
// Make newform 4029.2.a.g in Magma, downloaded from the LMFDB on 24 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_g();".
// 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_g();".
// 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_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_4029_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-8, -78, 350, 2286, -5812, -13790, 21542, 33434, -37344, -42176, 36947, 30865, -22609, -13727, 8820, 3744, -2187, -609, 332, 54, -28, -2, 1]>,<5,R![15, 495, -1976, -40390, 121150, 574166, -1678686, 297333, 2248668, -1328395, -1108032, 976013, 220795, -325019, -3811, 57103, -5209, -5416, 798, 261, -47, -5, 1]>],Snew);
    return Vf;
end function;