// Make newform 392.3.j.e in Magma, downloaded from the LMFDB on 29 March 2024. // To make the character of type GrpDrchElt, type "MakeCharacter_392_j();" // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_392_3_j_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_392_j();" function MakeCharacter_392_j() N := 392; order := 6; char_gens := [295, 197, 297]; v := [6, 3, 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_392_j_Hecke(Kf) return MakeCharacter_392_j(); end function; // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_392_3_j_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_392_3_j_e( : sign := -1) R := PolynomialRing(Rationals()); chi := MakeCharacter_392_j(); // SetVerbose("ModularSymbols", true); Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign))); Vf := Kernel([<3,R![558140625, 0, 9617430375, 0, 151117756444, 0, 241193289949, 0, 291491657033, 0, 109733966258, 0, 27476030709, 0, 4350754377, 0, 504732141, 0, 41993874, 0, 2641713, 0, 118973, 0, 3908, 0, 79, 0, 1]>],Snew); return Vf; end function;