + (2*a+6)*q^189 + (4*a-4)*q^190 + (-10*a-20)*q^191 + (-4*a+3)*q^192 + (8*a+5)*q^193 + (8*a+6)*q^194 + (6*a-12)*q^195 + (-a-5)*q^196 + (-4*a+1)*q^197 + (-4*a-4)*q^198 + (6*a-16)*q^199 + (-2*a+9)*q^200 + ... ------------------------------------------------------- Gamma_0(24) Weight 2 ------------------------------------------------------- J_0(24), dim = 1 ------------------------------------------------------- 24A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2^2 Torsion Bound = 2^3 |L(1)/Omega| = 1/2^3 Sha Bound = 2^3 ANALYTIC INVARIANTS: Omega+ = 2.1565156474997666435 + -0.99125450192921019734e-41i Omega- = 1.6857503548125960429i L(1) = 0.26956445593747083044 w1 = 2.1565156474997666435 + -0.99125450192921019734e-41i w2 = -1.6857503548125960429i c4 = 207.99999999997270926 + 0.55598426153455317657e-39i c6 = -2240.0000000150646579 + 0.16471274396119639423e-37i j = 3905.7777778459245576 + -0.11186411152501882634e-36i HECKE EIGENFORM: f(q) = q + -1*q^3 + -2*q^5 + 1*q^9 + 4*q^11 + -2*q^13 + 2*q^15 + 2*q^17 + -4*q^19 + -8*q^23 + -1*q^25 + -1*q^27 + 6*q^29 + 8*q^31 + -4*q^33 + 6*q^37 + 2*q^39 + -6*q^41 + 4*q^43 + -2*q^45 + -7*q^49 + -2*q^51 + -2*q^53 + -8*q^55 + 4*q^57 + 4*q^59 + -2*q^61 + 4*q^65 + -4*q^67 + 8*q^69 + 8*q^71 + 10*q^73 + 1*q^75 + -8*q^79 + 1*q^81 + -4*q^83 + -4*q^85 + -6*q^87 + -6*q^89 + -8*q^93 + 8*q^95 + 2*q^97 + 4*q^99 + -18*q^101 + 16*q^103 + -12*q^107 + -2*q^109 + -6*q^111 + 18*q^113 + 16*q^115 + -2*q^117 + 5*q^121 + 6*q^123 + 12*q^125 + -8*q^127 + -4*q^129 + -4*q^131 + 2*q^135 + -6*q^137 + -12*q^139 + -8*q^143 + -12*q^145 + 7*q^147 + 14*q^149 + -16*q^151 + 2*q^153 + -16*q^155 + -2*q^157 + 2*q^159 + 12*q^163 + 8*q^165 + 24*q^167 + -9*q^169 + -4*q^171 + 6*q^173 + -4*q^177 + 12*q^179 + 6*q^181 + 2*q^183 + -12*q^185 + 8*q^187 + 2*q^193 + -4*q^195 + -18*q^197 + 16*q^199 + ... ------------------------------------------------------- Gamma_0(26) Weight 2 ------------------------------------------------------- J_0(26), dim = 2 ------------------------------------------------------- 26A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 1.5467299538318833526 + 0.5868132788120751371e-22i Omega- = 0.10905020355811993018e-21 + 3.4793434834315132576i L(1) = 0.51557665127729445088 w1 = -0.77336497691594167632 + 1.7396717417157566288i w2 = 1.5467299538318833526 + 0.5868132788120751371e-22i c4 = 216.99999999999457642 + -0.59802200343477242453e-19i c6 = 6371.0000000067628017 + -0.55733495765730914546e-18i j = -581.3787551189112398 + 0.50643532147801631345e-18i HECKE EIGENFORM: f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -3*q^5 + -1*q^6 + -1*q^7 + -1*q^8 + -2*q^9 + 3*q^10 + 6*q^11 + 1*q^12 + 1*q^13 + 1*q^14 + -3*q^15 + 1*q^16 + -3*q^17 + 2*q^18 + 2*q^19 + -3*q^20 + -1*q^21 + -6*q^22 + -1*q^24 + 4*q^25 + -1*q^26 + -5*q^27 + -1*q^28 + 6*q^29 + 3*q^30 + -4*q^31 + -1*q^32 + 6*q^33 + 3*q^34 + 3*q^35 + -2*q^36 + -7*q^37 + -2*q^38 + 1*q^39 + 3*q^40 + 1*q^42 + -1*q^43 + 6*q^44 + 6*q^45 + 3*q^47 + 1*q^48 + -6*q^49 + -4*q^50 + -3*q^51 + 1*q^52 + 5*q^54 + -18*q^55 + 1*q^56 + 2*q^57 + -6*q^58 + -6*q^59 + -3*q^60 + 8*q^61 + 4*q^62 + 2*q^63 + 1*q^64 + -3*q^65 + -6*q^66 + 14*q^67 + -3*q^68 + -3*q^70 + -3*q^71 + 2*q^72 + 2*q^73 + 7*q^74 + 4*q^75 + 2*q^76 + -6*q^77 + -1*q^78 + 8*q^79 + -3*q^80 + 1*q^81 + 12*q^83 + -1*q^84 + 9*q^85 + 1*q^86 + 6*q^87 + -6*q^88 + -6*q^89 + -6*q^90 + -1*q^91 + -4*q^93 + -3*q^94 + -6*q^95 + -1*q^96 + -10*q^97 + 6*q^98 + -12*q^99 + 4*q^100 + -12*q^101 + 3*q^102 + -4*q^103 + -1*q^104 + 3*q^105 + 12*q^107 + -5*q^108 + -7*q^109 + 18*q^110 + -7*q^111 + -1*q^112 + -6*q^113 + -2*q^114 + 6*q^116 + -2*q^117 + 6*q^118 + 3*q^119 + 3*q^120 + 25*q^121 + -8*q^122 + -4*q^124 + 3*q^125 + -2*q^126 + 20*q^127 + -1*q^128 + -1*q^129 + 3*q^130 + -21*q^131 + 6*q^132 + -2*q^133 + -14*q^134 + 15*q^135 + 3*q^136 + -13*q^139 + 3*q^140 + 3*q^141 + 3*q^142 + 6*q^143 + -2*q^144 + -18*q^145 + -2*q^146 + -6*q^147 + -7*q^148 + -6*q^149 + -4*q^150 + 17*q^151 + -2*q^152 + 6*q^153 + 6*q^154 + 12*q^155 + 1*q^156 + 14*q^157 + -8*q^158 + 3*q^160 + -1*q^162 + -16*q^163 + -18*q^165 + -12*q^166 + 1*q^168 + 1*q^169 + -9*q^170 + -4*q^171 + -1*q^172 + -6*q^174 + -4*q^175 + 6*q^176 + -6*q^177 + 6*q^178 + 3*q^179 + 6*q^180 + 20*q^181 + 1*q^182 + 8*q^183 + 21*q^185 + 4*q^186 + -18*q^187 + 3*q^188 + 5*q^189 + 6*q^190 + -18*q^191 + 1*q^192 + -4*q^193 + 10*q^194 + -3*q^195 + -6*q^196 + 3*q^197 + 12*q^198 + 2*q^199 + -4*q^200 + ... ------------------------------------------------------- 26B (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 7 Torsion Bound = 7 |L(1)/Omega| = 1/7 Sha Bound = 7 ANALYTIC INVARIANTS: Omega+ = 4.3467574468433882646 + 0.8947838753713410092e-22i Omega- = 0.61407734160525436911e-23 + 1.8040571933815642736i L(1) = 0.62096534954905546638 w1 = -2.1733787234216941323 + 0.90202859669078213679i w2 = 0.61407734160525436911e-23 + 1.8040571933815642736i c4 = 129.00000000016127829 + 0.5034237925688686126e-20i c6 = -2240.9999998973346059 + 0.35654969074205170944e-19i j = -1290.0775242533624749 + -0.33549431741773713578e-18i HECKE EIGENFORM: f(q) = q + 1*q^2 + -3*q^3 + 1*q^4 + -1*q^5 + -3*q^6 + 1*q^7 + 1*q^8 + 6*q^9 + -1*q^10 + -2*q^11 + -3*q^12 + -1*q^13 + 1*q^14 + 3*q^15 + 1*q^16 + -3*q^17 + 6*q^18 + 6*q^19 + -1*q^20 + -3*q^21 + -2*q^22 + -4*q^23 + -3*q^24 + -4*q^25 + -1*q^26 + -9*q^27 + 1*q^28 + 2*q^29 + 3*q^30 + 4*q^31 + 1*q^32 + 6*q^33 + -3*q^34 + -1*q^35 + 6*q^36 + 3*q^37 + 6*q^38 + 3*q^39 + -1*q^40 + -3*q^42 + -5*q^43 + -2*q^44 + -6*q^45 + -4*q^46 + 13*q^47 + -3*q^48 + -6*q^49 + -4*q^50 + 9*q^51 + -1*q^52 + 12*q^53 + -9*q^54 + 2*q^55 + 1*q^56 + -18*q^57 + 2*q^58 + -10*q^59 + 3*q^60 + -8*q^61 + 4*q^62 + 6*q^63 + 1*q^64 + 1*q^65 + 6*q^66 + -2*q^67 + -3*q^68 + 12*q^69 + -1*q^70 + -5*q^71 + 6*q^72 + -10*q^73 + 3*q^74 + 12*q^75 + 6*q^76 + -2*q^77 + 3*q^78 + -4*q^79 + -1*q^80 + 9*q^81 + -3*q^84 + 3*q^85 + -5*q^86 + -6*q^87 + -2*q^88 + 6*q^89 + -6*q^90 + -1*q^91 + -4*q^92 + -12*q^93 + 13*q^94 + -6*q^95 + -3*q^96 + 14*q^97 + -6*q^98 + -12*q^99 + -4*q^100 + 4*q^101 + 9*q^102 + -8*q^103 + -1*q^104 + 3*q^105 + 12*q^106 + -4*q^107 + -9*q^108 + 19*q^109 + 2*q^110 + -9*q^111 + 1*q^112 + 2*q^113 + -18*q^114 + 4*q^115 + 2*q^116 + -6*q^117 + -10*q^118 + -3*q^119 + 3*q^120 + -7*q^121 + -8*q^122 + 4*q^124 + 9*q^125 + 6*q^126 + 16*q^127 + 1*q^128 + 15*q^129 + 1*q^130 + -1*q^131 + 6*q^132 + 6*q^133 + -2*q^134 + 9*q^135 + -3*q^136 + 12*q^137 + 12*q^138 + 7*q^139 + -1*q^140 + -39*q^141 + -5*q^142 + 2*q^143 + 6*q^144 + -2*q^145 + -10*q^146 + 18*q^147 + 3*q^148 + -18*q^149 + 12*q^150 + -9*q^151 + 6*q^152 + -18*q^153 + -2*q^154 + -4*q^155 + 3*q^156 + -10*q^157 + -4*q^158 + -36*q^159 + -1*q^160 + -4*q^161 + 9*q^162 + -4*q^163 + -6*q^165 + -3*q^168 + 1*q^169 + 3*q^170 + 36*q^171 + -5*q^172 + 20*q^173 + -6*q^174 + -4*q^175 + -2*q^176 + 30*q^177 + 6*q^178 + -9*q^179 + -6*q^180 + -1*q^182 + 24*q^183 + -4*q^184 + -3*q^185 + -12*q^186 + 6*q^187 + 13*q^188 + -9*q^189 + -6*q^190 + 10*q^191 + -3*q^192 + -16*q^193 + 14*q^194 + -3*q^195 + -6*q^196 + 9*q^197 + -12*q^198 + -10*q^199 + -4*q^200 + ... ------------------------------------------------------- Gamma_0(27) Weight 2 ------------------------------------------------------- J_0(27), dim = 1 ------------------------------------------------------- 27A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 1.7666387502854499573 + -0.1334392187887364652e-22i Omega- = 0.23112350666439109869e-22 + 3.0599080741143857498i L(1) = 0.5888795834284833191 w1 = 1.7666387502854499573 + -0.1334392187887364652e-22i w2 = 0.88331937514272497866 + -1.5299540370571928749i c4 = -0.18776672680640749198e-9 + -0.32522151079960285662e-9i c6 = 5831.99999951216479 + 0.26430446760609271727e-18i j = -0.26906338489013003736e-32 + -0.32180958100195476755e-61i HECKE EIGENFORM: f(q) = q + -2*q^4 + -1*q^7 + 5*q^13 + 4*q^16 + -7*q^19 + -5*q^25 + 2*q^28 + -4*q^31 + 11*q^37 + 8*q^43 + -6*q^49 + -10*q^52 + -1*q^61 + -8*q^64 + 5*q^67 + -7*q^73 + 14*q^76 + 17*q^79 + -5*q^91 + -19*q^97 + 10*q^100 + -13*q^103 + 2*q^109 + -4*q^112 + -11*q^121 + 8*q^124 + 20*q^127 + 7*q^133 + 23*q^139 + -22*q^148 + -19*q^151 + 14*q^157 + -25*q^163 + 12*q^169 + -16*q^172 + 5*q^175 + -7*q^181 + 23*q^193 + 12*q^196 + 11*q^199 + ... ------------------------------------------------------- Gamma_0(28) Weight 2 ------------------------------------------------------- J_0(28), dim = 2 ------------------------------------------------------- 28A (old = 14A), dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ------------------------------------------------------- Gamma_0(29) Weight 2 ------------------------------------------------------- J_0(29), dim = 2 ------------------------------------------------------- 29A (new) , dim = 2 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 2^3 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 7 Torsion Bound = 7 |L(1)/Omega| = 1/7 Sha Bound = 7 ANALYTIC INVARIANTS: Omega+ = 2.0406509598940708402 + -0.72907676164715401209e-20i Omega- = 9.6162259738752548483 + -0.18789996460360025936e-19i L(1) = 0.29152156569915297717 HECKE EIGENFORM: a^2+2*a-1 = 0, f(q) = q + a*q^2 + -a*q^3 + (-2*a-1)*q^4 + -1*q^5 + (2*a-1)*q^6 + (2*a+2)*q^7 + (a-2)*q^8 + (-2*a-2)*q^9 + -a*q^10 + (a+2)*q^11 + (-3*a+2)*q^12 + (2*a+1)*q^13 + (-2*a+2)*q^14 + a*q^15 + 3*q^16 + (-2*a-4)*q^17 + (2*a-2)*q^18 + 6*q^19 + (2*a+1)*q^20 + (2*a-2)*q^21 + 1*q^22 + (-4*a-6)*q^23 + (4*a-1)*q^24 + -4*q^25 + (-3*a+2)*q^26 + (a+2)*q^27 + (2*a-6)*q^28 + 1*q^29 + (-2*a+1)*q^30 + (-5*a-2)*q^31 + (a+4)*q^32 + -1*q^33 + -2*q^34 + (-2*a-2)*q^35 + (-2*a+6)*q^36 + -4*q^37 + 6*a*q^38 + (3*a-2)*q^39 + (-a+2)*q^40 + (6*a+10)*q^41 + (-6*a+2)*q^42 + (a+6)*q^43 + (-a-4)*q^44 + (2*a+2)*q^45 + (2*a-4)*q^46 + (3*a+4)*q^47 + -3*a*q^48 + 1*q^49 + -4*a*q^50 + 2*q^51 + (4*a-5)*q^52 + (-6*a-5)*q^53 + 1*q^54 + (-a-2)*q^55 + (-6*a-2)*q^56 + -6*a*q^57 + a*q^58 + (4*a+6)*q^59 + (3*a-2)*q^60 + 2*a*q^61 + (8*a-5)*q^62 + -8*q^63 + (2*a-5)*q^64 + (-2*a-1)*q^65 + -a*q^66 + (-4*a-4)*q^67 + (2*a+8)*q^68 + (-2*a+4)*q^69 + (2*a-2)*q^70 + (2*a-4)*q^71 + (6*a+2)*q^72 + 4*q^73 + -4*a*q^74 + 4*a*q^75 + (-12*a-6)*q^76 + (2*a+6)*q^77 + (-8*a+3)*q^78 + a*q^79 + -3*q^80 + (6*a+5)*q^81 + (-2*a+6)*q^82 + (-4*a-2)*q^83 + (10*a-2)*q^84 + (2*a+4)*q^85 + (4*a+1)*q^86 + -a*q^87 + (-2*a-3)*q^88 + (6*a+2)*q^89 + (-2*a+2)*q^90 + (-2*a+6)*q^91 + 14*q^92 + (-8*a+5)*q^93 + (-2*a+3)*q^94 + -6*q^95 + (-2*a-1)*q^96 + (-6*a-10)*q^97 + a*q^98 + (-2*a-6)*q^99 + (8*a+4)*q^100 + (-4*a-12)*q^101 + 2*a*q^102 + 2*a*q^103 + -7*a*q^104 + (-2*a+2)*q^105 + (7*a-6)*q^106 + (2*a-10)*q^107 + (-a-4)*q^108 + (-4*a+3)*q^109 + -1*q^110 + 4*a*q^111 + (6*a+6)*q^112 + (8*a+6)*q^113 + (12*a-6)*q^114 + (4*a+6)*q^115 + (-2*a-1)*q^116 + (2*a-6)*q^117 + (-2*a+4)*q^118 + (-4*a-12)*q^119 + (-4*a+1)*q^120 + (2*a-6)*q^121 + (-4*a+2)*q^122 + (2*a-6)*q^123 + (-11*a+12)*q^124 + 9*q^125 + -8*a*q^126 + (-4*a-14)*q^127 + (-11*a-6)*q^128 + (-4*a-1)*q^129 + (3*a-2)*q^130 + (-8*a+2)*q^131 + (2*a+1)*q^132 + (12*a+12)*q^133 + (4*a-4)*q^134 + (-a-2)*q^135 + (4*a+6)*q^136 + 12*q^137 + (8*a-2)*q^138 + 14*q^139 + (-2*a+6)*q^140 + (2*a-3)*q^141 + (-8*a+2)*q^142 + (a+4)*q^143 + (-6*a-6)*q^144 + -1*q^145 + 4*a*q^146 + -a*q^147 + (8*a+4)*q^148 + (2*a-3)*q^149 + (-8*a+4)*q^150 + (10*a+10)*q^151 + (6*a-12)*q^152 + (4*a+12)*q^153 + (2*a+2)*q^154 + (5*a+2)*q^155 + (13*a-4)*q^156 + (-6*a-6)*q^157 + (-2*a+1)*q^158 + (-7*a+6)*q^159 + (-a-4)*q^160 + (-4*a-20)*q^161 + (-7*a+6)*q^162 + (5*a+16)*q^163 + (-2*a-22)*q^164 + 1*q^165 + (6*a-4)*q^166 + (-2*a-8)*q^167 + (-10*a+6)*q^168 + (-4*a-8)*q^169 + 2*q^170 + (-12*a-12)*q^171 + (-9*a-8)*q^172 + (4*a+22)*q^173 + (2*a-1)*q^174 + (-8*a-8)*q^175 + (3*a+6)*q^176 + (2*a-4)*q^177 + (-10*a+6)*q^178 + (6*a+8)*q^179 + (2*a-6)*q^180 + (-8*a-11)*q^181 + (10*a-2)*q^182 + (4*a-2)*q^183 + (10*a+8)*q^184 + 4*q^185 + (21*a-8)*q^186 + (-4*a-10)*q^187 + (a-10)*q^188 + (2*a+6)*q^189 + -6*a*q^190 + (-8*a+6)*q^191 + (9*a-2)*q^192 + (-2*a-10)*q^193 + (2*a-6)*q^194 + (-3*a+2)*q^195 + (-2*a-1)*q^196 + 2*q^197 + (-2*a-2)*q^198 + (6*a+14)*q^199 + (-4*a+8)*q^200 + ... ------------------------------------------------------- Gamma_0(30) Weight 2 ------------------------------------------------------- J_0(30), dim = 3 ------------------------------------------------------- 30A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = +-+ discriminant = 1 #CompGroup(Fpbar) = ??? c_p = ??? c_inf = 1 ord((0)-(oo)) = 2*3 Torsion Bound = 2^2*3 |L(1)/Omega| = 1/2*3 Sha Bound = 2^3*3 ANALYTIC INVARIANTS: Omega+ = 3.3519482592414964497 + -0.24978584697288268586e-19i Omega- = 2.3167842226281642667i L(1) = 0.55865804320691607495 w1 = 1.6759741296207482248 + -1.1583921113140821333i w2 = -1.6759741296207482248 + -1.1583921113140821333i c4 = -71.000000000006388842 + -0.77649282879156822658e-11i c6 = -1836.9999999906914853 + -0.31702887426627591104e-8i j = 165.69953703859572874 + -0.46793266070001681022e-9i HECKE EIGENFORM: f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -1*q^5 + -1*q^6 + -4*q^7 + -1*q^8 + 1*q^9 + 1*q^10 + 1*q^12 + 2*q^13 + 4*q^14 + -1*q^15 + 1*q^16 + 6*q^17 + -1*q^18 + -4*q^19 + -1*q^20 + -4*q^21 + -1*q^24 + 1*q^25 + -2*q^26 + 1*q^27 + -4*q^28 + -6*q^29 + 1*q^30 + 8*q^31 + -1*q^32 + -6*q^34 + 4*q^35 + 1*q^36 + 2*q^37 + 4*q^38 + 2*q^39 + 1*q^40 + -6*q^41 + 4*q^42 + -4*q^43 + -1*q^45 + 1*q^48 + 9*q^49 + -1*q^50 + 6*q^51 + 2*q^52 + -6*q^53 + -1*q^54 + 4*q^56 + -4*q^57 + 6*q^58 + -1*q^60 + -10*q^61 + -8*q^62 + -4*q^63 + 1*q^64 + -2*q^65 + -4*q^67 + 6*q^68 + -4*q^70 + -1*q^72 + 2*q^73 + -2*q^74 + 1*q^75 + -4*q^76 + -2*q^78 + 8*q^79 + -1*q^80 + 1*q^81 + 6*q^82 + 12*q^83 + -4*q^84 + -6*q^85 + 4*q^86 + -6*q^87 + 18*q^89 + 1*q^90 + -8*q^91 + 8*q^93 + 4*q^95 + -1*q^96 + 2*q^97 + -9*q^98 + 1*q^100 + 18*q^101 + -6*q^102 + -4*q^103 + -2*q^104 + 4*q^105 + 6*q^106 + -12*q^107 + 1*q^108 + -10*q^109 + 2*q^111 + -4*q^112 + -18*q^113 + 4*q^114 + -6*q^116 + 2*q^117 + -24*q^119 + 1*q^120 + -11*q^121 + 10*q^122 + -6*q^123 + 8*q^124 + -1*q^125 + 4*q^126 + 20*q^127 + -1*q^128 + -4*q^129 + 2*q^130 + 16*q^133 + 4*q^134 + -1*q^135 + -6*q^136 + 6*q^137 + -4*q^139 + 4*q^140 + 1*q^144 + 6*q^145 + -2*q^146 + 9*q^147 + 2*q^148 + -6*q^149 + -1*q^150 + 8*q^151 + 4*q^152 + 6*q^153 + -8*q^155 + 2*q^156 + 2*q^157 + -8*q^158 + -6*q^159 + 1*q^160 + -1*q^162 + -4*q^163 + -6*q^164 + -12*q^166 + 4*q^168 + -9*q^169 + 6*q^170 + -4*q^171 + -4*q^172 + 18*q^173 + 6*q^174 + -4*q^175 + -18*q^178 + 24*q^179 + -1*q^180 + 14*q^181 + 8*q^182 + -10*q^183 + -2*q^185 + -8*q^186 + -4*q^189 + -4*q^190 + -24*q^191 + 1*q^192 + -22*q^193 + -2*q^194 + -2*q^195 + 9*q^196 + -6*q^197 + 8*q^199 + -1*q^200 + ... ------------------------------------------------------- 30B (old = 15A), dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ------------------------------------------------------- Gamma_0(31) Weight 2 ------------------------------------------------------- J_0(31), dim = 2 ------------------------------------------------------- 31A (new) , dim = 2 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 5 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 5 Torsion Bound = 5 |L(1)/Omega| = 1/5 Sha Bound = 5 ANALYTIC INVARIANTS: Omega+ = 2.24643861938020393 + -0.58316714178571559551e-18i Omega- = 14.573180834492855092 + 0.1606417351165064946e-17i L(1) = 0.44928772387604078599 HECKE EIGENFORM: a^2-a-1 = 0, f(q) = q + a*q^2 + -2*a*q^3 + (a-1)*q^4 + 1*q^5 + (-2*a-2)*q^6 + (2*a-3)*q^7 + (-2*a+1)*q^8 + (4*a+1)*q^9 + a*q^10 + 2*q^11 + -2*q^12 + -2*a*q^13 + (-a+2)*q^14 + -2*a*q^15 + -3*a*q^16 + (-2*a+4)*q^17 + (5*a+4)*q^18 + (-2*a+1)*q^19 + (a-1)*q^20 + (2*a-4)*q^21 + 2*a*q^22 + (6*a-4)*q^23 + (2*a+4)*q^24 + -4*q^25 + (-2*a-2)*q^26 + (-4*a-8)*q^27 + (-3*a+5)*q^28 + (-2*a+6)*q^29 + (-2*a-2)*q^30 + 1*q^31 + (a-5)*q^32 + -4*a*q^33 + (2*a-2)*q^34 + (2*a-3)*q^35 + (a+3)*q^36 + -2*q^37 + (-a-2)*q^38 + (4*a+4)*q^39 + (-2*a+1)*q^40 + 7*q^41 + (-2*a+2)*q^42 + (2*a-2)*q^43 + (2*a-2)*q^44 + (4*a+1)*q^45 + (2*a+6)*q^46 + (4*a-4)*q^47 + (6*a+6)*q^48 + (-8*a+6)*q^49 + -4*a*q^50 + (-4*a+4)*q^51 + -2*q^52 + (-4*a-4)*q^53 + (-12*a-4)*q^54 + 2*q^55 + (4*a-7)*q^56 + (2*a+4)*q^57 + (4*a-2)*q^58 + (2*a-1)*q^59 + -2*q^60 + (10*a-8)*q^61 + a*q^62 + (-2*a+5)*q^63 + (2*a+1)*q^64 + -2*a*q^65 + (-4*a-4)*q^66 + 8*q^67 + (4*a-6)*q^68 + (-4*a-12)*q^69 + (-a+2)*q^70 + (-10*a+7)*q^71 + (-6*a-7)*q^72 + (4*a+2)*q^73 + -2*a*q^74 + 8*a*q^75 + (a-3)*q^76 + (4*a-6)*q^77 + (8*a+4)*q^78 + (-6*a-2)*q^79 + -3*a*q^80 + (12*a+5)*q^81 + 7*a*q^82 + (-8*a-2)*q^83 + (-4*a+6)*q^84 + (-2*a+4)*q^85 + 2*q^86 + (-8*a+4)*q^87 + (-4*a+2)*q^88 + (6*a+2)*q^89 + (5*a+4)*q^90 + (2*a-4)*q^91 + (-4*a+10)*q^92 + -2*a*q^93 + 4*q^94 + (-2*a+1)*q^95 + (8*a-2)*q^96 + (-8*a-3)*q^97 + (-2*a-8)*q^98 + (8*a+2)*q^99 + (-4*a+4)*q^100 + -3*q^101 + -4*q^102 + (2*a+3)*q^103 + (2*a+4)*q^104 + (2*a-4)*q^105 + (-8*a-4)*q^106 + (-2*a+9)*q^107 + (-8*a+4)*q^108 + (-8*a-1)*q^109 + 2*a*q^110 + 4*a*q^111 + (3*a-6)*q^112 + (4*a-3)*q^113 + (6*a+2)*q^114 + (6*a-4)*q^115 + (6*a-8)*q^116 + (-10*a-8)*q^117 + (a+2)*q^118 + (10*a-16)*q^119 + (2*a+4)*q^120 + -7*q^121 + (2*a+10)*q^122 + -14*a*q^123 + (a-1)*q^124 + -9*q^125 + (3*a-2)*q^126 + (4*a+6)*q^127 + (a+12)*q^128 + -4*q^129 + (-2*a-2)*q^130 + 12*q^131 + -4*q^132 + (4*a-7)*q^133 + 8*a*q^134 + (-4*a-8)*q^135 + (-6*a+8)*q^136 + (-6*a+16)*q^137 + (-16*a-4)*q^138 + (12*a-6)*q^139 + (-3*a+5)*q^140 + -8*q^141 + (-3*a-10)*q^142 + -4*a*q^143 + (-15*a-12)*q^144 + (-2*a+6)*q^145 + (6*a+4)*q^146 + (4*a+16)*q^147 + (-2*a+2)*q^148 + 10*q^149 + (8*a+8)*q^150 + (-10*a+2)*q^151 + 5*q^152 + (6*a-4)*q^153 + (-2*a+4)*q^154 + 1*q^155 + 4*a*q^156 + (16*a-5)*q^157 + (-8*a-6)*q^158 + (16*a+8)*q^159 + (a-5)*q^160 + (-14*a+24)*q^161 + (17*a+12)*q^162 + (6*a+1)*q^163 + (7*a-7)*q^164 + -4*a*q^165 + (-10*a-8)*q^166 + -4*a*q^167 + (6*a-8)*q^168 + (4*a-9)*q^169 + (2*a-2)*q^170 + (-6*a-7)*q^171 + (-2*a+4)*q^172 + (8*a-10)*q^173 + (-4*a-8)*q^174 + (-8*a+12)*q^175 + -6*a*q^176 + (-2*a-4)*q^177 + (8*a+6)*q^178 + (6*a-8)*q^179 + (a+3)*q^180 + (-10*a+12)*q^181 + (-2*a+2)*q^182 + (-4*a-20)*q^183 + (2*a-16)*q^184 + -2*q^185 + (-2*a-2)*q^186 + (-4*a+8)*q^187 + (-4*a+8)*q^188 + (-12*a+16)*q^189 + (-a-2)*q^190 + (-10*a-3)*q^191 + (-6*a-4)*q^192 + (4*a-3)*q^193 + (-11*a-8)*q^194 + (4*a+4)*q^195 + (6*a-14)*q^196 + (12*a-8)*q^197 + (10*a+8)*q^198 + (-8*a-6)*q^199 + (8*a-4)*q^200 + ... ------------------------------------------------------- Gamma_0(32) Weight 2 ------------------------------------------------------- J_0(32), dim = 1 ------------------------------------------------------- 32A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 2^2 Torsion Bound = 2^2 |L(1)/Omega| = 1/2^2 Sha Bound = 2^2 ANALYTIC INVARIANTS: Omega+ = 2.6220575542921198112 + -0.91609413137570631098e-45i Omega- = 2.6220575542921198112i L(1) = 0.65551438857302995281 w1 = 1.3110287771460599056 + -1.3110287771460599056i w2 = -1.3110287771460599056 + -1.3110287771460599056i c4 = -191.99999999970916329 + -0.13416186755951148267e-42i c6 = 0.30044632178269532466e-38 + 0.25277970442954914368e-6i j = 1728 + -0.37083365438245488585e-48i HECKE EIGENFORM: f(q) = q + -2*q^5 + -3*q^9 + 6*q^13 + 2*q^17 + -1*q^25 + -10*q^29 + -2*q^37 + 10*q^41 + 6*q^45 + -7*q^49 + 14*q^53 + -10*q^61 + -12*q^65 + -6*q^73 + 9*q^81 + -4*q^85 + 10*q^89 + 18*q^97 + -2*q^101 + 6*q^109 + -14*q^113 + -18*q^117 + -11*q^121 + 12*q^125 + -22*q^137 + 20*q^145 + 14*q^149 + -6*q^153 + 22*q^157 + 23*q^169 + -26*q^173 + -18*q^181 + 4*q^185 + -14*q^193 + -2*q^197 + ... ------------------------------------------------------- Gamma_0(33) Weight 2 ------------------------------------------------------- J_0(33), dim = 3 ------------------------------------------------------- 33A (new) , dim = 1 CONGRUENCES: Modular Degree = 3 Ker(ModPolar) = Z/3 + Z/3 = B(Z/3 + Z/3) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2 Torsion Bound = 2^2 |L(1)/Omega| = 1/2^2 Sha Bound = 2^2 ANALYTIC INVARIANTS: Omega+ = 1.4946782954854872405 + -0.69134435991759407882e-18i Omega- = 0.23229572832919744763e-17 + 1.3723166787329470489i L(1) = 0.37366957387137181013 w1 = -1.4946782954854872405 + 0.69134435991759407882e-18i w2 = 0.23229572832919744763e-17 + 1.3723166787329470489i c4 = 552.99999999996643275 + 0.27791562436978358775e-14i c6 = -4085.00000005323332 + -0.86141572206278351666e-13i j = 1917.1782584598612555 + 0.5687529768019157528e-14i HECKE EIGENFORM: f(q) = q + 1*q^2 + -1*q^3 + -1*q^4 + -2*q^5 + -1*q^6 + 4*q^7 + -3*q^8 + 1*q^9 + -2*q^10 + 1*q^11 + 1*q^12 + -2*q^13 + 4*q^14 + 2*q^15 + -1*q^16 + -2*q^17 + 1*q^18 + 2*q^20 + -4*q^21 + 1*q^22 + 8*q^23 + 3*q^24 + -1*q^25 + -2*q^26 + -1*q^27 + -4*q^28 + -6*q^29 + 2*q^30 + -8*q^31 + 5*q^32 + -1*q^33 + -2*q^34 + -8*q^35 + -1*q^36 + 6*q^37 + 2*q^39 + 6*q^40 + -2*q^41 + -4*q^42 + -1*q^44 + -2*q^45 + 8*q^46 + 8*q^47 + 1*q^48 + 9*q^49 + -1*q^50 + 2*q^51 + 2*q^52 + 6*q^53 + -1*q^54 + -2*q^55 + -12*q^56 + -6*q^58 + -4*q^59 + -2*q^60 + 6*q^61 + -8*q^62 + 4*q^63 + 7*q^64 + 4*q^65 + -1*q^66 + -4*q^67 + 2*q^68 + -8*q^69 + -8*q^70 + -3*q^72 + -14*q^73 + 6*q^74 + 1*q^75 + 4*q^77 + 2*q^78 + -4*q^79 + 2*q^80 + 1*q^81 + -2*q^82 + 12*q^83 + 4*q^84 + 4*q^85 + 6*q^87 + -3*q^88 + -6*q^89 + -2*q^90 + -8*q^91 + -8*q^92 + 8*q^93 + 8*q^94 + -5*q^96 + 2*q^97 + 9*q^98 + 1*q^99 + 1*q^100 + 2*q^101 + 2*q^102 + 8*q^103 + 6*q^104 + 8*q^105 + 6*q^106 + -12*q^107 + 1*q^108 + -2*q^109 + -2*q^110 + -6*q^111 + -4*q^112 + -6*q^113 + -16*q^115 + 6*q^116 + -2*q^117 + -4*q^118 + -8*q^119 + -6*q^120 + 1*q^121 + 6*q^122 + 2*q^123 + 8*q^124 + 12*q^125 + 4*q^126 + -4*q^127 + -3*q^128 + 4*q^130 + -12*q^131 + 1*q^132 + -4*q^134 + 2*q^135 + 6*q^136 + 2*q^137 + -8*q^138 + -8*q^139 + 8*q^140 + -8*q^141 + -2*q^143 + -1*q^144 + 12*q^145 + -14*q^146 + -9*q^147 + -6*q^148 + -22*q^149 + 1*q^150 + 20*q^151 + -2*q^153 + 4*q^154 + 16*q^155 + -2*q^156 + 14*q^157 + -4*q^158 + -6*q^159 + -10*q^160 + 32*q^161 + 1*q^162 + 4*q^163 + 2*q^164 + 2*q^165 + 12*q^166 + 12*q^168 + -9*q^169 + 4*q^170 + -6*q^173 + 6*q^174 + -4*q^175 + -1*q^176 + 4*q^177 + -6*q^178 + 12*q^179 + 2*q^180 + 22*q^181 + -8*q^182 + -6*q^183 + -24*q^184 + -12*q^185 + 8*q^186 + -2*q^187 + -8*q^188 + -4*q^189 + 8*q^191 + -7*q^192 + -14*q^193 + 2*q^194 + -4*q^195 + -9*q^196 + -14*q^197 + 1*q^198 + 3*q^200 + ... ------------------------------------------------------- 33B (old = 11A), dim = 1 CONGRUENCES: Modular Degree = 3 Ker(ModPolar) = Z/3 + Z/3 = A(Z/3 + Z/3) ------------------------------------------------------- Gamma_0(34) Weight 2 ------------------------------------------------------- J_0(34), dim = 3 ------------------------------------------------------- 34A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 3 Torsion Bound = 2*3 |L(1)/Omega| = 1/2*3 Sha Bound = 2*3 ANALYTIC INVARIANTS: Omega+ = 2.2478316631568517669 + -0.70737079076773911788e-17i Omega- = 0.42066769969407749568e-17 + 1.8641750574724360854i L(1) = 0.37463861052614196114 w1 = -2.2478316631568517669 + 0.70737079076773911788e-17i w2 = 0.42066769969407749568e-17 + 1.8641750574724360854i c4 = 144.99999999986304794 + 0.14168747947496565355e-14i c6 = -1081.0000000817098705 + -0.1199521028435092289e-13i j = 2802.0450370329297368 + -0.1240356515218331531e-13i HECKE EIGENFORM: f(q) = q + 1*q^2 + -2*q^3 + 1*q^4 + -2*q^6 + -4*q^7 + 1*q^8 + 1*q^9 + 6*q^11 + -2*q^12 + 2*q^13 + -4*q^14 + 1*q^16 + -1*q^17 + 1*q^18 + -4*q^19 + 8*q^21 + 6*q^22 + -2*q^24 + -5*q^25 + 2*q^26 + 4*q^27 + -4*q^28 + -4*q^31 + 1*q^32 + -12*q^33 + -1*q^34 + 1*q^36 + -4*q^37 + -4*q^38 + -4*q^39 + 6*q^41 + 8*q^42 + 8*q^43 + 6*q^44 + -2*q^48 + 9*q^49 + -5*q^50 + 2*q^51 + 2*q^52 + -6*q^53 + 4*q^54 + -4*q^56 + 8*q^57 + -4*q^61 + -4*q^62 + -4*q^63 + 1*q^64 + -12*q^66 + 8*q^67 + -1*q^68 + 1*q^72 + 2*q^73 + -4*q^74 + 10*q^75 + -4*q^76 + -24*q^77 + -4*q^78 + 8*q^79 + -11*q^81 + 6*q^82 + 8*q^84 + 8*q^86 + 6*q^88 + -6*q^89 + -8*q^91 + 8*q^93 + -2*q^96 + 14*q^97 + 9*q^98 + 6*q^99 + -5*q^100 + 18*q^101 + 2*q^102 + -16*q^103 + 2*q^104 + -6*q^106 + -6*q^107 + 4*q^108 + -16*q^109 + 8*q^111 + -4*q^112 + -6*q^113 + 8*q^114 + 2*q^117 + 4*q^119 + 25*q^121 + -4*q^122 + -12*q^123 + -4*q^124 + -4*q^126 + -16*q^127 + 1*q^128 + -16*q^129 + -6*q^131 + -12*q^132 + 16*q^133 + 8*q^134 + -1*q^136 + 6*q^137 + 2*q^139 + 12*q^143 + 1*q^144 + 2*q^146 + -18*q^147 + -4*q^148 + 6*q^149 + 10*q^150 + -16*q^151 + -4*q^152 + -1*q^153 + -24*q^154 + -4*q^156 + 14*q^157 + 8*q^158 + 12*q^159 + -11*q^162 + 2*q^163 + 6*q^164 + 12*q^167 + 8*q^168 + -9*q^169 + -4*q^171 + 8*q^172 + 