
// Make newform 1152.3.g.e in Magma, downloaded from the LMFDB on 18 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1152_g();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1152_g_Hecke();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_1152_3_g_e();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1152_3_g_e();".
// 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 ConvertToHeckeField(input: pass_field := false, Kf := [])
    if not pass_field then
        poly := [16, 0, 0, 0, 1, 0, 0, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 8, 0, 0, 0], [0, 0, -10, 0, 0, 0, -2, 0], [0, -4, 18, -7, 0, 4, -6, 1], [0, 4, 6, 7, 0, -4, -2, -1], [0, 44, -10, 13, 0, 4, -2, 5], [0, 8, 0, -14, 0, -8, 0, 2], [0, 44, 0, -13, 0, 4, 0, -5]];
    Rf_basisdens := [1, 3, 3, 12, 4, 12, 3, 6];
    Rf_basisnums := ChangeUniverse([[z : z in elt] : elt in Rf_num], Kf);
    Rfbasis := [Rf_basisnums[i]/Rf_basisdens[i] : i in [1..Degree(Kf)]];
    inp_vec := Vector(Rfbasis)*ChangeRing(Transpose(Matrix([[elt : elt in row] : row in input])),Kf);
    return Eltseq(inp_vec);
end function;


// To make the character of type GrpDrchElt, type "MakeCharacter_1152_g();"
function MakeCharacter_1152_g()
    N := 1152;
    order := 2;
    char_gens := [127, 901, 641];
    v := [1, 2, 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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1152_g_Hecke();"
function MakeCharacter_1152_g_Hecke(Kf)
    N := 1152;
    order := 2;
    char_gens := [127, 901, 641];
    char_values := [[-1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0]];
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    values := ConvertToHeckeField(char_values : pass_field := true, Kf := Kf); // the value of chi on the gens as elements in the Hecke field
    F := Universe(values);// the Hecke field
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),values);
    return chi;
end function;


function ExtendMultiplicatively(weight, aps, character)
    prec := NextPrime(NthPrime(#aps)) - 1; // we will able to figure out a_0 ... a_prec
    primes := PrimesUpTo(prec);
    prime_powers := primes;
    assert #primes eq #aps;
    log_prec := Floor(Log(prec)/Log(2)); // prec < 2^(log_prec+1)
    F := Universe(aps);
    FXY<X, Y> := PolynomialRing(F, 2);
    // 1/(1 - a_p T + p^(weight - 1) * char(p) T^2) = 1 + a_p T + a_{p^2} T^2 + ...
    R<T> := PowerSeriesRing(FXY : Precision := log_prec + 1);
    recursion := Coefficients(1/(1 - X*T + Y*T^2));
    coeffs := [F!0: i in [1..(prec+1)]];
    coeffs[1] := 1; //a_1
    for i := 1 to #primes do
        p := primes[i];
        coeffs[p] := aps[i];
        b := p^(weight - 1) * F!character(p);
        r := 2;
        p_power := p * p;
