
// Make newform 432.2.l.a in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_432_l();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_432_2_l_a();".
// 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_432_l();"
function MakeCharacter_432_l()
    N := 432;
    order := 4;
    char_gens := [271, 325, 353];
    v := [2, 1, 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_432_l_Hecke(Kf)
    return MakeCharacter_432_l();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_432_2_l_a();".
// 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_432_2_l_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_432_l();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![2825761, 0, 0, 0, 330208416, 0, 0, 0, 1577636124, 0, 0, 0, 1060073440, 0, 0, 0, 145130342, 0, 0, 0, 6777696, 0, 0, 0, 98140, 0, 0, 0, 544, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;