24*q^173 + 20*q^175 + 6*q^176 + -6*q^178 + 12*q^179 + -4*q^181 + -8*q^182 + 8*q^183 + 8*q^186 + -6*q^187 + -16*q^189 + -24*q^191 + -2*q^192 + -10*q^193 + 14*q^194 + 9*q^196 + -12*q^197 + 6*q^198 + -16*q^199 + -5*q^200 + ... ------------------------------------------------------- 34B (old = 17A), dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ------------------------------------------------------- Gamma_0(35) Weight 2 ------------------------------------------------------- J_0(35), dim = 3 ------------------------------------------------------- 35A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 2.1087337174047165359 + -0.11820507992192260061e-16i Omega- = 0.14248536742437420368e-16 + -2.2050442761017105106i L(1) = 0.70291123913490551197 w1 = -1.0543668587023582751 + 1.1025221380508552612i w2 = 1.0543668587023582608 + 1.1025221380508552494i c4 = -416.00000000001532848 + 0.65861142994399898675e-9i c6 = 1447.9999991544513104 + 0.17828762769999045968e-7i j = 1679.0972828543355173 + -0.13958619309883181967e-8i HECKE EIGENFORM: f(q) = q + 1*q^3 + -2*q^4 + -1*q^5 + 1*q^7 + -2*q^9 + -3*q^11 + -2*q^12 + 5*q^13 + -1*q^15 + 4*q^16 + 3*q^17 + 2*q^19 + 2*q^20 + 1*q^21 + -6*q^23 + 1*q^25 + -5*q^27 + -2*q^28 + 3*q^29 + -4*q^31 + -3*q^33 + -1*q^35 + 4*q^36 + 2*q^37 + 5*q^39 + -12*q^41 + -10*q^43 + 6*q^44 + 2*q^45 + 9*q^47 + 4*q^48 + 1*q^49 + 3*q^51 + -10*q^52 + 12*q^53 + 3*q^55 + 2*q^57 + 2*q^60 + 8*q^61 + -2*q^63 + -8*q^64 + -5*q^65 + -4*q^67 + -6*q^68 + -6*q^69 + 2*q^73 + 1*q^75 + -4*q^76 + -3*q^77 + -1*q^79 + -4*q^80 + 1*q^81 + 12*q^83 + -2*q^84 + -3*q^85 + 3*q^87 + -12*q^89 + 5*q^91 + 12*q^92 + -4*q^93 + -2*q^95 + -1*q^97 + 6*q^99 + -2*q^100 + 6*q^101 + 5*q^103 + -1*q^105 + 6*q^107 + 10*q^108 + -7*q^109 + 2*q^111 + 4*q^112 + 6*q^113 + 6*q^115 + -6*q^116 + -10*q^117 + 3*q^119 + -2*q^121 + -12*q^123 + 8*q^124 + -1*q^125 + -16*q^127 + -10*q^129 + -6*q^131 + 6*q^132 + 2*q^133 + 5*q^135 + -12*q^137 + 14*q^139 + 2*q^140 + 9*q^141 + -15*q^143 + -8*q^144 + -3*q^145 + 1*q^147 + -4*q^148 + -6*q^149 + -1*q^151 + -6*q^153 + 4*q^155 + -10*q^156 + 14*q^157 + 12*q^159 + -6*q^161 + 2*q^163 + 24*q^164 + 3*q^165 + -3*q^167 + 12*q^169 + -4*q^171 + 20*q^172 + -9*q^173 + 1*q^175 + -12*q^176 + 12*q^179 + -4*q^180 + 20*q^181 + 8*q^183 + -2*q^185 + -9*q^187 + -18*q^188 + -5*q^189 + 9*q^191 + -8*q^192 + -4*q^193 + -5*q^195 + -2*q^196 + -16*q^199 + ... ------------------------------------------------------- 35B (new) , dim = 2 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 17 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2^3 Torsion Bound = 2^4 |L(1)/Omega| = 1/2^4 Sha Bound = 2^4 ANALYTIC INVARIANTS: Omega+ = 2.9819742701053530871 + 0.46554152239434347155e-17i Omega- = 3.0828285833203041519 + 0.96584367389443946279e-17i L(1) = 0.18637339188158456794 HECKE EIGENFORM: a^2+a-4 = 0, f(q) = q + a*q^2 + (-a-1)*q^3 + (-a+2)*q^4 + 1*q^5 + -4*q^6 + -1*q^7 + (a-4)*q^8 + (a+2)*q^9 + a*q^10 + (a+1)*q^11 + (-2*a+2)*q^12 + (a+3)*q^13 + -a*q^14 + (-a-1)*q^15 + -3*a*q^16 + (-a-3)*q^17 + (a+4)*q^18 + (2*a-2)*q^19 + (-a+2)*q^20 + (a+1)*q^21 + 4*q^22 + (-2*a-2)*q^23 + 4*a*q^24 + 1*q^25 + (2*a+4)*q^26 + (a-3)*q^27 + (a-2)*q^28 + (-3*a-1)*q^29 + -4*q^30 + (a-4)*q^32 + (-a-5)*q^33 + (-2*a-4)*q^34 + -1*q^35 + a*q^36 + 6*q^37 + (-4*a+8)*q^38 + (-3*a-7)*q^39 + (a-4)*q^40 + -2*a*q^41 + 4*q^42 + (2*a+6)*q^43 + (2*a-2)*q^44 + (a+2)*q^45 + -8*q^46 + (3*a-1)*q^47 + 12*q^48 + 1*q^49 + a*q^50 + (3*a+7)*q^51 + 2*q^52 + 2*a*q^53 + (-4*a+4)*q^54 + (a+1)*q^55 + (-a+4)*q^56 + (2*a-6)*q^57 + (2*a-12)*q^58 + -4*q^59 + (-2*a+2)*q^60 + -6*a*q^61 + (-a-2)*q^63 + (a+4)*q^64 + (a+3)*q^65 + (-4*a-4)*q^66 + -4*a*q^67 + -2*q^68 + (2*a+10)*q^69 + -a*q^70 + 8*q^71 + (-3*a-4)*q^72 + (4*a-2)*q^73 + 6*a*q^74 + (-a-1)*q^75 + (8*a-12)*q^76 + (-a-1)*q^77 + (-4*a-12)*q^78 + (-a-5)*q^79 + -3*a*q^80 + -7*q^81 + (2*a-8)*q^82 + 4*q^83 + (2*a-2)*q^84 + (-a-3)*q^85 + (4*a+8)*q^86 + (a+13)*q^87 + -4*a*q^88 + (2*a+4)*q^89 + (a+4)*q^90 + (-a-3)*q^91 + (-4*a+4)*q^92 + (-4*a+12)*q^94 + (2*a-2)*q^95 + 4*a*q^96 + (-5*a-7)*q^97 + a*q^98 + (2*a+6)*q^99 + (-a+2)*q^100 + (4*a-6)*q^101 + (4*a+12)*q^102 + (-a+3)*q^103 + (-2*a-8)*q^104 + (a+1)*q^105 + (-2*a+8)*q^106 + (-6*a-2)*q^107 + (6*a-10)*q^108 + (3*a+13)*q^109 + 4*q^110 + (-6*a-6)*q^111 + 3*a*q^112 + -14*q^113 + (-8*a+8)*q^114 + (-2*a-2)*q^115 + (-8*a+10)*q^116 + (4*a+10)*q^117 + -4*a*q^118 + (a+3)*q^119 + 4*a*q^120 + (a-6)*q^121 + (6*a-24)*q^122 + 8*q^123 + 1*q^125 + (-a-4)*q^126 + (4*a+4)*q^127 + (a+12)*q^128 + (-6*a-14)*q^129 + (2*a+4)*q^130 + (-2*a-6)*q^131 + (2*a-6)*q^132 + (-2*a+2)*q^133 + (4*a-16)*q^134 + (a-3)*q^135 + (2*a+8)*q^136 + (2*a-12)*q^137 + (8*a+8)*q^138 + (2*a-10)*q^139 + (a-2)*q^140 + (a-11)*q^141 + 8*a*q^142 + (3*a+7)*q^143 + (-3*a-12)*q^144 + (-3*a-1)*q^145 + (-6*a+16)*q^146 + (-a-1)*q^147 + (-6*a+12)*q^148 + (-4*a+2)*q^149 + -4*q^150 + (7*a+11)*q^151 + (-12*a+16)*q^152 + (-4*a-10)*q^153 + -4*q^154 + (-2*a-2)*q^156 + (-4*a+10)*q^157 + (-4*a-4)*q^158 + -8*q^159 + (a-4)*q^160 + (2*a+2)*q^161 + -7*a*q^162 + (2*a-2)*q^163 + (-6*a+8)*q^164 + (-a-5)*q^165 + 4*a*q^166 + (7*a+11)*q^167 + -4*a*q^168 + 5*a*q^169 + (-2*a-4)*q^170 + 4*q^171 + 4*q^172 + (-a-7)*q^173 + (12*a+4)*q^174 + -1*q^175 + -12*q^176 + (4*a+4)*q^177 + (2*a+8)*q^178 + 20*q^179 + a*q^180 + (10*a+8)*q^181 + (-2*a-4)*q^182 + 24*q^183 + 8*a*q^184 + 6*q^185 + (-3*a-7)*q^187 + (10*a-14)*q^188 + (-a+3)*q^189 + (-4*a+8)*q^190 + (a-11)*q^191 + (-4*a-8)*q^192 + (-6*a+4)*q^193 + (-2*a-20)*q^194 + (-3*a-7)*q^195 + (-a+2)*q^196 + (-2*a-4)*q^197 + (4*a+8)*q^198 + (-4*a-12)*q^199 + (a-4)*q^200 + ... ------------------------------------------------------- Gamma_0(36) Weight 2 ------------------------------------------------------- J_0(36), dim = 1 ------------------------------------------------------- 36A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 2*3 Torsion Bound = 2*3 |L(1)/Omega| = 1/2*3 Sha Bound = 2*3 ANALYTIC INVARIANTS: Omega+ = 4.2065463110251268671 + -0.24512255545791210966e-42i Omega- = 2.4286506450289842226i L(1) = 0.70109105183752114451 w1 = 2.1032731555125634335 + 1.2143253225144921113i w2 = 2.1032731555125634335 + -1.2143253225144921113i c4 = -0.52571389486013256708e-10 + 0.91056317614267246262e-10i c6 = -864.00000602945746137 + -0.15104054686297026568e-39i j = -0.26906338489013003736e-32 + -0.52498895775224995052e-63i HECKE EIGENFORM: f(q) = q + -4*q^7 + 2*q^13 + 8*q^19 + -5*q^25 + -4*q^31 + -10*q^37 + 8*q^43 + 9*q^49 + 14*q^61 + -16*q^67 + -10*q^73 + -4*q^79 + -8*q^91 + 14*q^97 + 20*q^103 + 2*q^109 + -11*q^121 + 20*q^127 + -32*q^133 + -16*q^139 + -4*q^151 + 14*q^157 + 8*q^163 + -9*q^169 + 20*q^175 + 26*q^181 + 2*q^193 + -28*q^199 + ... ------------------------------------------------------- Gamma_0(37) Weight 2 ------------------------------------------------------- J_0(37), dim = 2 ------------------------------------------------------- 37A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = + discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 2 ord((0)-(oo)) = 1 Torsion Bound = 1 |L(1)/Omega| = 0 Sha Bound = 0 ANALYTIC INVARIANTS: Omega+ = 2.9934586462319601052 + -0.12785801847156390955e-15i Omega- = 0.27086382816623465246e-15 + -2.4513893819867898361i L(1) = w1 = -2.9934586462319601052 + 0.12785801847156390955e-15i w2 = -0.27086382816623465246e-15 + 2.4513893819867898361i c4 = 47.999999999971709464 + -0.15500379532785060652e-13i c6 = -216.00000000976399004 + 0.22379484748281594807e-12i j = 2988.9729731740208105 + -0.24066742978407140058e-11i HECKE EIGENFORM: f(q) = q + -2*q^2 + -3*q^3 + 2*q^4 + -2*q^5 + 6*q^6 + -1*q^7 + 6*q^9 + 4*q^10 + -5*q^11 + -6*q^12 + -2*q^13 + 2*q^14 + 6*q^15 + -4*q^16 + -12*q^18 + -4*q^20 + 3*q^21 + 10*q^22 + 2*q^23 + -1*q^25 + 4*q^26 + -9*q^27 + -2*q^28 + 6*q^29 + -12*q^30 + -4*q^31 + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 + -1*q^37 + 6*q^39 + -9*q^41 + -6*q^42 + 2*q^43 + -10*q^44 + -12*q^45 + -4*q^46 + -9*q^47 + 12*q^48 + -6*q^49 + 2*q^50 + -4*q^52 + 1*q^53 + 18*q^54 + 10*q^55 + -12*q^58 + 8*q^59 + 12*q^60 + -8*q^61 + 8*q^62 + -6*q^63 + -8*q^64 + 4*q^65 + -30*q^66 + 8*q^67 + -6*q^69 + -4*q^70 + 9*q^71 + -1*q^73 + 2*q^74 + 3*q^75 + 5*q^77 + -12*q^78 + 4*q^79 + 8*q^80 + 9*q^81 + 18*q^82 + -15*q^83 + 6*q^84 + -4*q^86 + -18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^92 + 12*q^93 + 18*q^94 + -24*q^96 + 4*q^97 + 12*q^98 + -30*q^99 + -2*q^100 + 3*q^101 + 18*q^103 + -6*q^105 + -2*q^106 + -12*q^107 + -18*q^108 + -16*q^109 + -20*q^110 + 3*q^111 + 4*q^112 + -18*q^113 + -4*q^115 + 12*q^116 + -12*q^117 + -16*q^118 + 14*q^121 + 16*q^122 + 27*q^123 + -8*q^124 + 12*q^125 + 12*q^126 + 1*q^127 + -6*q^129 + -8*q^130 + -12*q^131 + 30*q^132 + -16*q^134 + 18*q^135 + -6*q^137 + 12*q^138 + 4*q^139 + 4*q^140 + 27*q^141 + -18*q^142 + 10*q^143 + -24*q^144 + -12*q^145 + 2*q^146 + 18*q^147 + -2*q^148 + -5*q^149 + -6*q^150 + 16*q^151 + -10*q^154 + 8*q^155 + 12*q^156 + 23*q^157 + -8*q^158 + -3*q^159 + -16*q^160 + -2*q^161 + -18*q^162 + -18*q^163 + -18*q^164 + -30*q^165 + 30*q^166 + -12*q^167 + -9*q^169 + 4*q^172 + 9*q^173 + 36*q^174 + 1*q^175 + 20*q^176 + -24*q^177 + -8*q^178 + 18*q^179 + -24*q^180 + 5*q^181 + -4*q^182 + 24*q^183 + 2*q^185 + -24*q^186 + -18*q^188 + 9*q^189 + -4*q^191 + 24*q^192 + -26*q^193 + -8*q^194 + -12*q^195 + -12*q^196 + 3*q^197 + 60*q^198 + 2*q^199 + ... ------------------------------------------------------- 37B (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = - discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 2 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 1.0885215929042291958 + -0.58407040734934424174e-17i Omega- = 0.94135561290761948146e-16 + -1.7676106702337894123i L(1) = 0.3628405309680763986 w1 = -0.94135561290761948146e-16 + 1.7676106702337894123i w2 = 1.0885215929042291958 + -0.58407040734934424174e-17i c4 = 1119.9999999999677548 + 0.18129127932846696033e-13i c6 = 36296.000000035998826 + 0.1582728301279095073e-11i j = 27736.323614470447545 + 0.16135807138535004293e-10i HECKE EIGENFORM: f(q) = q + 1*q^3 + -2*q^4 + -1*q^7 + -2*q^9 + 3*q^11 + -2*q^12 + -4*q^13 + 4*q^16 + 6*q^17 + 2*q^19 + -1*q^21 + 6*q^23 + -5*q^25 + -5*q^27 + 2*q^28 + -6*q^29 + -4*q^31 + 3*q^33 + 4*q^36 + 1*q^37 + -4*q^39 + -9*q^41 + 8*q^43 + -6*q^44 + 3*q^47 + 4*q^48 + -6*q^49 + 6*q^51 + 8*q^52 + -3*q^53 + 2*q^57 + 12*q^59 + 8*q^61 + 2*q^63 + -8*q^64 + -4*q^67 + -12*q^68 + 6*q^69 + -15*q^71 + 11*q^73 + -5*q^75 + -4*q^76 + -3*q^77 + -10*q^79 + 1*q^81 + 9*q^83 + 2*q^84 + -6*q^87 + 6*q^89 + 4*q^91 + -12*q^92 + -4*q^93 + 8*q^97 + -6*q^99 + 10*q^100 + 3*q^101 + -4*q^103 + 12*q^107 + 10*q^108 + 2*q^109 + 1*q^111 + -4*q^112 + -6*q^113 + 12*q^116 + 8*q^117 + -6*q^119 + -2*q^121 + -9*q^123 + 8*q^124 + -7*q^127 + 8*q^129 + -6*q^131 + -6*q^132 + -2*q^133 + -6*q^137 + -4*q^139 + 3*q^141 + -12*q^143 + -8*q^144 + -6*q^147 + -2*q^148 + 15*q^149 + 8*q^151 + -12*q^153 + 8*q^156 + -13*q^157 + -3*q^159 + -6*q^161 + -16*q^163 + 18*q^164 + 18*q^167 + 3*q^169 + -4*q^171 + -16*q^172 + 9*q^173 + 5*q^175 + 12*q^176 + 12*q^177 + 18*q^179 + -7*q^181 + 8*q^183 + 18*q^187 + -6*q^188 + 5*q^189 + -24*q^191 + -8*q^192 + -4*q^193 + 12*q^196 + 15*q^197 + 2*q^199 + ... ------------------------------------------------------- Gamma_0(38) Weight 2 ------------------------------------------------------- J_0(38), dim = 4 ------------------------------------------------------- 38A (new) , dim = 1 CONGRUENCES: Modular Degree = 2*3 Ker(ModPolar) = Z/2*3 + Z/2*3 = B(Z/2 + Z/2) + C(Z/3 + Z/3) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 1.8906322299422984681 + -0.25549454413743819076e-15i Omega- = 0.24413525194222918571e-15 + -1.202627757962398574i L(1) = 0.63021074331409948938 w1 = 0.94531611497114935613 + -0.60131387898119941475i w2 = -0.945316114971149112 + -0.60131387898119915925i c4 = -454.9999999998093033 + 0.35644607514515694776e-9i c6 = -77293.000001309909373 + 0.7077822448960960584e-7i j = 26.822757678307073771 + -0.13698781073461575829e-10i HECKE EIGENFORM: f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -1*q^6 + -1*q^7 + -1*q^8 + -2*q^9 + -6*q^11 + 1*q^12 + 5*q^13 + 1*q^14 + 1*q^16 + 3*q^17 + 2*q^18 + 1*q^19 + -1*q^21 + 6*q^22 + 3*q^23 + -1*q^24 + -5*q^25 + -5*q^26 + -5*q^27 + -1*q^28 + 9*q^29 + -4*q^31 + -1*q^32 + -6*q^33 + -3*q^34 + -2*q^36 + 2*q^37 + -1*q^38 + 5*q^39 + 1*q^42 + 8*q^43 + -6*q^44 + -3*q^46 + 1*q^48 + -6*q^49 + 5*q^50 + 3*q^51 + 5*q^52 + -3*q^53 + 5*q^54 + 1*q^56 + 1*q^57 + -9*q^58 + 9*q^59 + -10*q^61 + 4*q^62 + 2*q^63 + 1*q^64 + 6*q^66 + 5*q^67 + 3*q^68 + 3*q^69 + -6*q^71 + 2*q^72 + -7*q^73 + -2*q^74 + -5*q^75 + 1*q^76 + 6*q^77 + -5*q^78 + -10*q^79 + 1*q^81 + -6*q^83 + -1*q^84 + -8*q^86 + 9*q^87 + 6*q^88 + -12*q^89 + -5*q^91 + 3*q^92 + -4*q^93 + -1*q^96 + -10*q^97 + 6*q^98 + 12*q^99 + -5*q^100 + 18*q^101 + -3*q^102 + 14*q^103 + -5*q^104 + 3*q^106 + -9*q^107 + -5*q^108 + 11*q^109 + 2*q^111 + -1*q^112 + 6*q^113 + -1*q^114 + 9*q^116 + -10*q^117 + -9*q^118 + -3*q^119 + 25*q^121 + 10*q^122 + -4*q^124 + -2*q^126 + 2*q^127 + -1*q^128 + 8*q^129 + -6*q^132 + -1*q^133 + -5*q^134 + -3*q^136 + -9*q^137 + -3*q^138 + -4*q^139 + 6*q^142 + -30*q^143 + -2*q^144 + 7*q^146 + -6*q^147 + 2*q^148 + 5*q^150 + -10*q^151 + -1*q^152 + -6*q^153 + -6*q^154 + 5*q^156 + -22*q^157 + 10*q^158 + -3*q^159 + -3*q^161 + -1*q^162 + 20*q^163 + 6*q^166 + 12*q^167 + 1*q^168 + 12*q^169 + -2*q^171 + 8*q^172 + 6*q^173 + -9*q^174 + 5*q^175 + -6*q^176 + 9*q^177 + 12*q^178 + 2*q^181 + 5*q^182 + -10*q^183 + -3*q^184 + 4*q^186 + -18*q^187 + 5*q^189 + 3*q^191 + 1*q^192 + 14*q^193 + 10*q^194 + -6*q^196 + -12*q^198 + 11*q^199 + 5*q^200 + ... ------------------------------------------------------- 38B (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 5 Torsion Bound = 5 |L(1)/Omega| = 1/5 Sha Bound = 5 ANALYTIC INVARIANTS: Omega+ = 4.0962281652755201749 + 0.77398315064620442127e-15i Omega- = 0.36306476815698415383e-15 + 2.3559624213775919731i L(1) = 0.81924563305510403499 w1 = -2.0481140826377599059 + 1.1779812106887955996i w2 = 0.36306476815698415383e-15 + 2.3559624213775919731i c4 = 1.0000000001027878033 + 0.89942732848875459372e-13i c6 = -1024.9999999249986985 + 0.10904498003954723252e-12i j = -0.16447368428531379042e-2 + -0.44414675388747314801e-15i HECKE EIGENFORM: f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + -4*q^5 + -1*q^6 + 3*q^7 + 1*q^8 + -2*q^9 + -4*q^10 + 2*q^11 + -1*q^12 + -1*q^13 + 3*q^14 + 4*q^15 + 1*q^16 + 3*q^17 + -2*q^18 + -1*q^19 + -4*q^20 + -3*q^21 + 2*q^22 + -1*q^23 + -1*q^24 + 11*q^25 + -1*q^26 + 5*q^27 + 3*q^28 + -5*q^29 + 4*q^30 + -8*q^31 + 1*q^32 + -2*q^33 + 3*q^34 + -12*q^35 + -2*q^36 + -2*q^37 + -1*q^38 + 1*q^39 + -4*q^40 + -8*q^41 + -3*q^42 + 4*q^43 + 2*q^44 + 8*q^45 + -1*q^46 + 8*q^47 + -1*q^48 + 2*q^49 + 11*q^50 + -3*q^51 + -1*q^52 + -1*q^53 + 5*q^54 + -8*q^55 + 3*q^56 + 1*q^57 + -5*q^58 + 15*q^59 + 4*q^60 + 2*q^61 + -8*q^62 + -6*q^63 + 1*q^64 + 4*q^65 + -2*q^66 + 3*q^67 + 3*q^68 + 1*q^69 + -12*q^70 + 2*q^71 + -2*q^72 + 9*q^73 + -2*q^74 + -11*q^75 + -1*q^76 + 6*q^77 + 1*q^78 + -10*q^79 + -4*q^80 + 1*q^81 + -8*q^82 + -6*q^83 + -3*q^84 + -12*q^85 + 4*q^86 + 5*q^87 + 2*q^88 + 8*q^90 + -3*q^91 + -1*q^92 + 8*q^93 + 8*q^94 + 4*q^95 + -1*q^96 + -2*q^97 + 2*q^98 + -4*q^99 + 11*q^100 + 2*q^101 + -3*q^102 + -6*q^103 + -1*q^104 + 12*q^105 + -1*q^106 + -7*q^107 + 5*q^108 + -15*q^109 + -8*q^110 + 2*q^111 + 3*q^112 + 14*q^113 + 1*q^114 + 4*q^115 + -5*q^116 + 2*q^117 + 15*q^118 + 9*q^119 + 4*q^120 + -7*q^121 + 2*q^122 + 8*q^123 + -8*q^124 + -24*q^125 + -6*q^126 + 18*q^127 + 1*q^128 + -4*q^129 + 4*q^130 + 12*q^131 + -2*q^132 + -3*q^133 + 3*q^134 + -20*q^135 + 3*q^136 + -17*q^137 + 1*q^138 + -12*q^140 + -8*q^141 + 2*q^142 + -2*q^143 + -2*q^144 + 20*q^145 + 9*q^146 + -2*q^147 + -2*q^148 + -11*q^150 + 2*q^151 + -1*q^152 + -6*q^153 + 6*q^154 + 32*q^155 + 1*q^156 + -2*q^157 + -10*q^158 + 1*q^159 + -4*q^160 + -3*q^161 + 1*q^162 + -16*q^163 + -8*q^164 + 8*q^165 + -6*q^166 + -12*q^167 + -3*q^168 + -12*q^169 + -12*q^170 + 2*q^171 + 4*q^172 + -6*q^173 + 5*q^174 + 33*q^175 + 2*q^176 + -15*q^177 + 8*q^180 + 22*q^181 + -3*q^182 + -2*q^183 + -1*q^184 + 8*q^185 + 8*q^186 + 6*q^187 + 8*q^188 + 15*q^189 + 4*q^190 + 7*q^191 + -1*q^192 + -6*q^193 + -2*q^194 + -4*q^195 + 2*q^196 + 8*q^197 + -4*q^198 + -25*q^199 + 11*q^200 + ... ------------------------------------------------------- 38C (old = 19A), dim = 1 CONGRUENCES: Modular Degree = 3 Ker(ModPolar) = Z/3 + Z/3 = A(Z/3 + Z/3) ------------------------------------------------------- Gamma_0(39) Weight 2 ------------------------------------------------------- J_0(39), dim = 3 ------------------------------------------------------- 39A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2 Torsion Bound = 2^2 |L(1)/Omega| = 1/2^2 Sha Bound = 2^2 ANALYTIC INVARIANTS: Omega+ = 1.653375701346774334 + 0.15446361992811899919e-14i Omega- = 0.35046099624307500246e-14 + 2.2865886336506696131i L(1) = 0.41334392533669358351 w1 = -0.35046099624307500246e-14 + -2.2865886336506696131i w2 = -1.653375701346774334 + -0.15446361992811899919e-14i c4 = 216.99999999999760004 + -0.62973998578533171536e-12i c6 = 2755.0000000006076606 + -0.20981738516535295304e-10i j = 6718.1545036252441239 + -0.12660338165564227238e-9i HECKE EIGENFORM: f(q) = q + 1*q^2 + -1*q^3 + -1*q^4 + 2*q^5 + -1*q^6 + -4*q^7 + -3*q^8 + 1*q^9 + 2*q^10 + 4*q^11 + 1*q^12 + 1*q^13 + -4*q^14 + -2*q^15 + -1*q^16 + 2*q^17 + 1*q^18 + -2*q^20 + 4*q^21 + 4*q^22 + 3*q^24 + -1*q^25 + 1*q^26 + -1*q^27 + 4*q^28 + -10*q^29 + -2*q^30 + 4*q^31 + 5*q^32 + -4*q^33 + 2*q^34 + -8*q^35 + -1*q^36 + -2*q^37 + -1*q^39 + -6*q^40 + 6*q^41 + 4*q^42 + -12*q^43 + -4*q^44 + 2*q^45 + 1*q^48 + 9*q^49 + -1*q^50 + -2*q^51 + -1*q^52 + 6*q^53 + -1*q^54 + 8*q^55 + 12*q^56 + -10*q^58 + 12*q^59 + 2*q^60 + -2*q^61 + 4*q^62 + -4*q^63 + 7*q^64 + 2*q^65 + -4*q^66 + -8*q^67 + -2*q^68 + -8*q^70 + -3*q^72 + 2*q^73 + -2*q^74 + 1*q^75 + -16*q^77 + -1*q^78 + 8*q^79 + -2*q^80 + 1*q^81 + 6*q^82 + 4*q^83 + -4*q^84 + 4*q^85 + -12*q^86 + 10*q^87 + -12*q^88 + -2*q^89 + 2*q^90 + -4*q^91 + -4*q^93 + -5*q^96 + 10*q^97 + 9*q^98 + 4*q^99 + 1*q^100 + -18*q^101 + -2*q^102 + -3*q^104 + 8*q^105 + 6*q^106 + 12*q^107 + 1*q^108 + -2*q^109 + 8*q^110 + 2*q^111 + 4*q^112 + -6*q^113 + 10*q^116 + 1*q^117 + 12*q^118 + -8*q^119 + 6*q^120 + 5*q^121 + -2*q^122 + -6*q^123 + -4*q^124 + -12*q^125 + -4*q^126 + -16*q^127 + -3*q^128 + 12*q^129 + 2*q^130 + 4*q^131 + 4*q^132 + -8*q^134 + -2*q^135 + -6*q^136 + 6*q^137 + 12*q^139 + 8*q^140 + 4*q^143 + -1*q^144 + -20*q^145 + 2*q^146 + -9*q^147 + 2*q^148 + -6*q^149 + 1*q^150 + 4*q^151 + 2*q^153 + -16*q^154 + 8*q^155 + 1*q^156 + -18*q^157 + 8*q^158 + -6*q^159 + 10*q^160 + 1*q^162 + 8*q^163 + -6*q^164 + -8*q^165 + 4*q^166 + -8*q^167 + -12*q^168 + 1*q^169 + 4*q^170 + 12*q^172 + 6*q^173 + 10*q^174 + 4*q^175 + -4*q^176 + -12*q^177 + -2*q^178 + 4*q^179 + -2*q^180 + -10*q^181 + -4*q^182 + 2*q^183 + -4*q^185 + -4*q^186 + 8*q^187 + 4*q^189 + 8*q^191 + -7*q^192 + 18*q^193 + 10*q^194 + -2*q^195 + -9*q^196 + 18*q^197 + 4*q^198 + 8*q^199 + 3*q^200 + ... ------------------------------------------------------- 39B (new) , dim = 2 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 2^3 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2*7 Torsion Bound = 2^2*7 |L(1)/Omega| = 1/2^2*7 Sha Bound = 2^2*7 ANALYTIC INVARIANTS: Omega+ = 5.3485665640937583872 + 0.23816033991704107474e-14i Omega- = 2.926444751637510878 + 0.37044323325137031567e-15i L(1) = 0.1910202344319199424 HECKE EIGENFORM: a^2+2*a-1 = 0, f(q) = q + a*q^2 + 1*q^3 + (-2*a-1)*q^4 + (-2*a-2)*q^5 + a*q^6 + (2*a+2)*q^7 + (a-2)*q^8 + 1*q^9 + (2*a-2)*q^10 + -2*q^11 + (-2*a-1)*q^12 + -1*q^13 + (-2*a+2)*q^14 + (-2*a-2)*q^15 + 3*q^16 + (4*a+6)*q^17 + a*q^18 + (-2*a-2)*q^19 + (-2*a+6)*q^20 + (2*a+2)*q^21 + -2*a*q^22 + -4*q^23 + (a-2)*q^24 + 3*q^25 + -a*q^26 + 1*q^27 + (2*a-6)*q^28 + 2*q^29 + (2*a-2)*q^30 + (2*a-2)*q^31 + (a+4)*q^32 + -2*q^33 + (-2*a+4)*q^34 + -8*q^35 + (-2*a-1)*q^36 + (-4*a-6)*q^37 + (2*a-2)*q^38 + -1*q^39 + (6*a+2)*q^40 + (-2*a+6)*q^41 + (-2*a+2)*q^42 + -4*a*q^43 + (4*a+2)*q^44 + (-2*a-2)*q^45 + -4*a*q^46 + (-4*a-10)*q^47 + 3*q^48 + 1*q^49 + 3*a*q^50 + (4*a+6)*q^51 + (2*a+1)*q^52 + -2*q^53 + a*q^54 + (4*a+4)*q^55 + (-6*a-2)*q^56 + (-2*a-2)*q^57 + 2*a*q^58 + (4*a+6)*q^59 + (-2*a+6)*q^60 + (8*a+10)*q^61 + (-6*a+2)*q^62 + (2*a+2)*q^63 + (2*a-5)*q^64 + (2*a+2)*q^65 + -2*a*q^66 + (2*a+6)*q^67 + -14*q^68 + -4*q^69 + -8*a*q^70 + 2*q^71 + (a-2)*q^72 + (-4*a+2)*q^73 + (2*a-4)*q^74 + 3*q^75 + (-2*a+6)*q^76 + (-4*a-4)*q^77 + -a*q^78 + (-8*a-8)*q^79 + (-6*a-6)*q^80 + 1*q^81 + (10*a-2)*q^82 + (4*a+2)*q^83 + (2*a-6)*q^84 + (-4*a-20)*q^85 + (8*a-4)*q^86 + 2*q^87 + (-2*a+4)*q^88 + (2*a+14)*q^89 + (2*a-2)*q^90 + (-2*a-2)*q^91 + (8*a+4)*q^92 + (2*a-2)*q^93 + (-2*a-4)*q^94 + 8*q^95 + (a+4)*q^96 + (4*a+2)*q^97 + a*q^98 + -2*q^99 + (-6*a-3)*q^100 + (4*a+6)*q^101 + (-2*a+4)*q^102 + (-4*a+4)*q^103 + (-a+2)*q^104 + -8*q^105 + -2*a*q^106 + (-8*a-8)*q^107 + (-2*a-1)*q^108 + (8*a+2)*q^109 + (-4*a+4)*q^110 + (-4*a-6)*q^111 + (6*a+6)*q^112 + (-8*a-2)*q^113 + (2*a-2)*q^114 + (8*a+8)*q^115 + (-4*a-2)*q^116 + -1*q^117 + (-2*a+4)*q^118 + (4*a+20)*q^119 + (6*a+2)*q^120 + -7*q^121 + (-6*a+8)*q^122 + (-2*a+6)*q^123 + (10*a-2)*q^124 + (4*a+4)*q^125 + (-2*a+2)*q^126 + (4*a+4)*q^127 + (-11*a-6)*q^128 + -4*a*q^129 + (-2*a+2)*q^130 + -8*q^131 + (4*a+2)*q^132 + -8*q^133 + (2*a+2)*q^134 + (-2*a-2)*q^135 + (-10*a-8)*q^136 + (-2*a-10)*q^137 + -4*a*q^138 + (-8*a-4)*q^139 + (16*a+8)*q^140 + (-4*a-10)*q^141 + 2*a*q^142 + 2*q^143 + 3*q^144 + (-4*a-4)*q^145 + (10*a-4)*q^146 + 1*q^147 + 14*q^148 + (2*a-10)*q^149 + 3*a*q^150 + (6*a-6)*q^151 + (6*a+2)*q^152 + (4*a+6)*q^153 + (4*a-4)*q^154 + 8*a*q^155 + (2*a+1)*q^156 + -10*q^157 + (8*a-8)*q^158 + -2*q^159 + (-6*a-10)*q^160 + (-8*a-8)*q^161 + a*q^162 + (2*a+18)*q^163 + (-18*a-2)*q^164 + (4*a+4)*q^165 + (-6*a+4)*q^166 + (-4*a-2)*q^167 + (-6*a-2)*q^168 + 1*q^169 + (-12*a-4)*q^170 + (-2*a-2)*q^171 + (-12*a+8)*q^172 + (-4*a-10)*q^173 + 2*a*q^174 + (6*a+6)*q^175 + -6*q^176 + (4*a+6)*q^177 + (10*a+2)*q^178 + (-8*a-20)*q^179 + (-2*a+6)*q^180 + 14*q^181 + (2*a-2)*q^182 + (8*a+10)*q^183 + (-4*a+8)*q^184 + (4*a+20)*q^185 + (-6*a+2)*q^186 + (-8*a-12)*q^187 + (8*a+18)*q^188 + (2*a+2)*q^189 + 8*a*q^190 + 8*a*q^191 + (2*a-5)*q^192 + (8*a+2)*q^193 + (-6*a+4)*q^194 + (2*a+2)*q^195 + (-2*a-1)*q^196 + (6*a-2)*q^197 + -2*a*q^198 + (4*a+20)*q^199 + (3*a-6)*q^200 + ... ------------------------------------------------------- Gamma_0(40) Weight 2 ------------------------------------------------------- J_0(40), dim = 3 ------------------------------------------------------- 40A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2 Torsion Bound = 2^2 |L(1)/Omega| = 1/2^2 Sha Bound = 2^2 ANALYTIC INVARIANTS: Omega+ = 1.4844124734223870825 + 0.67078372006300930248e-15i Omega- = -2.0189058199784246674i L(1) = 0.37110311835559677063 w1 = 2.0189058199784246674i w2 = 1.4844124734223870825 + 0.67078372006300930248e-15i c4 = 335.99999999999671731 + -0.54929661408210525998e-12i c6 = 5184.0000000025045332 + -0.16259390717621393208e-10i j = 5927.0400000143388291 + -0.1970980279574890631e-10i HECKE EIGENFORM: f(q) = q + 1*q^5 + -4*q^7 + -3*q^9 + 4*q^11 + -2*q^13 + 2*q^17 + 4*q^19 + 4*q^23 + 1*q^25 + -2*q^29 + -8*q^31 + -4*q^35 + 6*q^37 + -6*q^41 + -8*q^43 + -3*q^45 + 4*q^47 + 9*q^49 + 6*q^53 + 4*q^55 + -4*q^59 + -2*q^61 + 12*q^63 + -2*q^65 + 8*q^67 + -6*q^73 + -16*q^77 + 9*q^81 + -16*q^83 + 2*q^85 + -6*q^89 + 8*q^91 + 4*q^95 + -14*q^97 + -12*q^99 + 6*q^101 + 4*q^103 + 14*q^109 + 18*q^113 + 4*q^115 + 6*q^117 + -8*q^119 + 5*q^121 + 1*q^125 + -12*q^127 + 12*q^131 + -16*q^133 + 10*q^137 + 12*q^139 + -8*q^143 + -2*q^145 + -10*q^149 + -16*q^151 + -6*q^153 + -8*q^155 + -2*q^157 + -16*q^161 + 16*q^163 + 12*q^167 + -9*q^169 + -12*q^171 + 14*q^173 + -4*q^175 + 20*q^179 + -10*q^181 + 6*q^185 + 8*q^187 + 8*q^191 + -14*q^193 + 22*q^197 + 8*q^199 + ... ------------------------------------------------------- 40B (old = 20A), dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ------------------------------------------------------- Gamma_0(41) Weight 2 ------------------------------------------------------- J_0(41), dim = 3 ------------------------------------------------------- 41A (new) , dim = 3 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 2^2*37 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 2*5 Torsion Bound = 2*5 |L(1)/Omega| = 1/2*5 Sha Bound = 2*5 ANALYTIC INVARIANTS: Omega+ = 3.181260746093144769 + -0.15765626094486573315e-13i Omega- = 0.43262957132767340751e-13 + -24.672174470523593452i L(1) = 0.3181260746093144769 HECKE EIGENFORM: a^3+a^2-5*a-1 = 0, f(q) = q + a*q^2 + (-1/2*a^2-a+3/2)*q^3 + (a^2-2)*q^4 + (-a-1)*q^5 + (-1/2*a^2-a-1/2)*q^6 + (1/2*a^2+a+1/2)*q^7 + (-a^2+a+1)*q^8 + a*q^9 + (-a^2-a)*q^10 + (3/2*a^2+a-9/2)*q^11 + (1/2*a^2-a-7/2)*q^12 + (-a^2+3)*q^13 + (1/2*a^2+3*a+1/2)*q^14 + (a^2+2*a-1)*q^15 + (-4*a+3)*q^16 + -2*q^17 + a^2*q^18 + (-3/2*a^2-a+13/2)*q^19 + (-3*a+1)*q^20 + (-a^2-3*a)*q^21 + (-1/2*a^2+3*a+3/2)*q^22 + (-2*a^2-2*a+8)*q^23 + (-1/2*a^2+a+3/2)*q^24 + (a^2+2*a-4)*q^25 + (a^2-2*a-1)*q^26 + (a^2+2*a-5)*q^27 + (3/2*a^2+a-1/2)*q^28 + (a^2+2*a-5)*q^29 + (a^2+4*a+1)*q^30 + (2*a+6)*q^31 + (-2*a^2+a-2)*q^32 + (a^2-a-8)*q^33 + -2*a*q^34 + (-a^2-4*a-1)*q^35 + (-a^2+3*a+1)*q^36 + (-3*a-3)*q^37 + (1/2*a^2-a-3/2)*q^38 + (-a^2+5)*q^39 + (-a^2+3*a)*q^40 + 1*q^41 + (-2*a^2-5*a-1)*q^42 + (a^2-5)*q^43 + (1/2*a^2-3*a+17/2)*q^44 + (-a^2-a)*q^45 + (-2*a-2)*q^46 + (3/2*a^2-3*a-13/2)*q^47 + (1/2*a^2+a+13/2)*q^48 + (2*a^2+5*a-6)*q^49 + (a^2+a+1)*q^50 + (a^2+2*a-3)*q^51 + (-a^2+4*a-5)*q^52 + (a^2+2*a-1)*q^53 + (a^2+1)*q^54 + (-a^2-4*a+3)*q^55 + (-3/2*a^2+a+1/2)*q^56 + (-2*a^2-a+11)*q^57 + (a^2+1)*q^58 + (-2*a^2-2*a+4)*q^59 + (a^2+2*a+3)*q^60 + (-a^2+2*a+5)*q^61 + (2*a^2+6*a)*q^62 + (1/2*a^2+3*a+1/2)*q^63 + (3*a^2-4*a-8)*q^64 + (2*a-2)*q^65 + (-2*a^2-3*a+1)*q^66 + (-3/2*a^2-a+9/2)*q^67 + (-2*a^2+4)*q^68 + (-2*a^2+14)*q^69 + (-3*a^2-6*a-1)*q^70 + (-3/2*a^2+a+25/2)*q^71 + (2*a^2-4*a-1)*q^72 + (4*a^2+a-15)*q^73 + (-3*a^2-3*a)*q^74 + (1/2*a^2-a-15/2)*q^75 + (3/2*a^2+3*a-25/2)*q^76 + (2*a^2+3*a-1)*q^77 + (a^2-1)*q^78 + (1/2*a^2-a+17/2)*q^79 + (4*a^2+a-3)*q^80 + (a^2-3*a-9)*q^81 + a*q^82 + (2*a^2+4*a-6)*q^83 + (-a^2-5*a-2)*q^84 + (2*a+2)*q^85 + (-a^2+1)*q^86 + (a^2-9)*q^87 + (-5/2*a^2+5*a-5/2)*q^88 + (-4*a^2-2*a+12)*q^89 + (-5*a-1)*q^90 + (-a^2+1)*q^91 + (2*a^2+2*a-16)*q^92 + (-4*a^2-8*a+8)*q^93 + (-9/2*a^2+a+3/2)*q^94 + (a^2+2*a-5)*q^95 + (3/2*a^2+7*a-5/2)*q^96 + (-2*a^2-4*a+8)*q^97 + (3*a^2+4*a+2)*q^98 + (-1/2*a^2+3*a+3/2)*q^99 + (-2*a^2+2*a+9)*q^100 + (3*a^2-5)*q^101 + (a^2+2*a+1)*q^102 + (a^2-6*a-7)*q^103 + (3*a^2-6*a+1)*q^104 + (3*a^2+8*a+1)*q^105 + (a^2+4*a+1)*q^106 + (4*a-4)*q^107 + (-3*a^2+2*a+11)*q^108 + (a^2-4*a-7)*q^109 + (-3*a^2-2*a-1)*q^110 + (3*a^2+6*a-3)*q^111 + (-1/2*a^2-9*a-1/2)*q^112 + (-4*a^2-5*a+15)*q^113 + (a^2+a-2)*q^114 + (2*a^2+4*a-6)*q^115 + (-3*a^2+2*a+11)*q^116 + (a^2-2*a-1)*q^117 + (-6*a-2)*q^118 + (-a^2-2*a-1)*q^119 + (-a^2-1)*q^120 + (-2*a^2-3*a+10)*q^121 + (3*a^2-1)*q^122 + (-1/2*a^2-a+3/2)*q^123 + (4*a^2+6*a-10)*q^124 + (-2*a^2+2*a+8)*q^125 + (5/2*a^2+3*a+1/2)*q^126 + (-2*a^2-2*a+12)*q^127 + (-3*a^2+5*a+7)*q^128 + (2*a^2+2*a-8)*q^129 + (2*a^2-2*a)*q^130 + (a^2-2*a-11)*q^131 + (-3*a^2-7*a+14)*q^132 + (-a^2-a+2)*q^133 + (1/2*a^2-3*a-3/2)*q^134 + (-2*a^2-2*a+4)*q^135 + (2*a^2-2*a-2)*q^136 + (-4*a^2-8*a+18)*q^137 + (2*a^2+4*a-2)*q^138 + (2*a^2+10*a-8)*q^139 + (-a^2-8*a-1)*q^140 + (4*a^2+5*a-9)*q^141 + (5/2*a^2+5*a-3/2)*q^142 + (a^2+4*a-13)*q^143 + (-4*a^2+3*a)*q^144 + (-2*a^2-2*a+4)*q^145 + (-3*a^2+5*a+4)*q^146 + (-1/2*a^2-5*a-25/2)*q^147 + (-9*a+3)*q^148 + (5*a^2+6*a-13)*q^149 + (-3/2*a^2-5*a+1/2)*q^150 + (1/2*a^2-3*a+13/2)*q^151 + (1/2*a^2-3*a+9/2)*q^152 + -2*a*q^153 + (a^2+9*a+2)*q^154 + (-2*a^2-8*a-6)*q^155 + (a^2+4*a-9)*q^156 + (3*a^2+8*a-13)*q^157 + (-3/2*a^2+11*a+1/2)*q^158 + (-a^2-4*a-3)*q^159 + (-a^2+11*a+4)*q^160 + (-2*a^2-4*a+2)*q^161 + (-4*a^2-4*a+1)*q^162 + (-2*a^2+2)*q^163 + (a^2-2)*q^164 + (a^2+4*a+7)*q^165 + (2*a^2+4*a+2)*q^166 + (1/2*a^2+3*a-11/2)*q^167 + (3*a+1)*q^168 + (-4*a-5)*q^169 + (2*a^2+2*a)*q^170 + (1/2*a^2-a-3/2)*q^171 + (-a^2-4*a+9)*q^172 + (2*a^2+4*a-16)*q^173 + (-a^2-4*a+1)*q^174 + (3/2*a^2+5*a-1/2)*q^175 + (13/2*a^2-9*a-39/2)*q^176 + (4*a+8)*q^177 + (2*a^2-8*a-4)*q^178 + (1/2*a^2-7*a-7/2)*q^179 + (-3*a^2+a)*q^180 + (-5*a^2-6*a+5)*q^181 + (a^2-4*a-1)*q^182 + (-3*a^2-4*a+7)*q^183 + (-2*a+6)*q^184 + (3*a^2+6*a+3)*q^185 + (-4*a^2-12*a-4)*q^186 + (-3*a^2-2*a+9)*q^187 + (5/2*a^2-15*a+17/2)*q^188 + (a^2+4*a-1)*q^189 + (a^2+1)*q^190 + (-1/2*a^2+9*a+19/2)*q^191 + (9/2*a^2+3*a-23/2)*q^192 + (-2*a^2-2*a-2)*q^193 + (-2*a^2-2*a-2)*q^194 + -4*q^195 + (-3*a^2+7*a+15)*q^196 + (-a^2+2*a+21)*q^197 + (7/2*a^2-a-1/2)*q^198 + (3/2*a^2+5*a+23/2)*q^199 + (2*a^2-3*a-4)*q^200 + ... ------------------------------------------------------- Gamma_0(42) Weight 2 ------------------------------------------------------- J_0(42), dim = 5 ------------------------------------------------------- 42A (new) , dim = 1 CONGRUENCES: Modular Degree = 2^2 Ker(ModPolar) = Z/2^2 + Z/2^2 = B(Z/2 + Z/2) + C(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -++ discriminant = 1 #CompGroup(Fpbar) = ??? c_p = ??? c_inf = 1 ord((0)-(oo)) = 2^2 Torsion Bound = 2^3 |L(1)/Omega| = 1/2^2 Sha Bound = 2^4 ANALYTIC INVARIANTS: Omega+ = 3.475447457496835589 + -0.66773145341333805804e-14i Omega- = 0.46797544746161905321e-14 + 1.576986771215808643i L(1) = 0.86886186437420889724 w1 = -1.7377237287484154546 + 0.78849338560790766014i w2 = 0.46797544746161905321e-14 + 1.576986771215808643i c4 = 192.99999999999337075 + 0.27145489463580715346e-11i c6 = -5921.0000000142305431 + -0.91972665928933416094e-10i j = -445.7500620012151321 + -0.6240112902509787748e-11i HECKE EIGENFORM: f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + -2*q^5 + -1*q^6 + -1*q^7 + 1*q^8 + 1*q^9 + -2*q^10 + -4*q^11 + -1*q^12 + 6*q^13 + -1*q^14 + 2*q^15 + 1*q^16 + 2*q^17 + 1*q^18 + -4*q^19 + -2*q^20 + 1*q^21 + -4*q^22 + 8*q^23 + -1*q^24 + -1*q^25 + 6*q^26 + -1*q^27 + -1*q^28 + -2*q^29 + 2*q^30 + 1*q^32 + 4*q^33 + 2*q^34 + 2*q^35 + 1*q^36 + -10*q^37 + -4*q^38 + -6*q^39 + -2*q^40 + -6*q^41 + 1*q^42 + -4*q^43 + -4*q^44 + -2*q^45 + 8*q^46 + -1*q^48 + 1*q^49 + -1*q^50 + -2*q^51 + 6*q^52 + 6*q^53 + -1*q^54 + 8*q^55 + -1*q^56 + 4*q^57 + -2*q^58 + 4*q^59 + 2*q^60 + 6*q^61 + -1*q^63 + 1*q^64 + -12*q^65 + 4*q^66 + 4*q^67 + 2*q^68 + -8*q^69 + 2*q^70 + 8*q^71 + 1*q^72 + 10*q^73 + -10*q^74 + 1*q^75 + -4*q^76 + 4*q^77 + -6*q^78 + -2*q^80 + 1*q^81 + -6*q^82 + -4*q^83 + 1*q^84 + -4*q^85 + -4*q^86 + 2*q^87 + -4*q^88 + -6*q^89 + -2*q^90 + -6*q^91 + 8*q^92 + 8*q^95 + -1*q^96 + -14*q^97 + 1*q^98 + -4*q^99 + -1*q^100 + -2*q^101 + -2*q^102 + 8*q^103 + 6*q^104 + -2*q^105 + 6*q^106 + 12*q^107 + -1*q^108 + -2*q^109 + 8*q^110 + 10*q^111 + -1*q^112 + -14*q^113 + 4*q^114 + -16*q^115 + -2*q^116 + 6*q^117 + 4*q^118 + -2*q^119 + 2*q^120 + 5*q^121 + 6*q^122 + 6*q^123 + 12*q^125 + -1*q^126 + 1*q^128 + 4*q^129 + -12*q^130 + -20*q^131 + 4*q^132 + 4*q^133 + 4*q^134 + 2*q^135 + 2*q^136 + 10*q^137 + -8*q^138 + 4*q^139 + 2*q^140 + 8*q^142 + -24*q^143 + 1*q^144 + 4*q^145 + 10*q^146 + -1*q^147 + -10*q^148 + 6*q^149 + 1*q^150 + -8*q^151 + -4*q^152 + 2*q^153 + 4*q^154 + -6*q^156 + -10*q^157 + -6*q^159 + -2*q^160 + -8*q^161 + 1*q^162 + 20*q^163 + -6*q^164 + -8*q^165 + -4*q^166 + -8*q^167 + 1*q^168 + 23*q^169 + -4*q^170 + -4*q^171 + -4*q^172 + 22*q^173 + 2*q^174 + 1*q^175 + -4*q^176 + -4*q^177 + -6*q^178 + -12*q^179 + -2*q^180 + -18*q^181 + -6*q^182 + -6*q^183 + 8*q^184 + 20*q^185 + -8*q^187 + 1*q^189 + 8*q^190 + -1*q^192 + 2*q^193 + -14*q^194 + 12*q^195 + 1*q^196 + -10*q^197 + -4*q^198 + 8*q^199 + -1*q^200 + ... ------------------------------------------------------- 42B (old = 21A), dim = 1 CONGRUENCES: Modular Degree = 2^2 Ker(ModPolar) = Z/2^2 + Z/2^2 = A(Z/2 + Z/2) + C(Z/2 + Z/2) ------------------------------------------------------- 42C (old = 14A), dim = 1 CONGRUENCES: Modular Degree = 2^2 Ker(ModPolar) = Z/2 + Z/2 + Z/2 + Z/2 = A(Z/2 + Z/2) + B(Z/2 + Z/2) ------------------------------------------------------- Gamma_0(43) Weight 2 ------------------------------------------------------- J_0(43), dim = 3 ------------------------------------------------------- 43A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = + discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 1 Torsion Bound = 1 |L(1)/Omega| = 0 Sha Bound = 0 ANALYTIC INVARIANTS: Omega+ = 5.4686895299676266201 + 0.32821187184894358827e-13i Omega- = 0.3298848030949229151e-13 + -2.7263648363408786932i L(1) = w1 = 2.7343447649837968158 + 1.3631824181704557572i w2 = 0.3298848030949229151e-13 + -2.7263648363408786932i c4 = 15.999999999944623588 + -0.12357626444677525174e-11i c6 = -280.00000002220308548 + 0.1563844624687032145e-10i j = -95.2558139365050836 + 0.12061045657571366696e-10i HECKE EIGENFORM: f(q) = q + -2*q^2 + -2*q^3 + 2*q^4 + -4*q^5 + 4*q^6 + 1*q^9 + 8*q^10 + 3*q^11 + -4*q^12 + -5*q^13 + 8*q^15 + -4*q^16 + -3*q^17 + -2*q^18 + -2*q^19 + -8*q^20 + -6*q^22 + -1*q^23 + 11*q^25 + 10*q^26 + 4*q^27 + -6*q^29 + -16*q^30 + -1*q^31 + 8*q^32 + -6*q^33 + 6*q^34 + 2*q^36 + 4*q^38 + 10*q^39 + 5*q^41 + -1*q^43 + 6*q^44 + -4*q^45 + 2*q^46 + 4*q^47 + 8*q^48 + -7*q^49 + -22*q^50 + 6*q^51 + -10*q^52 + -5*q^53 + -8*q^54 + -12*q^55 + 4*q^57 + 12*q^58 + -12*q^59 + 16*q^60 + 2*q^61 + 2*q^62 + -8*q^64 + 20*q^65 + 12*q^66 + -3*q^67 + -6*q^68 + 2*q^69 + 2*q^71 + 2*q^73 + -22*q^75 + -4*q^76 + -20*q^78 + -8*q^79 + 16*q^80 + -11*q^81 + -10*q^82 + 15*q^83 + 12*q^85 + 2*q^86 + 12*q^87 + -4*q^89 + 8*q^90 + -2*q^92 + 2*q^93 + -8*q^94 + 8*q^95 + -16*q^96 + 7*q^97 + 14*q^98 + 3*q^99 + 22*q^100 + -9*q^101 + -12*q^102 + 1*q^103 + 10*q^106 + -12*q^107 + 8*q^108 + 7*q^109 + 24*q^110 + -20*q^113 + -8*q^114 + 4*q^115 + -12*q^116 + -5*q^117 + 24*q^118 + -2*q^121 + -4*q^122 + -10*q^123 + -2*q^124 + -24*q^125 + 1*q^127 + 2*q^129 + -40*q^130 + 8*q^131 + -12*q^132 + 6*q^134 + -16*q^135 + 6*q^137 + -4*q^138 + 19*q^139 + -8*q^141 + -4*q^142 + -15*q^143 + -4*q^144 + 24*q^145 + -4*q^146 + 14*q^147 + 12*q^149 + 44*q^150 + -20*q^151 + -3*q^153 + 4*q^155 + 20*q^156 + -10*q^157 + 16*q^158 + 10*q^159 + -32*q^160 + 22*q^162 + 14*q^163 + 10*q^164 + 24*q^165 + -30*q^166 + -9*q^167 + 12*q^169 + -24*q^170 + -2*q^171 + -2*q^172 + 6*q^173 + -24*q^174 + -12*q^176 + 24*q^177 + 8*q^178 + 20*q^179 + -8*q^180 + 10*q^181 + -4*q^183 + -4*q^186 + -9*q^187 + 8*q^188 + -16*q^190 + -16*q^191 + 16*q^192 + 3*q^193 + -14*q^194 + -40*q^195 + -14*q^196 + 2*q^197 + -6*q^198 + 14*q^199 + ... ------------------------------------------------------- 43B (new) , dim = 2 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = - discriminant = 2^3 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 7 Torsion Bound = 7 |L(1)/Omega| = 2/7 Sha Bound = 2*7 ANALYTIC INVARIANTS: Omega+ = 2.0010226476244111036 + -0.15663436276163079176e-13i Omega- = 7.2792812035685855105 + -0.16272703740131209145e-12i L(1) = 0.57172075646411745818 HECKE EIGENFORM: a^2-2 = 0, f(q) = q + a*q^2 + -a*q^3 + (-a+2)*q^5 + -2*q^6 + (a-2)*q^7 + -2*a*q^8 + -1*q^9 + (2*a-2)*q^10 + (2*a-1)*q^11 + (2*a+1)*q^13 + (-2*a+2)*q^14 + (-2*a+2)*q^15 + -4*q^16 + (2*a+5)*q^17 + -a*q^18 + (-2*a-2)*q^19 + (2*a-2)*q^21 + (-a+4)*q^22 + (-4*a+1)*q^23 + 4*q^24 + (-4*a+1)*q^25 + (a+4)*q^26 + 4*a*q^27 + 3*a*q^29 + (2*a-4)*q^30 + -3*q^31 + (a-4)*q^33 + (5*a+4)*q^34 + (4*a-6)*q^35 + -6*a*q^37 + (-2*a-4)*q^38 + (-a-4)*q^39 + (-4*a+4)*q^40 + (-2*a-1)*q^41 + (-2*a+4)*q^42 + 1*q^43 + (a-2)*q^45 + (a-8)*q^46 + 6*q^47 + 4*a*q^48 + (-4*a-1)*q^49 + (a-8)*q^50 + (-5*a-4)*q^51 + (-2*a+11)*q^53 + 8*q^54 + (5*a-6)*q^55 + (4*a-4)*q^56 + (2*a+4)*q^57 + 6*q^58 + (2*a-2)*q^59 + (3*a+4)*q^61 + -3*a*q^62 + (-a+2)*q^63 + 8*q^64 + (3*a-2)*q^65 + (-4*a+2)*q^66 + (6*a+1)*q^67 + (-a+8)*q^69 + (-6*a+8)*q^70 + (-2*a-6)*q^71 + 2*a*q^72 + (3*a-12)*q^73 + -12*q^74 + (-a+8)*q^75 + (-5*a+6)*q^77 + (-4*a-2)*q^78 + (-2*a+2)*q^79 + (4*a-8)*q^80 + -5*q^81 + (-a-4)*q^82 + (4*a+9)*q^83 + (-a+6)*q^85 + a*q^86 + -6*q^87 + (2*a-8)*q^88 + (-3*a-6)*q^89 + (-2*a+2)*q^90 + (-3*a+2)*q^91 + 3*a*q^93 + 6*a*q^94 + -2*a*q^95 + (-2*a-1)*q^97 + (-a-8)*q^98 + (-2*a+1)*q^99 + (-2*a+3)*q^101 + (-4*a-10)*q^102 + (6*a+9)*q^103 + (-2*a-8)*q^104 + (6*a-8)*q^105 + (11*a-4)*q^106 + (-4*a-6)*q^107 + (12*a-3)*q^109 + (-6*a+10)*q^110 + 12*q^111 + (-4*a+8)*q^112 + (2*a-4)*q^113 + (4*a+4)*q^114 + (-9*a+10)*q^115 + (-2*a-1)*q^117 + (-2*a+4)*q^118 + (a-6)*q^119 + (-4*a+8)*q^120 + (-4*a-2)*q^121 + (4*a+6)*q^122 + (a+4)*q^123 + -4*a*q^125 + (2*a-2)*q^126 + (-2*a+1)*q^127 + 8*a*q^128 + -a*q^129 + (-2*a+6)*q^130 + (-4*a+4)*q^131 + 2*a*q^133 + (a+12)*q^134 + (8*a-8)*q^135 + (-10*a-8)*q^136 + (6*a-6)*q^137 + (8*a-2)*q^138 + (-6*a-3)*q^139 + -6*a*q^141 + (-6*a-4)*q^142 + 7*q^143 + 4*q^144 + (6*a-6)*q^145 + (-12*a+6)*q^146 + (a+8)*q^147 + -6*a*q^149 + (8*a-2)*q^150 + (-3*a+14)*q^151 + (4*a+8)*q^152 + (-2*a-5)*q^153 + (6*a-10)*q^154 + (3*a-6)*q^155 + -10*q^157 + (2*a-4)*q^158 + (-11*a+4)*q^159 + (9*a-10)*q^161 + -5*a*q^162 + (-3*a-16)*q^163 + (6*a-10)*q^165 + (9*a+8)*q^166 + (8*a-3)*q^167 + (4*a-8)*q^168 + (4*a-4)*q^169 + (6*a-2)*q^170 + (2*a+2)*q^171 + (-4*a+18)*q^173 + -6*a*q^174 + (9*a-10)*q^175 + (-8*a+4)*q^176 + (2*a-4)*q^177 + (-6*a-6)*q^178 + (-a-6)*q^179 + (-8*a-4)*q^181 + (2*a-6)*q^182 + (-4*a-6)*q^183 + (-2*a+16)*q^184 + (-12*a+12)*q^185 + 6*q^186 + (8*a+3)*q^187 + (-8*a+8)*q^189 + -4*q^190 + (10*a+8)*q^191 + -8*a*q^192 + (-12*a-1)*q^193 + (-a-4)*q^194 + (2*a-6)*q^195 + 10*a*q^197 + (a-4)*q^198 + (-4*a+2)*q^199 + (-2*a+16)*q^200 + ... ------------------------------------------------------- Gamma_0(44) Weight 2 ------------------------------------------------------- J_0(44), dim = 4 ------------------------------------------------------- 44A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 2.4139388627239761447 + -0.27237226084048045666e-13i Omega- = 0.10690031880778565423e-13 + -3.0540697209358646069i L(1) = 0.80464628757465871489 w1 = -1.2069694313619934173 + 1.5270348604679459221i w2 = 1.2069694313619827273 + 1.5270348604679186848i c4 = -128.00000000000462565 + 0.19861601802058593025e-11i c6 = 1664.0000000000109575 + -0.23787120809699730358e-8i j = 744.72727272731308838 + 0.11918365403142769722e-8i HECKE EIGENFORM: f(q) = q + 1*q^3 + -3*q^5 + 2*q^7 + -2*q^9 + -1*q^11 + -4*q^13 + -3*q^15 + 6*q^17 + 8*q^19 + 2*q^21 + -3*q^23 + 4*q^25 + -5*q^27 + 5*q^31 + -1*q^33 + -6*q^35 + -1*q^37 + -4*q^39 + -10*q^43 + 6*q^45 + -3*q^49 + 6*q^51 + -6*q^53 + 3*q^55 + 8*q^57 + 3*q^59 + -4*q^61 + -4*q^63 + 12*q^65 + -1*q^67 + -3*q^69 + 15*q^71 + -4*q^73 + 4*q^75 + -2*q^77 + 2*q^79 + 1*q^81 + 6*q^83 + -18*q^85 + -9*q^89 + -8*q^91 + 5*q^93 + -24*q^95 + -7*q^97 + 2*q^99 + 18*q^101 + 8*q^103 + -6*q^105 + 6*q^107 + 2*q^109 + -1*q^111 + -15*q^113 + 9*q^115 + 8*q^117 + 12*q^119 + 1*q^121 + 3*q^125 + -16*q^127 + -10*q^129 + -6*q^131 + 16*q^133 + 15*q^135 + 9*q^137 + 14*q^139 + 4*q^143 + -3*q^147 + 6*q^149 + -10*q^151 + -12*q^153 + -15*q^155 + 5*q^157 + -6*q^159 + -6*q^161 + -4*q^163 + 3*q^165 + -12*q^167 + 3*q^169 + -16*q^171 + 18*q^173 + 8*q^175 + 3*q^177 + -9*q^179 + -13*q^181 + -4*q^183 + 3*q^185 + -6*q^187 + -10*q^189 + -21*q^191 + 20*q^193 + 12*q^195 + 6*q^197 + 8*q^199 + ... ------------------------------------------------------- 44B (old = 11A), dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ------------------------------------------------------- Gamma_0(45) Weight 2 ------------------------------------------------------- J_0(45), dim = 3 ------------------------------------------------------- 45A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 2 Torsion Bound = 2^2 |L(1)/Omega| = 1/2 Sha Bound = 2^3 ANALYTIC INVARIANTS: Omega+ = 1.843181753279314291 + -0.67157963678560778001e-13i Omega- = 0.63466824256547273178e-13 + -3.2345541740741462519i L(1) = 0.92159087663965714552 w1 = 0.92159087663962541211 + 1.617277087037039547i w2 = 1.843181753279314291 + -0.67157963678560778001e-13i c4 = 9.000000000172382152 + 0.38832523329697040126e-10i c6 = 4346.9999997705467652 + 0.21543359707285154956e-9i j = -0.6666666667753570354e-1 + -0.8563701148922397039e-12i HECKE EIGENFORM: f(q) = q + 1*q^2 + -1*q^4 + -1*q^5 + -3*q^8 + -1*q^10 + 4*q^11 + -2*q^13 + -1*q^16 + -2*q^17 + 4*q^19 + 1*q^20 + 4*q^22 + 1*q^25 + -2*q^26 + 2*q^29 + 5*q^32 + -2*q^34 + -10*q^37 + 4*q^38 + 3*q^40 + -10*q^41 + 4*q^43 + -4*q^44 + -8*q^47 + -7*q^49 + 1*q^50 + 2*q^52 + 10*q^53 + -4*q^55 + 2*q^58 + 4*q^59 + -2*q^61 + 7*q^64 + 2*q^65 + 12*q^67 + 2*q^68 + 8*q^71 + 10*q^73 + -10*q^74 + -4*q^76 + 1*q^80 + -10*q^82 + -12*q^83 + 2*q^85 + 4*q^86 + -12*q^88 + 6*q^89 + -8*q^94 + -4*q^95 + 2*q^97 + -7*q^98 + -1*q^100 + -6*q^101 + -16*q^103 + 6*q^104 + 10*q^106 + 12*q^107 + 14*q^109 + -4*q^110 + -2*q^113 + -2*q^116 + 4*q^118 + 5*q^121 + -2*q^122 + -1*q^125 + -8*q^127 + -3*q^128 + 2*q^130 + 12*q^131 + 12*q^134 + 6*q^136 + 6*q^137 + -4*q^139 + 8*q^142 + -8*q^143 + -2*q^145 + 10*q^146 + 10*q^148 + -22*q^149 + -8*q^151 + -12*q^152 + 14*q^157 + -5*q^160 + -4*q^163 + 10*q^164 + -12*q^166 + -9*q^169 + 2*q^170 + -4*q^172 + 18*q^173 + -4*q^176 + 6*q^178 + -20*q^179 + -10*q^181 + 10*q^185 + -8*q^187 + 8*q^188 + -4*q^190 + -16*q^191 + 2*q^193 + 2*q^194 + 7*q^196 + -6*q^197 + -8*q^199 + -3*q^200 + ... ------------------------------------------------------- 45B (old = 15A), dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ------------------------------------------------------- Gamma_0(46) Weight 2 ------------------------------------------------------- J_0(46), dim = 5 ------------------------------------------------------- 46A (new) , dim = 1 CONGRUENCES: Modular Degree = 5 Ker(ModPolar) = Z/5 + Z/5 = B(Z/5 + Z/5) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 2 Torsion Bound = 2 |L(1)/Omega| = 1/2 Sha Bound = 2 ANALYTIC INVARIANTS: Omega+ = 1.3218082226480421038 + 0.21868456344929778986e-12i Omega- = 0.32680346263286859375e-12 + 3.6368235333081729652i L(1) = 0.66090411132402105188 w1 = 0.66090411132385765015 + -1.8184117666539771403i w2 = -1.3218082226480421038 + -0.21868456344929778986e-12i c4 = 488.99999999983443349 + -0.37110734207082758289e-9i c6 = 12554.999999992367085 + -0.10228037924480642808e-7i j = -4964.766007137001296 + 0.1244925904468536394e-7i HECKE EIGENFORM: f(q) = q + -1*q^2 + 1*q^4 + 4*q^5 + -4*q^7 + -1*q^8 + -3*q^9 + -4*q^10 + 2*q^11 + -2*q^13 + 4*q^14 + 1*q^16 + -2*q^17 + 3*q^18 + -2*q^19 + 4*q^20 + -2*q^22 + 1*q^23 + 11*q^25 + 2*q^26 + -4*q^28 + 2*q^29 + -1*q^32 + 2*q^34 + -16*q^35 + -3*q^36 + -4*q^37 + 2*q^38 + -4*q^40 + 6*q^41 + 10*q^43 + 2*q^44 + -12*q^45 + -1*q^46 + 9*q^49 + -11*q^50 + -2*q^52 + -4*q^53 + 8*q^55 + 4*q^56 + -2*q^58 + 12*q^59 + -8*q^61 + 12*q^63 + 1*q^64 + -8*q^65 + -10*q^67 + -2*q^68 + 16*q^70 + 3*q^72 + 6*q^73 + 4*q^74 + -2*q^76 + -8*q^77 + -12*q^79 + 4*q^80 + 9*q^81 + -6*q^82 + 14*q^83 + -8*q^85 + -10*q^86 + -2*q^88 + -6*q^89 + 12*q^90 + 8*q^91 + 1*q^92 + -8*q^95 + 6*q^97 + -9*q^98 + -6*q^99 + 11*q^100 + -10*q^101 + -8*q^103 + 2*q^104 + 4*q^106 + -10*q^107 + -8*q^110 + -4*q^112 + -14*q^113 + 4*q^115 + 2*q^116 + 6*q^117 + -12*q^118 + 8*q^119 + -7*q^121 + 8*q^122 + 24*q^125 + -12*q^126 + 16*q^127 + -1*q^128 + 8*q^130 + 12*q^131 + 8*q^133 + 10*q^134 + 2*q^136 + 6*q^137 + -4*q^139 + -16*q^140 + -4*q^143 + -3*q^144 + 8*q^145 + -6*q^146 + -4*q^148 + -4*q^149 + -8*q^151 + 2*q^152 + 6*q^153 + 8*q^154 + 12*q^157 + 12*q^158 + -4*q^160 + -4*q^161 + -9*q^162 + -8*q^163 + 6*q^164 + -14*q^166 + 16*q^167 + -9*q^169 + 8*q^170 + 6*q^171 + 10*q^172 + -6*q^173 + -44*q^175 + 2*q^176 + 6*q^178 + -16*q^179 + -12*q^180 + -24*q^181 + -8*q^182 + -1*q^184 + -16*q^185 + -4*q^187 + 8*q^190 + 20*q^191 + 26*q^193 + -6*q^194 + 9*q^196 + 18*q^197 + 6*q^198 + -4*q^199 + -11*q^200 + ... ------------------------------------------------------- 46B (old = 23A), dim = 2 CONGRUENCES: Modular Degree = 5 Ker(ModPolar) = Z/5 + Z/5 = A(Z/5 + Z/5) ------------------------------------------------------- Gamma_0(47) Weight 2 ------------------------------------------------------- J_0(47), dim = 4 ------------------------------------------------------- 47A (new) , dim = 4 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 19*103 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 23 Torsion Bound = 23 |L(1)/Omega| = 1/23 Sha Bound = 23 ANALYTIC INVARIANTS: Omega+ = 10.221061625636338339 + -0.5130408686162000692e-12i Omega- = 22.557493156153663639 + -0.38344457575559500693e-11i L(1) = 0.44439398372331905821 HECKE EIGENFORM: a^4-a^3-5*a^2+5*a-1 = 0, f(q) = q + a*q^2 + (a^3-a^2-6*a+4)*q^3 + (a^2-2)*q^4 + (-4*a^3+2*a^2+20*a-10)*q^5 + (-a^2-a+1)*q^6 + (3*a^3-a^2-16*a+7)*q^7 + (a^3-4*a)*q^8 + (3*a^3-a^2-14*a+6)*q^9 + (-2*a^3+10*a-4)*q^10 + (2*a^3-2*a^2-10*a+6)*q^11 + (-3*a^3+a^2+13*a-8)*q^12 + (-4*a^3+2*a^2+22*a-8)*q^13 + (2*a^3-a^2-8*a+3)*q^14 + (-4*a^3+4*a^2+22*a-16)*q^15 + (a^3-a^2-5*a+5)*q^16 + (a^3+a^2-6*a)*q^17 + (2*a^3+a^2-9*a+3)*q^18 + (-2*a^3+10*a-2)*q^19 + (6*a^3-4*a^2-34*a+18)*q^20 + (2*a^3-2*a^2-12*a+9)*q^21 + (-4*a+2)*q^22 + (-2*a^3+12*a-4)*q^23 + (-2*a^3+9*a-5)*q^24 + (4*a^3-4*a^2-20*a+19)*q^25 + (-2*a^3+2*a^2+12*a-4)*q^26 + (-2*a^3+10*a-5)*q^27 + (-5*a^3+4*a^2+25*a-12)*q^28 + (-2*a^3+2*a^2+10*a-10)*q^29 + (2*a^2+4*a-4)*q^30 + (4*a^3-2*a^2-22*a+8)*q^31 + (-2*a^3+8*a+1)*q^32 + (4*a^3-2*a^2-18*a+12)*q^33 + (2*a^3-a^2-5*a+1)*q^34 + (2*a^2-2*a-10)*q^35 + (-3*a^3+3*a^2+21*a-10)*q^36 + (3*a^3-a^2-14*a+8)*q^37 + (-2*a^3+8*a-2)*q^38 + (-2*a^3+8*a-6)*q^39 + (6*a^3-4*a^2-32*a+14)*q^40 + (-2*a+2)*q^41 + (-2*a^2-a+2)*q^42 + (-2*a^3+2*a^2+14*a-8)*q^43 + (-4*a^3+22*a-12)*q^44 + (-2*a-8)*q^45 + (-2*a^3+2*a^2+6*a-2)*q^46 + 1*q^47 + (4*a^3-3*a^2-21*a+14)*q^48 + (-3*a^3+a^2+14*a-5)*q^49 + (-a+4)*q^50 + (-3*a^3+a^2+12*a-7)*q^51 + (8*a^3-2*a^2-38*a+14)*q^52 + (5*a^3-3*a^2-30*a+13)*q^53 + (-2*a^3+5*a-2)*q^54 + (-4*a^3+4*a^2+24*a-20)*q^55 + (-5*a^3+2*a^2+29*a-11)*q^56 + (2*a^3-8*a+4)*q^57 + -2*q^58 + (7*a^3-a^2-36*a+11)*q^59 + (10*a^3-4*a^2-48*a+32)*q^60 + (-7*a^3+5*a^2+38*a-23)*q^61 + (2*a^3-2*a^2-12*a+4)*q^62 + (-2*a^3+14*a+1)*q^63 + (-4*a^3+21*a-12)*q^64 + (-8*a^3+40*a-4)*q^65 + (2*a^3+2*a^2-8*a+4)*q^66 + (-12*a^3+6*a^2+60*a-26)*q^67 + (-a^3+3*a^2+3*a+2)*q^68 + (2*a-2)*q^69 + (2*a^3-2*a^2-10*a)*q^70 + (7*a^3-3*a^2-34*a+12)*q^71 + (-4*a^3+4*a^2+23*a-9)*q^72 + (-2*a^2-4*a+12)*q^73 + (2*a^3+a^2-7*a+3)*q^74 + (15*a^3-11*a^2-78*a+52)*q^75 + (2*a^3-2*a^2-12*a+2)*q^76 + (2*a^3-4*a^2-8*a+10)*q^77 + (-2*a^3-2*a^2+4*a-2)*q^78 + (7*a^3-3*a^2-34*a+20)*q^79 + (-10*a^3+6*a^2+52*a-30)*q^80 + (-10*a^3+6*a^2+52*a-26)*q^81 + (-2*a^2+2*a)*q^82 + (8*a^3-4*a^2-40*a+24)*q^83 + (-6*a^3+3*a^2+26*a-18)*q^84 + (8*a^3-4*a^2-46*a+20)*q^85 + (4*a^2+2*a-2)*q^86 + (-8*a^3+6*a^2+42*a-28)*q^87 + (-4*a^3+2*a^2+16*a-8)*q^88 + (5*a^3+a^2-26*a+1)*q^89 + (-2*a^2-8*a)*q^90 + (10*a^3-2*a^2-50*a+10)*q^91 + (4*a^3-4*a^2-16*a+6)*q^92 + (2*a^3-8*a+6)*q^93 + a*q^94 + (-8*a^3+4*a^2+44*a-16)*q^95 + (5*a^3-a^2-24*a+14)*q^96 + (-9*a^3+7*a^2+46*a-21)*q^97 + (-2*a^3-a^2+10*a-3)*q^98 + (-2*a^2-6*a+8)*q^99 + (-8*a^3+7*a^2+44*a-38)*q^100 + (-7*a^3+a^2+38*a-16)*q^101 + (-2*a^3-3*a^2+8*a-3)*q^102 + (-7*a^3+3*a^2+34*a-20)*q^103 + (10*a^3-2*a^2-50*a+16)*q^104 + (-12*a^3+10*a^2+64*a-42)*q^105 + (2*a^3-5*a^2-12*a+5)*q^106 + (-2*a^3-2*a^2+12*a+6)*q^107 + (2*a^3-5*a^2-12*a+8)*q^108 + (12*a^3-8*a^2-58*a+32)*q^109 + (4*a^2-4)*q^110 + (3*a^3-5*a^2-20*a+15)*q^111 + (7*a^3-4*a^2-36*a+19)*q^112 + (10*a^3-8*a^2-54*a+32)*q^113 + (2*a^3+2*a^2-6*a+2)*q^114 + (-4*a^3+24*a-4)*q^115 + (4*a^3-4*a^2-22*a+20)*q^116 + (10*a^3-48*a+10)*q^117 + (6*a^3-a^2-24*a+7)*q^118 + (-8*a^3+6*a^2+38*a-15)*q^119 + (6*a^3-2*a^2-26*a+18)*q^120 + (4*a^3-24*a+5)*q^121 + (-2*a^3+3*a^2+12*a-7)*q^122 + (2*a^3-10*a+6)*q^123 + (-8*a^3+2*a^2+38*a-14)*q^124 + (-16*a^3+12*a^2+88*a-60)*q^125 + (-2*a^3+4*a^2+11*a-2)*q^126 + (2*a^3-4*a^2-16*a+20)*q^127 + (a^2-8*a-6)*q^128 + (-6*a^3+26*a-16)*q^129 + (-8*a^3+36*a-8)*q^130 + (-7*a^3+a^2+36*a-3)*q^131 + (-4*a^3+6*a^2+30*a-22)*q^132 + (8*a^3-4*a^2-42*a+14)*q^133 + (-6*a^3+34*a-12)*q^134 + (4*a^3-2*a^2-16*a+14)*q^135 + (-2*a^3+17*a-3)*q^136 + (2*a^3-6*a+10)*q^137 + (2*a^2-2*a)*q^138 + (-8*a^3+6*a^2+34*a-30)*q^139 + (-4*a^2-6*a+22)*q^140 + (a^3-a^2-6*a+4)*q^141 + (4*a^3+a^2-23*a+7)*q^142 + (-4*a-4)*q^143 + (6*a^3-3*a^2-31*a+16)*q^144 + (20*a^3-12*a^2-104*a+60)*q^145 + (-2*a^3-4*a^2+12*a)*q^146 + (2*a^2+2*a-3)*q^147 + (-3*a^3+5*a^2+21*a-14)*q^148 + (9*a^3-7*a^2-50*a+28)*q^149 + (4*a^3-3*a^2-23*a+15)*q^150 + (-12*a^3+6*a^2+58*a-28)*q^151 + (4*a^3-2*a^2-24*a+6)*q^152 + (-5*a^3+3*a^2+34*a-13)*q^153 + (-2*a^3+2*a^2+2)*q^154 + (8*a^3-40*a+4)*q^155 + (-6*a^2-8*a+10)*q^156 + (5*a^3-3*a^2-26*a+13)*q^157 + (4*a^3+a^2-15*a+7)*q^158 + (6*a^3-26*a+17)*q^159 + (-16*a^3+10*a^2+84*a-38)*q^160 + (6*a^3-4*a^2-26*a+6)*q^161 + (-4*a^3+2*a^2+24*a-10)*q^162 + (-4*a^3+4*a^2+22*a-14)*q^163 + (-2*a^3+2*a^2+4*a-4)*q^164 + (-16*a^3+8*a^2+80*a-52)*q^165 + (4*a^3-16*a+8)*q^166 + (4*a^3-2*a^2-24*a+12)*q^167 + (-3*a^3+14*a-10)*q^168 + (-20*a^3+8*a^2+108*a-41)*q^169 + (4*a^3-6*a^2-20*a+8)*q^170 + (6*a^3-4*a^2-36*a+12)*q^171 + (8*a^3-2*a^2-30*a+16)*q^172 + (-11*a^3+5*a^2+54*a-35)*q^173 + (-2*a^3+2*a^2+12*a-8)*q^174 + (25*a^3-15*a^2-128*a+69)*q^175 + (6*a^3-4*a^2-32*a+20)*q^176 + (-2*a^3-2*a^2+4*a+1)*q^177 + (6*a^3-a^2-24*a+5)*q^178 + (-8*a^3+4*a^2+48*a-14)*q^179 + (-2*a^3-8*a^2+4*a+16)*q^180 + (2*a^2-2*a-14)*q^181 + (8*a^3-40*a+10)*q^182 + (-14*a^3+8*a^2+70*a-47)*q^183 + (4*a^3-26*a+8)*q^184 + (-8*a^3+4*a^2+38*a-28)*q^185 + (2*a^3+2*a^2-4*a+2)*q^186 + (-4*a^3-2*a^2+26*a-12)*q^187 + (a^2-2)*q^188 + (-a^3-a^2+6*a-7)*q^189 + (-4*a^3+4*a^2+24*a-8)*q^190 + (12*a^3-8*a^2-64*a+40)*q^191 + (-4*a^3+7*a^2+31*a-23)*q^192 + (2*a^3+2*a^2-8*a+8)*q^193 + (-2*a^3+a^2+24*a-9)*q^194 + (12*a^3-4*a^2-56*a+32)*q^195 + (3*a^3-2*a^2-21*a+8)*q^196 + (12*a^3-4*a^2-68*a+22)*q^197 + (-2*a^3-6*a^2+8*a)*q^198 + (14*a^3-10*a^2-74*a+42)*q^199 + (-a^3+4*a^2+4*a-16)*q^200 + ... ------------------------------------------------------- Gamma_0(48) Weight 2 ------------------------------------------------------- J_0(48), dim = 3 ------------------------------------------------------- 48A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2 Torsion Bound = 2^3 |L(1)/Omega| = 1/2^2 Sha Bound = 2^4 ANALYTIC INVARIANTS: Omega+ = 1.6857503548126045883 + -0.99125282273795768619e-41i Omega- = 2.1565156474997666435i L(1) = 0.42143758870315114708 w1 = 2.1565156474997666435i w2 = 1.6857503548126045883 + -0.99125282273795768619e-41i c4 = 207.99999999996910483 + 0.418106793594213999e-38i c6 = 2240.0000000149783626 + 0.10010075317058168738e-36i j = 3905.7777778458011906 + 0.14310321664900083096e-36i HECKE EIGENFORM: f(q) = q + 1*q^3 + -2*q^5 + 1*q^9 + -4*q^11 + -2*q^13 + -2*q^15 + 2*q^17 + 4*q^19 + 8*q^23 + -1*q^25 + 1*q^27 + 6*q^29 + -8*q^31 + -4*q^33 + 6*q^37 + -2*q^39 + -6*q^41 + -4*q^43 + -2*q^45 + -7*q^49 + 2*q^51 + -2*q^53 + 8*q^55 + 4*q^57 + -4*q^59 + -2*q^61 + 4*q^65 + 4*q^67 + 8*q^69 + -8*q^71 + 10*q^73 + -1*q^75 + 8*q^79 + 1*q^81 + 4*q^83 + -4*q^85 + 6*q^87 + -6*q^89 + -8*q^93 + -8*q^95 + 2*q^97 + -4*q^99 + -18*q^101 + -16*q^103 + 12*q^107 + -2*q^109 + 6*q^111 + 18*q^113 + -16*q^115 + -2*q^117 + 5*q^121 + -6*q^123 + 12*q^125 + 8*q^127 + -4*q^129 + 4*q^131 + -2*q^135 + -6*q^137 + 12*q^139 + 8*q^143 + -12*q^145 + -7*q^147 + 14*q^149 + 16*q^151 + 2*q^153 + 16*q^155 + -2*q^157 + -2*q^159 + -12*q^163 + 8*q^165 + -24*q^167 + -9*q^169 + 4*q^171 + 6*q^173 + -4*q^177 + -12*q^179 + 6*q^181 + -2*q^183 + -12*q^185 + -8*q^187 + 2*q^193 + 4*q^195 + -18*q^197 + -16*q^199 + ... ------------------------------------------------------- 48B (old = 24A), dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ------------------------------------------------------- Gamma_0(49) Weight 2 ------------------------------------------------------- J_0(49), dim = 1 ------------------------------------------------------- 49A (new) , dim = 1 CONGRUENCES: Modular Degree = 1 Ker(ModPolar) = {0} ARITHMETIC INVARIANTS: W_q = - discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 2 Torsion Bound = 2 |L(1)/Omega| = 1/2 Sha Bound = 2 ANALYTIC INVARIANTS: Omega+ = 1.9333117056167290171 + 0.28774604696549251387e-12i Omega- = 0.32927673660477893476e-12 + -5.1150619798331913969i L(1) = 0.96665585280836450853 w1 = -0.9666558528085291469 + 2.5575309899164518254i w2 = 1.9333117056167290171 + 0.28774604696549251387e-12i c4 = 105.00000000003379759 + -0.67106840300624147883e-10i c6 = 1322.9999999983997019 + -0.10807238675668079684e-8i j = -3375.0000000337360249 + 0.282649340465540423e-8i HECKE EIGENFORM: f(q) = q + 1*q^2 + -1*q^4 + -3*q^8 + -3*q^9 + 4*q^11 + -1*q^16 + -3*q^18 + 4*q^22 + 8*q^23 + -5*q^25 + 2*q^29 + 5*q^32 + 3*q^36 + -6*q^37 + -12*q^43 + -4*q^44 + 8*q^46 + -5*q^50 + -10*q^53 + 2*q^58 + 7*q^64 + 4*q^67 + 16*q^71 + 9*q^72 + -6*q^74 + 8*q^79 + 9*q^81 + -12*q^86 + -12*q^88 + -8*q^92 + -12*q^99 + 5*q^100 + -10*q^106 + -20*q^107 + 18*q^109 + 2*q^113 + -2*q^116 + 5*q^121 + 16*q^127 + -3*q^128 + 4*q^134 + -10*q^137 + 16*q^142 + 3*q^144 + 6*q^148 + 22*q^149 + -24*q^151 + 8*q^158 + 9*q^162 + -20*q^163 + -13*q^169 + 12*q^172 + -4*q^176 + 4*q^179 + -24*q^184 + 8*q^191 + 18*q^193 + -26*q^197 + -12*q^198 + 15*q^200 + ... ------------------------------------------------------- Gamma_0(50) Weight 2 ------------------------------------------------------- J_0(50), dim = 2 ------------------------------------------------------- 50A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 2.1394949442871262789 + 0.48260832932000089625e-12i Omega- = 0.34154978527787931749e-11 + 3.993933476564393161i L(1) = 0.71316498142904209298 w1 = 1.0697474721418553905 + -1.9969667382819552763i w2 = -2.1394949442871262789 + -0.48260832932000089625e-12i c4 = 24.999999999799961965 + -0.32749484676594779916e-9i c6 = 1474.9999999843674027 + 0.27641116813628485083e-8i j = -12.499999999964648334 + 0.54198406585615746782e-9i HECKE EIGENFORM: f(q) = q + -1*q^2 + 1*q^3 + 1*q^4 + -1*q^6 + 2*q^7 + -1*q^8 + -2*q^9 + -3*q^11 + 1*q^12 + -4*q^13 + -2*q^14 + 1*q^16 + -3*q^17 + 2*q^18 + 5*q^19 + 2*q^21 + 3*q^22 + 6*q^23 + -1*q^24 + 4*q^26 + -5*q^27 + 2*q^28 + 2*q^31 + -1*q^32 + -3*q^33 + 3*q^34 + -2*q^36 + 2*q^37 + -5*q^38 + -4*q^39 + -3*q^41 + -2*q^42 + -4*q^43 + -3*q^44 + -6*q^46 + 12*q^47 + 1*q^48 + -3*q^49 + -3*q^51 + -4*q^52 + 6*q^53 + 5*q^54 + -2*q^56 + 5*q^57 + 2*q^61 + -2*q^62 + -4*q^63 + 1*q^64 + 3*q^66 + -13*q^67 + -3*q^68 + 6*q^69 + 12*q^71 + 2*q^72 + 11*q^73 + -2*q^74 + 5*q^76 + -6*q^77 + 4*q^78 + -10*q^79 + 1*q^81 + 3*q^82 + -9*q^83 + 2*q^84 + 4*q^86 + 3*q^88 + 15*q^89 + -8*q^91 + 6*q^92 + 2*q^93 + -12*q^94 + -1*q^96 + 2*q^97 + 3*q^98 + 6*q^99 + -18*q^101 + 3*q^102 + -4*q^103 + 4*q^104 + -6*q^106 + -3*q^107 + -5*q^108 + -10*q^109 + 2*q^111 + 2*q^112 + -9*q^113 + -5*q^114 + 8*q^117 + -6*q^119 + -2*q^121 + -2*q^122 + -3*q^123 + 2*q^124 + 4*q^126 + 2*q^127 + -1*q^128 + -4*q^129 + 12*q^131 + -3*q^132 + 10*q^133 + 13*q^134 + 3*q^136 + -3*q^137 + -6*q^138 + 5*q^139 + 12*q^141 + -12*q^142 + 12*q^143 + -2*q^144 + -11*q^146 + -3*q^147 + 2*q^148 + 2*q^151 + -5*q^152 + 6*q^153 + 6*q^154 + -4*q^156 + 2*q^157 + 10*q^158 + 6*q^159 + 12*q^161 + -1*q^162 + 11*q^163 + -3*q^164 + 9*q^166 + 12*q^167 + -2*q^168 + 3*q^169 + -10*q^171 + -4*q^172 + -24*q^173 + -3*q^176 + -15*q^178 + -15*q^179 + 2*q^181 + 8*q^182 + 2*q^183 + -6*q^184 + -2*q^186 + 9*q^187 + 12*q^188 + -10*q^189 + -18*q^191 + 1*q^192 + -19*q^193 + -2*q^194 + -3*q^196 + -18*q^197 + -6*q^198 + 20*q^199 + ... ------------------------------------------------------- 50B (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 5 Torsion Bound = 5 |L(1)/Omega| = 1/5 Sha Bound = 5 ANALYTIC INVARIANTS: Omega+ = 4.7840561329431396944 + 0.10791450308671268601e-11i Omega- = 0.15274570751635901036e-11 + 1.7861413502420092651i L(1) = 0.95681122658862793887 w1 = 2.3920280664708061186 + -0.89307067512046506003i w2 = -0.15274570751635901036e-11 + -1.7861413502420092651i c4 = 144.99999999963654503 + 0.5697725481299604929e-9i c6 = -2104.9999999892359423 + -0.89041264193120328264e-8i j = -3810.7812500330699062 + -0.40655809394326913281e-7i HECKE EIGENFORM: f(q) = q + 1*q^2 + -1*q^3 + 1*q^4 + -1*q^6 + -2*q^7 + 1*q^8 + -2*q^9 + -3*q^11 + -1*q^12 + 4*q^13 + -2*q^14 + 1*q^16 + 3*q^17 + -2*q^18 + 5*q^19 + 2*q^21 + -3*q^22 + -6*q^23 + -1*q^24 + 4*q^26 + 5*q^27 + -2*q^28 + 2*q^31 + 1*q^32 + 3*q^33 + 3*q^34 + -2*q^36 + -2*q^37 + 5*q^38 + -4*q^39 + -3*q^41 + 2*q^42 + 4*q^43 + -3*q^44 + -6*q^46 + -12*q^47 + -1*q^48 + -3*q^49 + -3*q^51 + 4*q^52 + -6*q^53 + 5*q^54 + -2*q^56 + -5*q^57 + 2*q^61 + 2*q^62 + 4*q^63 + 1*q^64 + 3*q^66 + 13*q^67 + 3*q^68 + 6*q^69 + 12*q^71 + -2*q^72 + -11*q^73 + -2*q^74 + 5*q^76 + 6*q^77 + -4*q^78 + -10*q^79 + 1*q^81 + -3*q^82 + 9*q^83 + 2*q^84 + 4*q^86 + -3*q^88 + 15*q^89 + -8*q^91 + -6*q^92 + -2*q^93 + -12*q^94 + -1*q^96 + -2*q^97 + -3*q^98 + 6*q^99 + -18*q^101 + -3*q^102 + 4*q^103 + 4*q^104 + -6*q^106 + 3*q^107 + 5*q^108 + -10*q^109 + 2*q^111 + -2*q^112 + 9*q^113 + -5*q^114 + -8*q^117 + -6*q^119 + -2*q^121 + 2*q^122 + 3*q^123 + 2*q^124 + 4*q^126 + -2*q^127 + 1*q^128 + -4*q^129 + 12*q^131 + 3*q^132 + -10*q^133 + 13*q^134 + 3*q^136 + 3*q^137 + 6*q^138 + 5*q^139 + 12*q^141 + 12*q^142 + -12*q^143 + -2*q^144 + -11*q^146 + 3*q^147 + -2*q^148 + 2*q^151 + 5*q^152 + -6*q^153 + 6*q^154 + -4*q^156 + -2*q^157 + -10*q^158 + 6*q^159 + 12*q^161 + 1*q^162 + -11*q^163 + -3*q^164 + 9*q^166 + -12*q^167 + 2*q^168 + 3*q^169 + -10*q^171 + 4*q^172 + 24*q^173 + -3*q^176 + 15*q^178 + -15*q^179 + 2*q^181 + -8*q^182 + -2*q^183 + -6*q^184 + -2*q^186 + -9*q^187 + -12*q^188 + -10*q^189 + -18*q^191 + -1*q^192 + 19*q^193 + -2*q^194 + -3*q^196 + 18*q^197 + 6*q^198 + 20*q^199 + ... ------------------------------------------------------- Gamma_0(51) Weight 2 ------------------------------------------------------- J_0(51), dim = 5 ------------------------------------------------------- 51A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 2.5801770483855944422 + 0.91285341939843292657e-12i Omega- = 0.74207954424703401266e-12 + -3.9053546347514513137i L(1) = 0.86005901612853148072 w1 = 1.2900885241924261813 + 1.9526773173761820836i w2 = 1.2900885241931682609 + -1.9526773173752692301i c4 = -32.000000000543706266 + 0.48802481535949926268e-11i c6 = 871.99999999960948657 + 0.64965233980320135215e-8i j = 71.389978217057511477 + -0.10510974465026924464e-8i HECKE EIGENFORM: f(q) = q + 1*q^3 + -2*q^4 + 3*q^5 + -4*q^7 + 1*q^9 + -3*q^11 + -2*q^12 + -1*q^13 + 3*q^15 + 4*q^16 + -1*q^17 + -1*q^19 + -6*q^20 + -4*q^21 + 9*q^23 + 4*q^25 + 1*q^27 + 8*q^28 + 6*q^29 + 2*q^31 + -3*q^33 + -12*q^35 + -2*q^36 + -4*q^37 + -1*q^39 + -3*q^41 + -7*q^43 + 6*q^44 + 3*q^45 + -6*q^47 + 4*q^48 + 9*q^49 + -1*q^51 + 2*q^52 + -6*q^53 + -9*q^55 + -1*q^57 + 6*q^59 + -6*q^60 + 8*q^61 + -4*q^63 + -8*q^64 + -3*q^65 + -4*q^67 + 2*q^68 + 9*q^69 + 12*q^71 + 2*q^73 + 4*q^75 + 2*q^76 + 12*q^77 + -10*q^79 + 12*q^80 + 1*q^81 + -6*q^83 + 8*q^84 + -3*q^85 + 6*q^87 + 4*q^91 + -18*q^92 + 2*q^93 + -3*q^95 + -16*q^97 + -3*q^99 + -8*q^100 + 5*q^103 + -12*q^105 + 9*q^107 + -2*q^108 + 20*q^109 + -4*q^111 + -16*q^112 + -9*q^113 + 27*q^115 + -12*q^116 + -1*q^117 + 4*q^119 + -2*q^121 + -3*q^123 + -4*q^124 + -3*q^125 + -13*q^127 + -7*q^129 + 3*q^131 + 6*q^132 + 4*q^133 + 3*q^135 + -6*q^137 + 2*q^139 + 24*q^140 + -6*q^141 + 3*q^143 + 4*q^144 + 18*q^145 + 9*q^147 + 8*q^148 + -18*q^149 + 8*q^151 + -1*q^153 + 6*q^155 + 2*q^156 + 11*q^157 + -6*q^159 + -36*q^161 + 2*q^163 + 6*q^164 + -9*q^165 + 21*q^167 + -12*q^169 + -1*q^171 + 14*q^172 + 15*q^173 + -16*q^175 + -12*q^176 + 6*q^177 + -6*q^179 + -6*q^180 + 14*q^181 + 8*q^183 + -12*q^185 + 3*q^187 + 12*q^188 + -4*q^189 + 18*q^191 + -8*q^192 + -22*q^193 + -3*q^195 + -18*q^196 + 3*q^197 + -16*q^199 + ... ------------------------------------------------------- 51B (new) , dim = 2 CONGRUENCES: Modular Degree = 2^3 Ker(ModPolar) = Z/2 + Z/2 + Z/2^2 + Z/2^2 = A(Z/2 + Z/2) + C(Z/2^2 + Z/2^2) ARITHMETIC INVARIANTS: W_q = +- discriminant = 17 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 2 ord((0)-(oo)) = 2^2 Torsion Bound = 2^3 |L(1)/Omega| = 1/2^3 Sha Bound = 2^3 ANALYTIC INVARIANTS: Omega+ = 1.804428599557572703 + -0.21781595956460547839e-11i Omega- = 2.4377710478606711244 + 0.54706633807116629692e-11i L(1) = 0.22555357494469658787 HECKE EIGENFORM: a^2+a-4 = 0, f(q) = q + a*q^2 + -1*q^3 + (-a+2)*q^4 + (-a+1)*q^5 + -a*q^6 + (a-4)*q^8 + 1*q^9 + (2*a-4)*q^10 + (-a-1)*q^11 + (a-2)*q^12 + (a+3)*q^13 + (a-1)*q^15 + -3*a*q^16 + 1*q^17 + a*q^18 + (3*a+3)*q^19 + (-4*a+6)*q^20 + -4*q^22 + (-a-5)*q^23 + (-a+4)*q^24 + -3*a*q^25 + (2*a+4)*q^26 + -1*q^27 + (4*a+2)*q^29 + (-2*a+4)*q^30 + (-2*a-2)*q^31 + (a-4)*q^32 + (a+1)*q^33 + a*q^34 + (-a+2)*q^36 + 2*a*q^37 + 12*q^38 + (-a-3)*q^39 + (6*a-8)*q^40 + (a-1)*q^41 + (-3*a-3)*q^43 + (-2*a+2)*q^44 + (-a+1)*q^45 + (-4*a-4)*q^46 + (2*a-6)*q^47 + 3*a*q^48 + -7*q^49 + (3*a-12)*q^50 + -1*q^51 + 2*q^52 + (-4*a+2)*q^53 + -a*q^54 + (-a+3)*q^55 + (-3*a-3)*q^57 + (-2*a+16)*q^58 + (-2*a+2)*q^59 + (4*a-6)*q^60 + (-2*a+4)*q^61 + -8*q^62 + (a+4)*q^64 + (-a-1)*q^65 + 4*q^66 + 4*q^67 + (-a+2)*q^68 + (a+5)*q^69 + (4*a+4)*q^71 + (a-4)*q^72 + (4*a-2)*q^73 + (-2*a+8)*q^74 + 3*a*q^75 + (6*a-6)*q^76 + (-2*a-4)*q^78 + (6*a+6)*q^79 + (-6*a+12)*q^80 + 1*q^81 + (-2*a+4)*q^82 + (-2*a-6)*q^83 + (-a+1)*q^85 + -12*q^86 + (-4*a-2)*q^87 + 4*a*q^88 + (2*a+4)*q^89 + (2*a-4)*q^90 + (2*a-6)*q^92 + (2*a+2)*q^93 + (-8*a+8)*q^94 + (3*a-9)*q^95 + (-a+4)*q^96 + (-2*a-8)*q^97 + -7*a*q^98 + (-a-1)*q^99 + (-9*a+12)*q^100 + (2*a+16)*q^101 + -a*q^102 + (-3*a+9)*q^103 + (-2*a-8)*q^104 + (6*a-16)*q^106 + (3*a+3)*q^107 + (a-2)*q^108 + (-2*a-12)*q^109 + (4*a-4)*q^110 + -2*a*q^111 + (-a-3)*q^113 + -12*q^114 + (3*a-1)*q^115 + (10*a-12)*q^116 + (a+3)*q^117 + (4*a-8)*q^118 + (-6*a+8)*q^120 + (a-6)*q^121 + (6*a-8)*q^122 + (-a+1)*q^123 + (-4*a+4)*q^124 + (-a+7)*q^125 + (-5*a+7)*q^127 + (a+12)*q^128 + (3*a+3)*q^129 + -4*q^130 + (a+17)*q^131 + (2*a-2)*q^132 + 4*a*q^134 + (a-1)*q^135 + (a-4)*q^136 + (-4*a-10)*q^137 + (4*a+4)*q^138 + (-2*a-6)*q^139 + (-2*a+6)*q^141 + 16*q^142 + (-3*a-7)*q^143 + -3*a*q^144 + (6*a-14)*q^145 + (-6*a+16)*q^146 + 7*q^147 + (6*a-8)*q^148 + (-4*a+2)*q^149 + (-3*a+12)*q^150 + 8*q^151 + -12*a*q^152 + 1*q^153 + (-2*a+6)*q^155 + -2*q^156 + (-3*a-1)*q^157 + 24*q^158 + (4*a-2)*q^159 + (6*a-8)*q^160 + a*q^162 + (2*a-10)*q^163 + (4*a-6)*q^164 + (a-3)*q^165 + (-4*a-8)*q^166 + (-5*a+7)*q^167 + 5*a*q^169 + (2*a-4)*q^170 + (3*a+3)*q^171 + (-6*a+6)*q^172 + (-5*a-11)*q^173 + (2*a-16)*q^174 + 12*q^176 + (2*a-2)*q^177 + (2*a+8)*q^178 + (-2*a-6)*q^179 + (-4*a+6)*q^180 + 6*q^181 + (2*a-4)*q^183 + 16*q^184 + (4*a-8)*q^185 + 8*q^186 + (-a-1)*q^187 + (12*a-20)*q^188 + (-12*a+12)*q^190 + (-2*a-10)*q^191 + (-a-4)*q^192 + (-4*a-18)*q^193 + (-6*a-8)*q^194 + (a+1)*q^195 + (7*a-14)*q^196 + (7*a+9)*q^197 + -4*q^198 + 16*q^199 + (15*a-12)*q^200 + ... ------------------------------------------------------- 51C (old = 17A), dim = 1 CONGRUENCES: Modular Degree = 2^2 Ker(ModPolar) = Z/2^2 + Z/2^2 = B(Z/2^2 + Z/2^2) ------------------------------------------------------- Gamma_0(52) Weight 2 ------------------------------------------------------- J_0(52), dim = 5 ------------------------------------------------------- 52A (new) , dim = 1 CONGRUENCES: Modular Degree = 3 Ker(ModPolar) = Z/3 + Z/3 = C(Z/3 + Z/3) ARITHMETIC INVARIANTS: W_q = -+ discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 2 Torsion Bound = 2 |L(1)/Omega| = 1/2 Sha Bound = 2 ANALYTIC INVARIANTS: Omega+ = 1.690966417291821379 + 0.9529667958010773441e-12i Omega- = 0.95354123294140990805e-12 + -2.8023148362626574491i L(1) = 0.84548320864591068951 w1 = -0.84548320864543391889 + -1.401157418131805208i w2 = -0.84548320864638746013 + 1.4011574181308522412i c4 = -48.000000004027310653 + -0.29720767253575937312e-9i c6 = 8640.0000000064995211 + -0.35681109341584885707e-6i j = 2.556213018390103804 + 0.25823114250569746199e-9i HECKE EIGENFORM: f(q) = q + 2*q^5 + -2*q^7 + -3*q^9 + -2*q^11 + -1*q^13 + 6*q^17 + -6*q^19 + 8*q^23 + -1*q^25 + 2*q^29 + 10*q^31 + -4*q^35 + -6*q^37 + -6*q^41 + 4*q^43 + -6*q^45 + -2*q^47 + -3*q^49 + 6*q^53 + -4*q^55 + -10*q^59 + -2*q^61 + 6*q^63 + -2*q^65 + 10*q^67 + 10*q^71 + 2*q^73 + 4*q^77 + -4*q^79 + 9*q^81 + -6*q^83 + 12*q^85 + -6*q^89 + 2*q^91 + -12*q^95 + 2*q^97 + 6*q^99 + -2*q^101 + -8*q^103 + -16*q^107 + -14*q^109 + 14*q^113 + 16*q^115 + 3*q^117 + -12*q^119 + -7*q^121 + -12*q^125 + -8*q^127 + -16*q^131 + 12*q^133 + 18*q^137 + 16*q^139 + 2*q^143 + 4*q^145 + 18*q^149 + 6*q^151 + -18*q^153 + 20*q^155 + 2*q^157 + -16*q^161 + -10*q^163 + 6*q^167 + 1*q^169 + 18*q^171 + -10*q^173 + 2*q^175 + 12*q^179 + -6*q^181 + -12*q^185 + -12*q^187 + 4*q^191 + 2*q^193 + -6*q^197 + -16*q^199 + ... ------------------------------------------------------- 52B (old = 26A), dim = 1 CONGRUENCES: Modular Degree = 2^2 Ker(ModPolar) = Z/2 + Z/2 + Z/2 + Z/2 = C(Z/2 + Z/2 + Z/2 + Z/2) ------------------------------------------------------- 52C (old = 26B), dim = 1 CONGRUENCES: Modular Degree = 2^2*3 Ker(ModPolar) = Z/2 + Z/2 + Z/2*3 + Z/2*3 = A(Z/3 + Z/3) + B(Z/2 + Z/2 + Z/2 + Z/2) ------------------------------------------------------- Gamma_0(53) Weight 2 ------------------------------------------------------- J_0(53), dim = 4 ------------------------------------------------------- 53A (new) , dim = 1 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = B(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = + discriminant = 1 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 1 Torsion Bound = 1 |L(1)/Omega| = 0 Sha Bound = 0 ANALYTIC INVARIANTS: Omega+ = 4.6876410488565271208 + -0.48168680901967596905e-11i Omega- = 0.21472984590632507544e-11 + -3.0811813402838080833i L(1) = w1 = -2.3438205244293372096 + 1.5405906701443124757i w2 = 2.3438205244271899111 + 1.5405906701394956076i c4 = -15.000000000900455138 + -0.19891484707449980639e-9i c6 = -297.00000000216029806 + -0.27047006883900401884e-8i j = 63.679245293172081097 + 0.13229127777817996054e-8i HECKE EIGENFORM: f(q) = q + -1*q^2 + -3*q^3 + -1*q^4 + 3*q^6 + -4*q^7 + 3*q^8 + 6*q^9 + 3*q^12 + -3*q^13 + 4*q^14 + -1*q^16 + -3*q^17 + -6*q^18 + -5*q^19 + 12*q^21 + 7*q^23 + -9*q^24 + -5*q^25 + 3*q^26 + -9*q^27 + 4*q^28 + -7*q^29 + 4*q^31 + -5*q^32 + 3*q^34 + -6*q^36 + 5*q^37 + 5*q^38 + 9*q^39 + 6*q^41 + -12*q^42 + -2*q^43 + -7*q^46 + -2*q^47 + 3*q^48 + 9*q^49 + 5*q^50 + 9*q^51 + 3*q^52 + -1*q^53 + 9*q^54 + -12*q^56 + 15*q^57 + 7*q^58 + -2*q^59 + -8*q^61 + -4*q^62 + -24*q^63 + 7*q^64 + -12*q^67 + 3*q^68 + -21*q^69 + 1*q^71 + 18*q^72 + -4*q^73 + -5*q^74 + 15*q^75 + 5*q^76 + -9*q^78 + -1*q^79 + 9*q^81 + -6*q^82 + -1*q^83 + -12*q^84 + 2*q^86 + 21*q^87 + -14*q^89 + 12*q^91 + -7*q^92 + -12*q^93 + 2*q^94 + 15*q^96 + 1*q^97 + -9*q^98 + 5*q^100 + -2*q^101 + -9*q^102 + -1*q^103 + -9*q^104 + 1*q^106 + 6*q^107 + 9*q^108 + 16*q^109 + -15*q^111 + 4*q^112 + 15*q^113 + -15*q^114 + 7*q^116 + -18*q^117 + 2*q^118 + 12*q^119 + -11*q^121 + 8*q^122 + -18*q^123 + -4*q^124 + 24*q^126 + 13*q^127 + 3*q^128 + 6*q^129 + -2*q^131 + 20*q^133 + 12*q^134 + -9*q^136 + 12*q^137 + 21*q^138 + -20*q^139 + 6*q^141 + -1*q^142 + -6*q^144 + 4*q^146 + -27*q^147 + -5*q^148 + -5*q^149 + -15*q^150 + -3*q^151 + -15*q^152 + -18*q^153 + -9*q^156 + -4*q^157 + 1*q^158 + 3*q^159 + -28*q^161 + -9*q^162 + -6*q^163 + -6*q^164 + 1*q^166 + 21*q^167 + 36*q^168 + -4*q^169 + -30*q^171 + 2*q^172 + 10*q^173 + -21*q^174 + 20*q^175 + 6*q^177 + 14*q^178 + 11*q^179 + -2*q^181 + -12*q^182 + 24*q^183 + 21*q^184 + 12*q^186 + 2*q^188 + 36*q^189 + -21*q^191 + -21*q^192 + -16*q^193 + -1*q^194 + -9*q^196 + -18*q^197 + 4*q^199 + -15*q^200 + ... ------------------------------------------------------- 53B (new) , dim = 3 CONGRUENCES: Modular Degree = 2 Ker(ModPolar) = Z/2 + Z/2 = A(Z/2 + Z/2) ARITHMETIC INVARIANTS: W_q = - discriminant = 2^2*37 #CompGroup(Fpbar) = ? c_p = ? c_inf = 1 ord((0)-(oo)) = 13 Torsion Bound = 13 |L(1)/Omega| = 2/13 Sha Bound = 2*13 ANALYTIC INVARIANTS: Omega+ = 3.3415343014964929662 + 0.99125939515556958004e-12i Omega- = 0.18093847764884716842e-10 + -11.443904371146073371i L(1) = 0.5140822002302296871 HECKE EIGENFORM: a^3+a^2-3*a-1 = 0, f(q) = q + a*q^2 + (-a^2-a+3)*q^3 + (a^2-2)*q^4 + (a^2-3)*q^5 + -1*q^6 + (a^2-1)*q^7 + (-a^2-a+1)*q^8 + (-3*a^2-2*a+7)*q^9 + (-a^2+1)*q^10 + (a^2+2*a-3)*q^11 + (2*a^2+a-6)*q^12 + 1*q^13 + (-a^2+2*a+1)*q^14 + (3*a^2+2*a-9)*q^15 + (-2*a^2-2*a+3)*q^16 + (2*a-1)*q^17 + (a^2-2*a-3)*q^18 + (a+4)*q^19 + (-a^2-2*a+5)*q^20 + (a^2-3)*q^21 + (a^2+1)*q^22 + (2*a^2-a-4)*q^23 + (-a^2+4)*q^24 + (-2*a^2-2*a+3)*q^25 + a*q^26 + (-4*a^2-a+14)*q^27 + (a^2-2*a+1)*q^28 + (-3*a^2-4*a+4)*q^29 + (-a^2+3)*q^30 + (-a^2+4*a+3)*q^31 + (2*a^2-a-4)*q^32 + (3*a^2+2*a-11)*q^33 + (2*a^2-a)*q^34 + (-2*a+2)*q^35 + (3*a^2+4*a-13)*q^36 + (a^2+6*a-2)*q^37 + (a^2+4*a)*q^38 + (-a^2-a+3)*q^39 + (a^2+2*a-3)*q^40 + (-2*a-4)*q^41 + (-a^2+1)*q^42 + (-3*a^2-6*a+11)*q^43 + (-3*a^2+7)*q^44 + (6*a^2+6*a-20)*q^45 + (-3*a^2+2*a+2)*q^46 + (-2*a^2-4*a)*q^47 + (-3*a^2-a+11)*q^48 + (2*a^2-2*a-7)*q^49 + (-3*a-2)*q^50 + (a^2+a-5)*q^51 + (a^2-2)*q^52 + 1*q^53 + (3*a^2+2*a-4)*q^54 + (-4*a^2-2*a+10)*q^55 + (-a^2-1)*q^56 + (-4*a^2-4*a+11)*q^57 + (-a^2-5*a-3)*q^58 + (4*a^2+2*a-8)*q^59 + (-5*a^2-4*a+17)*q^60 + (3*a^2-2*a-11)*q^61 + (5*a^2-1)*q^62 + (2*a-6)*q^63 + (a^2+6*a-4)*q^64 + (a^2-3)*q^65 + (-a^2-2*a+3)*q^66 + (3*a^2+6*a-3)*q^67 + (-3*a^2+2*a+4)*q^68 + (4*a^2+2*a-11)*q^69 + (-2*a^2+2*a)*q^70 + (-3*a^2-7*a+3)*q^71 + (-a^2+9)*q^72 + (a^2+4*a+1)*q^73 + (5*a^2+a+1)*q^74 + (-3*a^2-a+11)*q^75 + (3*a^2+a-7)*q^76 + (-2*a^2+2*a+4)*q^77 + -1*q^78 + (5*a^2+3*a-13)*q^79 + (3*a^2+4*a-9)*q^80 + (-5*a^2-4*a+22)*q^81 + (-2*a^2-4*a)*q^82 + (3*a+10)*q^83 + (-a^2-2*a+5)*q^84 + (-3*a^2+5)*q^85 + (-3*a^2+2*a-3)*q^86 + (-4*a^2-a+16)*q^87 + (a^2-2*a-5)*q^88 + (-4*a^2+4*a+10)*q^89 + (-2*a+6)*q^90 + (a^2-1)*q^91 + (a^2-5*a+5)*q^92 + (-3*a^2-2*a+5)*q^93 + (-2*a^2-6*a-2)*q^94 + (3*a^2-11)*q^95 + (4*a^2+2*a-11)*q^96 + (5*a^2-12)*q^97 + (-4*a^2-a+2)*q^98 + (8*a^2+2*a-26)*q^99 + (a^2+2*a-6)*q^100 + (a^2+2*a+9)*q^101 + (-2*a+1)*q^102 + (-2*a^2-a+8)*q^103 + (-a^2-a+1)*q^104 + (-2*a^2-2*a+8)*q^105 + a*q^106 + (-3*a^2-2*a+11)*q^107 + (7*a^2+7*a-25)*q^108 + (-4*a-8)*q^109 + (2*a^2-2*a-4)*q^110 + (2*a^2+a-12)*q^111 + (-a^2-3)*q^112 + (3*a^2+2*a-10)*q^113 + (-a-4)*q^114 + (-a^2-4*a+9)*q^115 + (2*a^2+2*a-9)*q^116 + (-3*a^2-2*a+7)*q^117 + (-2*a^2+4*a+4)*q^118 + (-3*a^2+4*a+3)*q^119 + (3*a^2+2*a-11)*q^120 + (-2*a^2-2*a+1)*q^121 + (-5*a^2-2*a+3)*q^122 + (4*a^2+4*a-10)*q^123 + (-3*a^2+6*a-1)*q^124 + (-2*a^2+4*a+6)*q^125 + (2*a^2-6*a)*q^126 + (-5*a^2-3*a+13)*q^127 + (a^2+a+9)*q^128 + (-11*a^2-8*a+39)*q^129 + (-a^2+1)*q^130 + (a^2-7)*q^131 + (-7*a^2-4*a+21)*q^132 + (3*a^2+2*a-3)*q^133 + (3*a^2+6*a+3)*q^134 + (11*a^2+8*a-39)*q^135 + (a^2-3*a-3)*q^136 + (9*a^2+6*a-13)*q^137 + (-2*a^2+a+4)*q^138 + (-3*a^2-8*a+9)*q^139 + (4*a^2-2*a-6)*q^140 + (2*a+4)*q^141 + (-4*a^2-6*a-3)*q^142 + (a^2+2*a-3)*q^143 + (-5*a^2-2*a+25)*q^144 + (5*a^2+6*a-13)*q^145 + (3*a^2+4*a+1)*q^146 + (7*a^2+5*a-19)*q^147 + (-6*a^2+4*a+9)*q^148 + (2*a^2-2*a-5)*q^149 + (2*a^2+2*a-3)*q^150 + (-10*a^2-9*a+22)*q^151 + (-4*a^2-6*a+3)*q^152 + (5*a^2-2*a-13)*q^153 + (4*a^2-2*a-2)*q^154 + (-2*a^2+2*a-4)*q^155 + (2*a^2+a-6)*q^156 + (a^2-4*a+5)*q^157 + (-2*a^2+2*a+5)*q^158 + (-a^2-a+3)*q^159 + (-a^2-4*a+9)*q^160 + (3*a^2-6*a+1)*q^161 + (a^2+7*a-5)*q^162 + (7*a^2+10*a-7)*q^163 + (-2*a^2-2*a+6)*q^164 + (-10*a^2-6*a+32)*q^165 + (3*a^2+10*a)*q^166 + (-7*a^2-a+13)*q^167 + (a^2+2*a-3)*q^168 + -12*q^169 + (3*a^2-4*a-3)*q^170 + (-11*a^2-10*a+25)*q^171 + (11*a^2-25)*q^172 + (-8*a^2-12*a+22)*q^173 + (3*a^2+4*a-4)*q^174 + (-a^2-3)*q^175 + (3*a^2-2*a-13)*q^176 + (8*a^2+4*a-26)*q^177 + (8*a^2-2*a-4)*q^178 + (-6*a^2+a+10)*q^179 + (-14*a^2-6*a+40)*q^180 + (2*a^2+2*a+2)*q^181 + (-a^2+2*a+1)*q^182 + (11*a^2+8*a-31)*q^183 + (4*a-3)*q^184 + (-7*a^2-2*a+11)*q^185 + (a^2-4*a-3)*q^186 + (a^2-2*a+5)*q^187 + -2*q^188 + (3*a^2+6*a-11)*q^189 + (-3*a^2-2*a+3)*q^190 + (-a^2+3*a-3)*q^191 + (4*a^2+3*a-18)*q^192 + (-5*a^2+4*a+19)*q^193 + (-5*a^2+3*a+5)*q^194 + (3*a^2+2*a-9)*q^195 + (-a^2-6*a+10)*q^196 + (2*a^2-6*a-10)*q^197 + (-6*a^2-2*a+8)*q^198 + (3*a^2-4*a-23)*q^199 + (a^2+3*a+5)*q^200 + ... ------------------------------------------------------- Gamma_0(54) Weight 2 ------------------------------------------------------- J_0(54), dim = 4 ------------------------------------------------------- 54A (new) , dim = 1 CONGRUENCES: Modular Degree = 2*3 Ker(ModPolar) = Z/2*3 + Z/2*3 = B(Z/2 + Z/2) + C(Z/3 + Z/3) ARITHMETIC INVARIANTS: W_q = +- discriminant = 1 #CompGroup(Fpbar) = ?? c_p = ?? c_inf = 1 ord((0)-(oo)) = 3 Torsion Bound = 3 |L(1)/Omega| = 1/3 Sha Bound = 3 ANALYTIC INVARIANTS: Omega+ = 2.1047244759626368404 + -0.22416211913948226307e-44i Omega- = -1.7849162019780213849i L(1) = 0.7015748253208789468 w1 = -1.0523622379813184202 + -0.89245810098901069243i w2 = -1.0523622379813184202 + 0.89245810098901069243i c4 = -567.00000001092421705 + 0.27570867024903825679e-11i c6 = -9477.0000005110583053 + -0.99138327750225395165e-8i j = 1157.6249999808747012 + -0.8050131060920818169e-9i HECKE EIGENFORM: f(q) = q + -1*q^2 + 1*q^4 + 3*q^5 + -1*q^7 + -1*q^8 + -3*q^10 + -3*q^11 + -4*q^13 + 1*q^14 + 1*q^16 + 2*q^19 + 3*q^20 + 3*q^22 + -6*q^23 + 4*q^25 + 4*q^26 + -1*q^28 + 6*q^29 + 5*q^31 + -1*q^32 + -3*q^35 + 2*q^37 + -2*q^38 + -3*q^40 + -6*q^41 + -10*q