
// Make newform 136.4.n.a in Magma, downloaded from the LMFDB on 18 December 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_136_n();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_136_4_n_a();".
// 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_136_n();"
function MakeCharacter_136_n()
    N := 136;
    order := 8;
    char_gens := [103, 69, 105];
    v := [8, 8, 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_136_n_Hecke( : Kf := Kf)
    return MakeCharacter_136_n();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_136_4_n_a();".
// 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_136_4_n_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_136_n();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<3,R![5914779649024, 91174817316864, 354812465742848, -602390311234560, 535890017010176, -278604064364544, 79303767382400, -11702034734208, 2420781430032, -319316087616, 55510319872, 1465404672, -3077053952, -642078816, 339689344, 92472672, 20928264, 1184688, 34688, -3264, 32, -24, 8, 0, 1]>],Snew);
    return Vf;
end function;