
// Make newform 273.2.br.b in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_273_br();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_br_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_br();"
function MakeCharacter_273_br()
    N := 273;
    order := 6;
    char_gens := [92, 157, 106];
    v := [3, 1, 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_273_br_Hecke(Kf)
    return MakeCharacter_273_br();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_br_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_br_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_273_br();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![85, 0, -16257, 0, 296869, 0, -2140397, 0, 7791329, 0, -16585032, 0, 22618426, 0, -20933043, 0, 13630402, 0, -6379285, 0, 2167391, 0, -534323, 0, 94449, 0, -11647, 0, 950, 0, -46, 0, 1]>],Snew);
    return Vf;
end function;