// Make newform 8047.2.a.e in Magma, downloaded from the LMFDB on 29 March 2024. // To make the character of type GrpDrchElt, type "MakeCharacter_8047_a();" // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_8047_2_a_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_8047_a();" function MakeCharacter_8047_a() N := 8047; order := 1; char_gens := [3096, 4954]; v := [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_8047_a_Hecke(Kf) return MakeCharacter_8047_a(); end function; // To make the Hecke irreducible modular symbols subspace (type ModSym) // containing the newform, type "MakeNewformModSym_8047_2_a_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_8047_2_a_e( : sign := -1) R := PolynomialRing(Rationals()); chi := MakeCharacter_8047_a(); // SetVerbose("ModularSymbols", true); Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign))); Vf := Kernel([<2,R![-21530657600, 880880169200, 27740332544480, -1467318804303128, -1828006236548828, 605776150555028271, -2119161873645716062, -112602174378065608432, 509606455268858764106, 11932043328299378772483, -54281112246538427087949, -811416770155248742313441, 3494598634047433167221177, 38077750650033825537605919, -153681776485708545481300973, -1295298841469199162233965529, 4938238260513840039272664330, 33094148676573696424130888971, -121011682180087498468853415474, -652319987780555217933534174355, 2329220583901196776771242791000, 10130512686663570129623250517170, -35984618455647706336843495760209, -126072219547187211827254013484027, 453739076977087696803315704665148, 1274763944821513722018167584936950, 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1]>],Snew); return Vf; end function;