
// Make newform 43.11.b.b in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_43_b();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_43_11_b_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_43_b();"
function MakeCharacter_43_b()
    N := 43;
    order := 2;
    char_gens := [3];
    v := [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_43_b_Hecke(Kf)
    return MakeCharacter_43_b();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_43_11_b_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_43_11_b_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_43_b();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,11,sign)));
    Vf := Kernel([<2,R![352071488546277002403513591206921700578741452800, 0, 511433958746312030591699028631089437386903388160, 0, 27691795003068448373311456929648484142867808256, 0, 471064038813839115831123752234514589140647936, 0, 3811730889571886694084793063032262114672640, 0, 17794680640802242747632697917947049410560, 0, 53196403161753041263367818625725497344, 0, 108381260925329218078175062880157696, 0, 156500620212826514918491437195264, 0, 164147942518267550365187975680, 0, 126818822345000643121214912, 0, 72536579805274767410672, 0, 30598068664092954704, 0, 9383345726625472, 0, 2031551938232, 0, 293978421, 0, 25486, 0, 1]>],Snew);
    return Vf;
end function;