\\ Pari/GP code for working with modular form 189.4.e.h \\ Dimensions subspaces of M_4(189,chi): [N,k,chi] = [189,4,Mod(109,189)] 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] = [189,4,Mod(109,189)] 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)