
// Make newform 504.2.bk.b in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_504_bk();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_504_2_bk_b();".
// 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_bk();"
function MakeCharacter_504_bk()
    N := 504;
    order := 6;
    char_gens := [127, 253, 281, 73];
    v := [3, 3, 6, 5];
    // 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_bk_Hecke(Kf)
    return MakeCharacter_504_bk();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_504_2_bk_b();".
// 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_bk_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_504_bk();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![5184, 0, 24192, 0, 101448, 0, 49968, 0, 17145, 0, 3144, 0, 417, 0, 24, 0, 1]>],Snew);
    return Vf;
end function;