// Make newform 6003.2.a.w in Magma, downloaded from the LMFDB on 29 March 2024. // To make the character of type GrpDrchElt, type "MakeCharacter_6003_a();" // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_6003_2_a_w();". // 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_6003_a();" function MakeCharacter_6003_a() N := 6003; order := 1; char_gens := [668, 3133, 4555]; v := [1, 1, 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_6003_a_Hecke(Kf) return MakeCharacter_6003_a(); end function; // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_6003_2_a_w();". // 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_6003_2_a_w( : sign := -1) R := PolynomialRing(Rationals()); chi := MakeCharacter_6003_a(); // SetVerbose("ModularSymbols", true); Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign))); Vf := Kernel([<2,R![-2304, 20480, 127808, -165728, -1303368, 328920, 5796104, 411998, -14283343, -2648895, 21734883, 4790260, -21761458, -4804662, 14939088, 3059124, -7218058, -1304378, 2489025, 380781, -614174, -76251, 107407, 10288, -12975, -893, 1028, 45, -48, -1, 1]>,<5,R![1081344, -339845120, -1913546240, -1826159104, 7634770432, 16108980480, -3876068544, -30552967296, -9974091536, 27358373152, 15959374456, -14117867344, -10854165502, 4606353530, 4352963400, -998371522, -1138096813, 147178504, 202717929, -14812592, -25041479, 1000846, 2143650, -43372, -124647, 1088, 4692, -12, -103, 0, 1]>],Snew); return Vf; end function;