
// Make newform 6034.2.a.o in Magma, downloaded from the LMFDB on 18 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6034_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_o();".
// 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_6034_a();"
function MakeCharacter_6034_a()
    N := 6034;
    order := 1;
    char_gens := [1725, 869];
    v := [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_6034_a_Hecke(Kf)
    return MakeCharacter_6034_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_o();".
// 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_6034_2_a_o( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6034_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-96, 2778, 34401, 94752, -99978, -669070, -249066, 1660310, 1397844, -1916369, -2279602, 1050400, 1814545, -220351, -809618, -32223, 215545, 27463, -34938, -6271, 3378, 718, -179, -42, 4, 1]>,<5,R![-1792, 4224, 133520, -472160, -1566776, 5809328, 6761641, -24475108, -12115239, 38647572, 9630315, -28743088, -4074828, 11699046, 978222, -2838640, -136589, 428141, 10933, -40445, -463, 2323, 8, -74, 0, 1]>,<11,R![314754048, -808086528, -1406587968, 4594588032, 1528593408, -9140815960, -178837409, 9157045686, -385635338, -5285882073, 47761013, 1855253812, 102047046, -400209650, -49147292, 51967732, 9755569, -3817431, -985636, 135633, 51515, -1060, -1317, -54, 13, 1]>],Snew);
    return Vf;
end function;