
// Make newform 273.2.bz.b 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_b();".
// 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_b();".
// 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_b( : 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, 1872, 8820, 29952, 140913, 286326, -387306, -828684, 753906, -3187380, 5353128, -2603688, 6938545, 1164058, 310598, 1728846, -2849324, 236316, 74752, -907016, 918370, -118398, -22188, 68726, -60669, 4042, 1316, -2840, 3022, -244, 0, 40, -63, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;