
// Make newform 225.4.k.d in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_225_k();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_225_4_k_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_225_k();"
function MakeCharacter_225_k()
    N := 225;
    order := 6;
    char_gens := [101, 127];
    v := [2, 3];
    // 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_225_k_Hecke(Kf)
    return MakeCharacter_225_k();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_225_4_k_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_225_4_k_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_225_k();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<2,R![6879707136, 0, -141416202240, 0, 2790449823744, 0, -2326399727616, 0, 1277150389504, 0, -390927000752, 0, 85199554593, 0, -12169374108, 0, 1274916666, 0, -92476512, 0, 4999971, 0, -189744, 0, 5274, 0, -92, 0, 1]>],Snew);
    return Vf;
end function;