
// Make newform 3234.2.e.d in Magma, downloaded from the LMFDB on 17 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_3234_e();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_3234_2_e_d();".
// 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_3234_e();"
function MakeCharacter_3234_e()
    N := 3234;
    order := 2;
    char_gens := [1079, 199, 2059];
    v := [2, 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_3234_e_Hecke(Kf)
    return MakeCharacter_3234_e();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_3234_2_e_d();".
// 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_3234_2_e_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_3234_e();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![1024, 0, 28672, 0, 301056, 0, 1498112, 0, 3727360, 0, 4574208, 0, 2870592, 0, 995200, 0, 201024, 0, 24160, 0, 1696, 0, 64, 0, 1]>,<13,R![-207224, -510912, -211312, 247808, 138220, -40000, -26512, 2432, 2134, -48, -76, 0, 1]>],Snew);
    return Vf;
end function;