// Make newform 1110.2.bb.e in Magma, downloaded from the LMFDB on 28 March 2024. // To make the character of type GrpDrchElt, type "MakeCharacter_1110_bb();" // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_1110_2_bb_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_1110_bb();" function MakeCharacter_1110_bb() N := 1110; order := 6; char_gens := [371, 667, 631]; v := [6, 3, 4]; // 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_1110_bb_Hecke(Kf) return MakeCharacter_1110_bb(); end function; // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_1110_2_bb_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_1110_2_bb_e( : sign := -1) R := PolynomialRing(Rationals()); chi := MakeCharacter_1110_bb(); // SetVerbose("ModularSymbols", true); Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign))); Vf := Kernel([<7,R![65536, 0, -3280896, 0, 122601728, 0, -1687392256, 0, 16141091520, 0, -89236701824, 0, 351706556496, 0, -775494567232, 0, 1212726432384, 0, -1118969333736, 0, 724430184292, 0, -241516105148, 0, 56021701833, 0, -8079770872, 0, 845619582, 0, -62859988, 0, 3530955, 0, -143744, 0, 4326, 0, -84, 0, 1]>,<11,R![-4480, -3680, 13032, 3592, -9250, 250, 1383, -14, -66, 0, 1]>],Snew); return Vf; end function;