
// Make newform 504.2.cj.e in Magma, downloaded from the LMFDB on 15 November 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_504_cj();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_504_2_cj_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_504_cj();"
function MakeCharacter_504_cj()
    N := 504;
    order := 6;
    char_gens := [127, 253, 281, 73];
    v := [6, 3, 6, 2];
    // 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_504_cj_Hecke(Kf)
    return MakeCharacter_504_cj();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_504_2_cj_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_504_2_cj_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_504_cj();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![4096, 0, -1912832, 0, 886791168, 0, -3023744000, 0, 7421657792, 0, -7430619264, 0, 5037013168, 0, -2228479968, 0, 724270609, 0, -168147456, 0, 29482826, 0, -3789184, 0, 370859, 0, -26528, 0, 1402, 0, -48, 0, 1]>],Snew);
    return Vf;
end function;