
// Make newform 4029.2.a.h in Magma, downloaded from the LMFDB on 18 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_h();".
// 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_h();".
// 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_h( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_4029_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-30, -52, 3194, 7562, -32478, -78284, 93730, 267668, -105162, -447641, 22936, 429415, 59478, -253536, -67735, 94057, 35177, -21376, -10486, 2666, 1835, -107, -175, -11, 7, 1]>,<5,R![-670191, -808660, 6537625, 6049370, -24494793, -19121120, 46603526, 33598469, -49872271, -35897043, 31136203, 24064026, -11171635, -10192518, 2047230, 2704957, -66654, -435036, -43650, 38952, 7916, -1532, -526, 0, 12, 1]>],Snew);
    return Vf;
end function;