
// Make newform 273.2.n.c in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_273_n();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_n_c();".
// 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_n();"
function MakeCharacter_273_n()
    N := 273;
    order := 4;
    char_gens := [92, 157, 106];
    v := [2, 4, 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_n_Hecke(Kf)
    return MakeCharacter_273_n();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_n_c();".
// 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_n_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_273_n();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![16, 0, 0, 0, 128096, 0, 0, 0, 71654640, 0, 0, 0, 6574724744, 0, 0, 0, 14491468736, 0, 0, 0, 8327581624, 0, 0, 0, 2040089601, 0, 0, 0, 253103622, 0, 0, 0, 17482631, 0, 0, 0, 700244, 0, 0, 0, 16135, 0, 0, 0, 198, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;