
// Make newform 273.2.bz.a in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_273_bz();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_bz_a();".
// 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_273_bz();"
function MakeCharacter_273_bz()
    N := 273;
    order := 12;
    char_gens := [92, 157, 106];
    v := [12, 2, 9];
    // 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_273_bz_Hecke(Kf)
    return MakeCharacter_273_bz();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_bz_a();".
// 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_273_2_bz_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_273_bz();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![144, 576, 4500, 35676, 94041, 271782, 1161342, 289836, -1311342, -3130140, -3353112, 4765164, 6704953, -1471238, -957418, -1563126, -3066212, -111264, 870280, 991048, 981706, 177534, -17820, -57946, -63405, -8954, 452, 2452, 3022, 284, 0, -44, -63, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;