
// Make newform 504.2.ch.b in Magma, downloaded from the LMFDB on 11 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_504_ch();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_504_2_ch_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_ch();"
function MakeCharacter_504_ch()
    N := 504;
    order := 6;
    char_gens := [127, 253, 281, 73];
    v := [6, 3, 3, 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_504_ch_Hecke(Kf)
    return MakeCharacter_504_ch();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_504_2_ch_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_ch_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_504_ch();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![186624, 0, -1762560, 0, 12848256, 0, -29457024, 0, 45801904, 0, -42674992, 0, 28587144, 0, -12338064, 0, 3879393, 0, -820581, 0, 126330, 0, -12429, 0, 882, 0, -37, 0, 1]>],Snew);
    return Vf;
end function;