// Make newform 280.2.bj.e in Magma, downloaded from the LMFDB on 28 March 2024. // To make the character of type GrpDrchElt, type "MakeCharacter_280_bj();" // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_280_2_bj_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_280_bj();" function MakeCharacter_280_bj() N := 280; order := 6; char_gens := [71, 141, 57, 241]; v := [3, 3, 6, 5]; // 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_280_bj_Hecke(Kf) return MakeCharacter_280_bj(); end function; // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_280_2_bj_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_280_2_bj_e( : sign := -1) R := PolynomialRing(Rationals()); chi := MakeCharacter_280_bj(); // SetVerbose("ModularSymbols", true); Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign))); Vf := Kernel([<3,R![4096, 21504, 8704, -151872, 11984, 446496, -99516, -947640, 776561, 536664, -764820, -189744, 637314, -269256, -67428, 73188, 2835, -18120, 5528, 492, -494, 0, 48, -12, 1]>,<13,R![81088, -108288, -135600, 196672, 22412, -69028, -424, 9034, 221, -512, -34, 10, 1]>],Snew); return Vf; end function;