// Make newform 1155.2.l.e in Magma, downloaded from the LMFDB on 29 March 2024. // To make the character of type GrpDrchElt, type "MakeCharacter_1155_l();" // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_1155_2_l_e();". // This may take a long time! To see verbose output, uncomment the SetVerbose line below. // The default sign is -1. You can change this with the optional parameter "sign". // To make the character of type GrpDrchElt, type "MakeCharacter_1155_l();" function MakeCharacter_1155_l() N := 1155; order := 2; char_gens := [386, 232, 661, 211]; v := [1, 2, 2, 1]; // chi(gens[i]) = zeta^v[i] assert UnitGenerators(DirichletGroup(N)) eq char_gens; F := CyclotomicField(order); chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]); return MinimalBaseRingCharacter(chi); end function; function MakeCharacter_1155_l_Hecke(Kf) return MakeCharacter_1155_l(); end function; // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_1155_2_l_e();". // This may take a long time! To see verbose output, uncomment the SetVerbose line below. // The default sign is -1. You can change this with the optional parameter "sign". function MakeNewformModSym_1155_2_l_e( : sign := -1) R := PolynomialRing(Rationals()); chi := MakeCharacter_1155_l(); // SetVerbose("ModularSymbols", true); Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign))); Vf := Kernel([<2,R![-32, 400, -1340, -876, 10202, -5784, -25191, 19438, 29705, -21856, -20275, 12178, 8561, -3728, -2237, 634, 347, -56, -29, 2, 1]>,<17,R![-18091520, -8692864, 165682064, -93590816, -288310328, 269949872, 118520520, -189126632, 8033804, 50229300, -11041120, -5804480, 1897072, 328436, -146479, -9008, 5899, 96, -121, 0, 1]>],Snew); return Vf; end function;