
// Make newform 273.2.bn.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_273_bn();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_bn_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_bn();"
function MakeCharacter_273_bn()
    N := 273;
    order := 6;
    char_gens := [92, 157, 106];
    v := [3, 3, 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_bn_Hecke(Kf)
    return MakeCharacter_273_bn();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_273_2_bn_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_bn_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_273_bn();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![5329, 0, -76869, 0, 866668, 0, -2841495, 0, 6082917, 0, -8471069, 0, 8650580, 0, -6322345, 0, 3506480, 0, -1467191, 0, 476580, 0, -118297, 0, 22737, 0, -3260, 0, 346, 0, -24, 0, 1]>,<19,R![988065390810566656, 0, -1041554280591799296, 0, 688818690034452992, 0, -276527170606576960, 0, 80206200781961696, 0, -16343135174965828, 0, 2492206528841969, 0, -274315955031900, 0, 22755034468233, 0, -1379168855338, 0, 63880260025, 0, -2233263114, 0, 60174841, 0, -1204554, 0, 17833, 0, -172, 0, 1]>],Snew);
    return Vf;
end function;