
// Make newform 6039.2.a.p in Magma, downloaded from the LMFDB on 18 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6039_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6039_2_a_p();".
// 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_6039_a();"
function MakeCharacter_6039_a()
    N := 6039;
    order := 1;
    char_gens := [1343, 5491, 5248];
    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_6039_a_Hecke(Kf)
    return MakeCharacter_6039_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6039_2_a_p();".
// 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_6039_2_a_p( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6039_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-657, -3127, 7823, 37557, -49313, -168345, 180363, 377281, -383917, -476787, 494190, 358492, -399524, -161462, 207955, 40855, -70329, -4003, 15295, -615, -2056, 226, 155, -25, -5, 1]>],Snew);
    return Vf;
end function;