        //deals with powers of p
        while p_power le prec do
            Append(~prime_powers, p_power);
            coeffs[p_power] := Evaluate(recursion[r + 1], [aps[i], b]);
            p_power *:= p;
            r +:= 1;
        end while;    
    end for;
    Sort(~prime_powers);
    for pp in prime_powers do
        for k := 1 to Floor(prec/pp) do
            if GCD(k, pp) eq 1 then
                coeffs[pp*k] := coeffs[pp]*coeffs[k];
            end if;
        end for;
    end for;
    return coeffs;
end function;


function qexpCoeffs()
    // To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
    weight := 3;
    raw_aps := [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 0, 0, 2, 0, 0], [0, 2, 0, 0, 0, 0, 1, 0], [0, 0, 0, -1, 2, 0, 0, 0], [0, 0, -2, 0, 0, -1, 0, 0], [2, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, -5, 3, 0, 0, 0], [0, 0, -3, 0, 0, 2, 0, 0], [0, -6, 0, 0, 0, 0, 1, 0], [0, 0, 0, -1, 6, 0, 0, 0], [0, 2, 0, 0, 0, 0, -2, 0], [-14, 0, 0, 0, 0, 0, 0, 1], [0, 0, 6, 0, 0, -12, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0], [-38, 0, 0, 0, 0, 0, 0, 6], [0, 0, -8, 0, 0, 3, 0, 0], [0, -1, 0, 0, 0, 0, -4, 0], [0, 0, 0, 2, 10, 0, 0, 0], [14, 0, 0, 0, 0, 0, 0, -4], [0, 0, 0, -11, 8, 0, 0, 0], [0, 0, 14, 0, 0, 1, 0, 0], [0, -2, 0, 0, 0, 0, -6, 0], [-10, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 26, 10, 0, 0, 0], [0, 0, -18, 0, 0, 5, 0, 0], [0, 16, 0, 0, 0, 0, 0, 0], [0, 0, 0, -27, 5, 0, 0, 0], [0, 0, -18, 0, 0, 12, 0, 0], [0, 0, 0, -21, 0, 0, 0, 0], [0, 0, 14, 0, 0, -21, 0, 0], [-6, 0, 0, 0, 0, 0, 0, -7], [0, 0, 25, 0, 0, -14, 0, 0], [0, -14, 0, 0, 0, 0, -3, 0], [0, 0, 0, 17, 6, 0, 0, 0], [0, 2, 0, 0, 0, 0, -2, 0], [-146, 0, 0, 0, 0, 0, 0, -1], [0, -10, 0, 0, 0, 0, -1, 0], [-18, 0, 0, 0, 0, 0, 0, 10], [0, 0, 0, 19, 10, 0, 0, 0], [0, 0, 30, 0, 0, 13, 0, 0], [0, 0, 22, 0, 0, -4, 0, 0], [0, 0, -20, 0, 0, -11, 0, 0], [0, -23, 0, 0, 0, 0, 0, 0], [110, 0, 0, 0, 0, 0, 0, 23], [0, 0, 0, -2, 6, 0, 0, 0], [0, 18, 0, 0, 0, 0, -7, 0], [-14, 0, 0, 0, 0, 0, 0, 6], [0, 21, 0, 0, 0, 0, 4, 0], [0, 0, 0, -12, -20, 0, 0, 0], [0, 32, 0, 0, 0, 0, 0, 0], [0, 0, 0, -43, -12, 0, 0, 0], [0, 0, -20, 0, 0, 45, 0, 0], [-354, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 44, -12, 0, 0, 0], [0, 0, -28, 0, 0, -16, 0, 0], [0, 0, 0, -13, -30, 0, 0, 0], [0, 0, 22, 0, 0, -28, 0, 0], [0, 4, 0, 0, 0, 0, -14, 0], [-2, 0, 0, 0, 0, 0, 0, 10], [0, 0, 0, 17, -20, 0, 0, 0], [0, 0, 4, 0, 0, -24, 0, 0], [-6, 0, 0, 0, 0, 0, 0, -2], [0, -21, 0, 0, 0, 0, 16, 0], [-126, 0, 0, 0, 0, 0, 0, -7], [0, 0, 0, 58, -14, 0, 0, 0], [0, 24, 0, 0, 0, 0, 0, 0], [0, 0, 10, 0, 0, -49, 0, 0], [-422, 0, 0, 0, 0, 0, 0, -15], [0, 0, -11, 0, 0, 34, 0, 0], [0, -2, 0, 0, 0, 0, -13, 0], [0, 0, 0, 45, -38, 0, 0, 0], [250, 