// Make newform 304.7.e.f in Magma, downloaded from the LMFDB on 28 March 2024. // To make the character of type GrpDrchElt, type "MakeCharacter_304_e();" // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_304_7_e_f();". // 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_304_e();" function MakeCharacter_304_e() N := 304; order := 2; char_gens := [191, 229, 97]; v := [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_304_e_Hecke(Kf) return MakeCharacter_304_e(); end function; // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_304_7_e_f();". // 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_304_7_e_f( : sign := -1) R := PolynomialRing(Rationals()); chi := MakeCharacter_304_e(); // SetVerbose("ModularSymbols", true); Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,7,sign))); Vf := Kernel([<3,R![168388842790260315557454819149466480672768, 0, 10609592946753900124789669800202815406080, 0, 271706354102188949415241684971901943808, 0, 3728046037946895369837864860459728896, 0, 30481574816636869715940113634557952, 0, 157476006868426299883291416035328, 0, 536459107634770490181682278912, 0, 1244694785752086796215951552, 0, 2012347978223457503436120, 0, 2296993151475612398217, 0, 1856543264788122710, 0, 1053135007523999, 0, 408990954956, 0, 103327031, 0, 15270, 0, 1]>,<5,R![141141770235800680000000000000, -15318501392143675200000000000, -285802921234660476000000000, 34975999622247208880000000, -122104984797818034000000, -15306384299741128000000, 51278810184681815000, 2673466273350301500, -4407651447848150, -209584640719535, 137484061124, 7991401275, -1422438, -144873, 0, 1]>],Snew); return Vf; end function;