
// Make newform 429.2.bd.b in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_429_bd();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_429_2_bd_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_429_bd();"
function MakeCharacter_429_bd()
    N := 429;
    order := 12;
    char_gens := [287, 79, 67];
    v := [12, 6, 7];
    // 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_429_bd_Hecke(Kf)
    return MakeCharacter_429_bd();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_429_2_bd_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_429_2_bd_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_429_bd();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![256, 0, 6528, 0, -143312, 0, -5069400, 0, 162263953, 0, -908902578, 0, 181783527, 0, 9462584610, 0, 15881211714, 0, 2518218486, 0, -11610853045, 0, -4302447660, 0, 6594588448, 0, 3028230096, 0, -1888579690, 0, -786915066, 0, 468589024, 0, 60611412, 0, -48945579, 0, -3393546, 0, 3593002, 0, 88014, 0, -159570, 0, -1722, 0, 5093, 0, 0, 0, -87, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;