0, 0, 0, 0, 0, 0, 9], [0, 0, 0, -21, -37, 0, 0, 0], [46, 0, 0, 0, 0, 0, 0, -20], [0, 1, 0, 0, 0, 0, 28, 0], [622, 0, 0, 0, 0, 0, 0, -9], [0, -6, 0, 0, 0, 0, 5, 0], [162, 0, 0, 0, 0, 0, 0, -28], [0, 0, -38, 0, 0, 61, 0, 0], [0, 27, 0, 0, 0, 0, 8, 0], [0, 0, 0, 61, 5, 0, 0, 0], [-226, 0, 0, 0, 0, 0, 0, 12], [0, 0, 0, -87, -22, 0, 0, 0], [0, 0, 6, 0, 0, 29, 0, 0], [0, 5, 0, 0, 0, 0, -8, 0], [0, 32, 0, 0, 0, 0, -12, 0], [0, 0, 0, 0, 0, 19, 0, 0], [0, -40, 0, 0, 0, 0, 0, 0], [0, 0, -28, 0, 0, -64, 0, 0], [0, 4, 0, 0, 0, 0, 14, 0], [0, 0, 0, -25, -50, 0, 0, 0], [0, 0, 0, 71, 47, 0, 0, 0], [0, 0, -3, 0, 0, -38, 0, 0], [-418, 0, 0, 0, 0, 0, 0, -1], [0, 0, -93, 0, 0, -34, 0, 0], [0, 0, 0, 43, 40, 0, 0, 0], [0, 45, 0, 0, 0, 0, 12, 0], [0, 0, 0, 63, 7, 0, 0, 0], [0, 0, 30, 0, 0, -108, 0, 0], [150, 0, 0, 0, 0, 0, 0, 26], [0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, -106, 86, 0, 0, 0], [0, 6, 0, 0, 0, 0, -21, 0], [-314, 0, 0, 0, 0, 0, 0, 10], [0, 0, 66, 0, 0, 29, 0, 0], [714, 0, 0, 0, 0, 0, 0, 17], [0, 0, 0, 44, -4, 0, 0, 0], [0, 0, 84, 0, 0, -72, 0, 0], [0, 0, -40, 0, 0, 27, 0, 0], [0, 0, 0, 105, 25, 0, 0, 0], [0, 0, -29, 0, 0, 22, 0, 0], [0, -10, 0, 0, 0, 0, 35, 0], [0, 0, 0, -99, 30, 0, 0, 0], [0, -12, 0, 0, 0, 0, -4, 0], [-934, 0, 0, 0, 0, 0, 0, -7], [-414, 0, 0, 0, 0, 0, 0, -12], [0, 0, 0, -81, 36, 0, 0, 0], [0, 25, 0, 0, 0, 0, -40, 0], [0, 0, -143, 0, 0, 18, 0, 0], [0, 0, 0, -51, 108, 0, 0, 0], [798, 0, 0, 0, 0, 0, 0, 31], [0, -60, 0, 0, 0, 0, 14, 0], [0, 0, -118, 0, 0, 7, 0, 0], [-418, 0, 0, 0, 0, 0, 0, 39], [0, 0, -10, 0, 0, -60, 0, 0], [0, -6, 0, 0, 0, 0, 21, 0], [0, 0, 56, 0, 0, -97, 0, 0], [-658, 0, 0, 0, 0, 0, 0, -33], [0, 0, 0, -31, 25, 0, 0, 0], [638, 0, 0, 0, 0, 0, 0, -14], [0, 0, 0, -83, 96, 0, 0, 0], [0, 0, -41, 0, 0, 70, 0, 0], [0, 0, 0, 27, -20, 0, 0, 0], [0, 0, 0, 29, 37, 0, 0, 0], [0, 0, 43, 0, 0, 94, 0, 0], [0, 0, 0, 125, 60, 0, 0, 0], [0, 0, 4, 0, 0, 75, 0, 0], [0, 30, 0, 0, 0, 0, -38, 0], [-186, 0, 0, 0, 0, 0, 0, -73], [0, 96, 0, 0, 0, 0, 0, 0], [-806, 0, 0, 0, 0, 0, 0, -47], [0, 0, 0, 147, 35, 0, 0, 0], [0, 0, 51, 0, 0, -106, 0, 0], [0, -54, 0, 0, 0, 0, 49, 0], [98, 0, 0, 0, 0, 0, 0, 33], [0, 0, 0, -12, 60, 0, 0, 0], [0, 0, 49, 0, 0, 122, 0, 0], [0, 116, 0, 0, 0, 0, 14, 0], [0, 0, 95, 0, 0, -130, 0, 0], [0, 50, 0, 0, 0, 0, 25, 0], [0, 0, 44, 0, 0, -21, 0, 0], [0, 0, 0, -13, -53, 0, 0, 0], [722, 0, 0, 0, 0, 0, 0, -40], [0, 0, 0, -19, -50, 0, 0, 0], [0, 22, 0, 0, 0, 0, -14, 0], [0, 0, 0, -149, 115, 0, 0, 0], [0, 0, -28, 0, 0, 53, 0, 0], [0, 41, 0, 0, 0, 0, -36, 0], [0, 0, 0, 191, -25, 0, 0, 0], [0, -92, 0, 0, 0, 0, 2, 0], [0, 0, -4, 0, 0, 151, 0, 0], [850, 0, 0, 0, 0, 0, 0, 17], [-162, 0, 0, 0, 0, 0, 0, 92], [0, 0, 0, 37, 10, 0, 0, 0], [0, -124, 0, 0, 0, 0, 28, 0], [-182, 