
// Make newform 4029.2.a.f in Magma, downloaded from the LMFDB on 16 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_4029_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_4029_2_a_f();".
// 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_4029_a();"
function MakeCharacter_4029_a()
    N := 4029;
    order := 1;
    char_gens := [2687, 3556, 3163];
    v := [1, 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_4029_a_Hecke(Kf)
    return MakeCharacter_4029_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_4029_2_a_f();".
// 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_4029_2_a_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_4029_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-106, 62, 2766, -924, -16442, 3192, 45543, -3720, -70521, -402, 65338, 4195, -37281, -3433, 13344, 1282, -2996, -251, 409, 25, -31, -1, 1]>,<5,R![-1435, -34377, 1555, 843173, -517966, -5074560, 5187419, 6048822, -6785542, -3332584, 3869409, 1041463, -1206777, -197707, 224135, 23104, -25418, -1617, 1723, 62, -64, -1, 1]>],Snew);
    return Vf;
end function;