Rationals part of the special values of the L-functions of level 1

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Instructions

Enter a semicolon-separated list of weights k to obtain a table of rational parts of special values of L-functions attached to level 1 modular forms.


Output format:           HUMAN                MAGMA
   

Definition of the L-ratios

Fix a weight k. Let Sym = CuspSymk(SL2(Z);Z) denote the space of integral cuspidal modular symbols of weight k on SL2(Z) (see Loic Merel's paper in Springer Lecture Notes 1585). Let L(s) be the product of the L-functions attached to the normalized eigenforms of weight k. The image of Sym under the period mapping defines a lattice in Cd, where d is the dimension of Sk(SL2(Z)). Let T be the torus got by quotienting Cd out by this lattice. For j an odd integer between 1 and k-1, the L-ratio listed in our table is 
            L(A,j)*(j-1)!
          -----------------
           (2pi)^(j-1)*Omega
where Omega is the vol(R) of real points in T, with respect to the measure defined by a basis of cusp forms with integer Fourier expansion coefficients. For i an even integer between 1 and k-1, the L-ratio is defined as above, except Omega is the volume of the subgroup of T(C) on which complex conjugation acts as -1.

The scope of this table

I have computed the ratios for weights up to 236, and a few more. Click the "List known levels" button above to see exactly what I've computed.