
// Make newform 532.2.k.b in Magma, downloaded from the LMFDB on 22 December 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_532_k();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_532_2_k_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_532_k();"
function MakeCharacter_532_k()
    N := 532;
    order := 3;
    char_gens := [267, 381, 477];
    v := [3, 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_532_k_Hecke(Kf)
    return MakeCharacter_532_k();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_532_2_k_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_532_2_k_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_532_k();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![16, -476, 16893, 78341, 505002, 54911, 966081, 77645, 1200945, 21711, 843683, 43964, 413343, 15827, 127765, 5866, 28421, 1063, 4117, 193, 425, 15, 26, 1, 1]>],Snew);
    return Vf;
end function;