MFD Home Search Tips Glossary Credits Email William Stein

Space of Modular Forms

Full modular forms space of level 3, weight 6, and trivial character

DETAILS

Dimensions

Dimension

Cuspidal Subspace

Eisenstein Subspace

New Cuspidal Subspace

New Eisenstein Subspace

Data

Discriminant of Hecke Algebra

Factored Level

[<3,1>]

Order of Character

Newform number 1 of degree 1 (click here for much more data)

Associated Abelian Varieties

Isogeny class of abelian varieties (optimal quotient)

q-Expansion of Newform (coefficients are Hecke eigenvalues)

First n terms: n= 10 ***************************** 100
Download in MAGMA-readable format (right click)

Trace(f) = sum Tr(a_n)*qⁿ

q - 6*q^2 + 9*q^3 + 4*q^4 + 6*q^5 - 54*q^6 - 40*q^7 + 168*q^8 + 81*q^9 - 36*q^10 - 564*q^11 + 36*q^12 + 638*q^13 + 240*q^14 + 54*q^15 - 1136*q^16 + 882*q^17 - 486*q^18 - 556*q^19 + 24*q^20 - 360*q^21 + 3384*q^22 - 840*q^23 + 1512*q^24 - 3089*q^25 - 3828*q^26 + 729*q^27 - 160*q^28 + 4638*q^29 - 324*q^30 + 4400*q^31 + 1440*q^32 - 5076*q^33 - 5292*q^34 - 240*q^35 + 324*q^36 - 2410*q^37 + 3336*q^38 + 5742*q^39 + 1008*q^40 - 6870*q^41 + 2160*q^42 + 9644*q^43 - 2256*q^44 + 486*q^45 + 5040*q^46 - 18672*q^47 - 10224*q^48 - 15207*q^49 + 18534*q^50 + 7938*q^51 + 2552*q^52 + 33750*q^53 - 4374*q^54 - 3384*q^55 - 6720*q^56 - 5004*q^57 - 27828*q^58 - 18084*q^59 + 216*q^60 + 39758*q^61 - 26400*q^62 - 3240*q^63 + 27712*q^64 + 3828*q^65 + 30456*q^66 - 23068*q^67 + 3528*q^68 - 7560*q^69 + 1440*q^70 - 4248*q^71 + 13608*q^72 - 41110*q^73 + 14460*q^74 - 27801*q^75 - 2224*q^76 + 22560*q^77 - 34452*q^78 + 21920*q^79 - 6816*q^80 + 6561*q^81 + 41220*q^82 + 82452*q^83 - 1440*q^84 + 5292*q^85 - 57864*q^86 + 41742*q^87 - 94752*q^88 - 94086*q^89 - 2916*q^90 - 25520*q^91 - 3360*q^92 + 39600*q^93 + 112032*q^94 - 3336*q^95 + 12960*q^96 + 49442*q^97 + 91242*q^98 - 45684*q^99 - 12356*q^100 + O(q^101)