
// Make newform 273.2.ba.c in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_273_ba();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_ba_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_ba();"
function MakeCharacter_273_ba()
    N := 273;
    order := 6;
    char_gens := [92, 157, 106];
    v := [3, 1, 3];
    // 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_ba_Hecke(Kf)
    return MakeCharacter_273_ba();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_ba_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_ba_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_273_ba();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![3721, 0, 105591, 0, 2651284, 0, 8932777, 0, 19540733, 0, 24845331, 0, 22453924, 0, 14586711, 0, 7227508, 0, 2718281, 0, 796976, 0, 179569, 0, 31455, 0, 4136, 0, 404, 0, 26, 0, 1]>,<19,R![15752961, 0, 344564766, 0, 5848742214, 0, 32333317380, 0, 129535430122, 0, 195077579046, 0, 204799184636, 0, 125273490896, 0, 54238711263, 0, 11228945442, 0, 1623897188, 0, 125670468, 0, 6930322, 0, 248412, 0, 6474, 0, 100, 0, 1]>],Snew);
    return Vf;
end function;