
// Make newform 273.2.bt.b in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_273_bt();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_bt_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_bt();"
function MakeCharacter_273_bt()
    N := 273;
    order := 12;
    char_gens := [92, 157, 106];
    v := [12, 2, 5];
    // 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_bt_Hecke(Kf)
    return MakeCharacter_273_bt();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_bt_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_bt_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_273_bt();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![59049, 669222, 3792258, 11795220, 21521619, 20070342, 23363478, 69922008, 155258613, 99595710, 20420874, 41355270, 242842212, 84950940, 5373984, -2900766, 152167654, 22154080, 514796, -3569838, 41488543, 2099310, 19768, -434822, 5319379, 78396, 312, -18394, 335772, 1192, 2, -308, 10786, 8, 0, -2, 168, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;