
// Make newform 273.2.r.b in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_273_r();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_r_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_r();"
function MakeCharacter_273_r()
    N := 273;
    order := 6;
    char_gens := [92, 157, 106];
    v := [3, 5, 2];
    // 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_r_Hecke(Kf)
    return MakeCharacter_273_r();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_r_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_r_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_273_r();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![367, 0, 148395, 0, 1648423, 0, 7852455, 0, 21268707, 0, 36750070, 0, 43068692, 0, 35519813, 0, 21096866, 0, 9145849, 0, 2908599, 0, 676187, 0, 113325, 0, 13303, 0, 1036, 0, 48, 0, 1]>],Snew);
    return Vf;
end function;