\\ Pari/GP code for working with modular form 416.2.a.f \\ Dimensions subspaces of M_2(416,chi): [N,k,chi] = [416,2,Mod(1,416)] mfdim([N,k,chi],4) \\ all space mfdim([N,k,chi],3) \\ Eisenstein mfdim([N,k,chi],1) \\ Cusps mfdim([N,k,chi],0) \\ New \\ Compute space of new eigenforms: [N,k,chi] = [416,2,Mod(1,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf) \\ Coefficient field, relative polynomial: f.mod \\ as an extension of the cyclotomic field Q(t)/Phi \\ select newform: f = lf[1] \\ Warning: the index may be different \\ defining polynomial: f.mod \\ as an extension of the character field \\ q-expansion: mfcoefs(f, 20) \\ embeddings in the coefficient field: mfembed(f) \\ L function, special value at s=1: L = lfunmf(mf,f); lfun(L,1)