
// Make newform 4140.3.d.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_4140_d();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_4140_3_d_c();".
// 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_4140_d();"
function MakeCharacter_4140_d()
    N := 4140;
    order := 2;
    char_gens := [2071, 461, 1657, 3961];
    v := [2, 2, 2, 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_4140_d_Hecke(Kf)
    return MakeCharacter_4140_d();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_4140_3_d_c();".
// 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_4140_3_d_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_4140_d();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<7,R![12094542306440711766016, 0, 63507320713643340857344, 0, 74169893386904850333696, 0, 36165033901355670241280, 0, 9338538397675839015936, 0, 1424840298882821309952, 0, 135820228576108313232, 0, 8342589709149555936, 0, 337296882595376408, 0, 9148609299263408, 0, 169468469656969, 0, 2167506294182, 0, 19123041207, 0, 114285060, 0, 441911, 0, 998, 0, 1]>],Snew);
    return Vf;
end function;