0, 0, 0, 0, 0, 0, 17], [0, 38, 0, 0, 0, 0, 7, 0], [-1138, 0, 0, 0, 0, 0, 0, 40], [0, 0, -12, 0, 0, 39, 0, 0], [0, 0, 0, 136, -160, 0, 0, 0], [0, 0, 120, 0, 0, -8, 0, 0], [0, 0, 0, -77, 32, 0, 0, 0], [0, 0, 138, 0, 0, 21, 0, 0], [642, 0, 0, 0, 0, 0, 0, -87], [0, 0, 96, 0, 0, -5, 0, 0], [0, -73, 0, 0, 0, 0, 28, 0], [902, 0, 0, 0, 0, 0, 0, 15], [0, 0, 0, -4, 20, 0, 0, 0], [0, 46, 0, 0, 0, 0, -21, 0], [0, 0, 0, 129, -90, 0, 0, 0], [-994, 0, 0, 0, 0, 0, 0, -1], [0, 0, 20, 0, 0, 16, 0, 0], [978, 0, 0, 0, 0, 0, 0, -18], [0, 12, 0, 0, 0, 0, 14, 0], [814, 0, 0, 0, 0, 0, 0, 48], [0, -106, 0, 0, 0, 0, -46, 0], [0, 0, 72, 0, 0, -120, 0, 0], [0, 0, 0, 133, 2, 0, 0, 0], [0, 100, 0, 0, 0, 0, 12, 0], [0, 0, 0, -8, -40, 0, 0, 0], [-10, 0, 0, 0, 0, 0, 0, 10], [206, 0, 0, 0, 0, 0, 0, -49], [0, 0, 0, 44, -60, 0, 0, 0], [0, 32, 0, 0, 0, 0, 36, 0], [0, 0, 0, 151, -148, 0, 0, 0], [0, 0, 62, 0, 0, -287, 0, 0], [-458, 0, 0, 0, 0, 0, 0, -49], [-294, 0, 0, 0, 0, 0, 0, -82], [0, -29, 0, 0, 0, 0, 84, 0], [0, 0, 0, -285, -74, 0, 0, 0], [0, 0, -108, 0, 0, 21, 0, 0], [0, -99, 0, 0, 0, 0, -28, 0], [0, 0, 0, -194, -130, 0, 0, 0], [0, 0, -21, 0, 0, 238, 0, 0], [-418, 0, 0, 0, 0, 0, 0, 2], [0, 0, 0, -105, -140, 0, 0, 0], [0, 0, -18, 0, 0, -131, 0, 0], [0, 126, 0, 0, 0, 0, 34, 0], [0, 52, 0, 0, 0, 0, -82, 0], [674, 0, 0, 0, 0, 0, 0, 52], [0, 0, -90, 0, 0, 231, 0, 0], [0, 0, 0, 37, -67, 0, 0, 0], [0, 166, 0, 0, 0, 0, 27, 0], [0, 0, 0, -113, -4, 0, 0, 0], [502, 0, 0, 0, 0, 0, 0, -1], [0, 0, 76, 0, 0, -223, 0, 0], [0, 0, 0, -49, -145, 0, 0, 0], [0, 0, -284, 0, 0, 49, 0, 0], [0, -141, 0, 0, 0, 0, 28, 0], [-294, 0, 0, 0, 0, 0, 0, -15], [0, 0, 0, 366, 94, 0, 0, 0], [0, 20, 0, 0, 0, 0, -70, 0], [0, 0, -112, 0, 0, -139, 0, 0], [0, 72, 0, 0, 0, 0, -8, 0], [-970, 0, 0, 0, 0, 0, 0, 71], [0, 0, 215, 0, 0, -90, 0, 0], [0, 0, -18, 0, 0, -99, 0, 0], [0, 0, 0, -76, -100, 0, 0, 0], [0, 0, -65, 0, 0, -170, 0, 0], [0, -24, 0, 0, 0, 0, -16, 0], [-786, 0, 0, 0, 0, 0, 0, 92], [0, 0, 0, 223, 156, 0, 0, 0], [0, -11, 0, 0, 0, 0, 56, 0], [0, 34, 0, 0, 0, 0, 17, 0], [0, -115, 0, 0, 0, 0, -12, 0], [0, 0, -72, 0, 0, -40, 0, 0], [0, 0, 258, 0, 0, -169, 0, 0], [-70, 0, 0, 0, 0, 0, 0, 97], [0, 0, 0, -120, -40, 0, 0, 0], [0, 16, 0, 0, 0, 0, -36, 0], [0, 0, -140, 0, 0, 39, 0, 0], [0, -146, 0, 0, 0, 0, -30, 0], [0, 0, -172, 0, 0, -96, 0, 0], [0, -96, 0, 0, 0, 0, 56, 0], [790, 0, 0, 0, 0, 0, 0, -65], [0, 0, 0, -126, 82, 0, 0, 0], [0, -2, 0, 0, 0, 0, 7, 0], [-258, 0, 0, 0, 0, 0, 0, -152], [0, 0, 0, 15, 54, 0, 0, 0], [0, -106, 0, 0, 0, 0, -14, 0], [214, 0, 0, 0, 0, 0, 0, 39], [0, 0, 74, 0, 0, 276, 0, 0], [0, 0, 0, -21, -106, 0, 0, 0], [402, 0, 0, 0, 0, 0, 0, 84], [0, 0, -154, 0, 0, -215, 0, 0], [0, 234, 0, 0, 0, 0, 14, 0], [262, 0, 0, 0, 0, 0, 0, -9], [-118, 0, 0, 0, 0, 0, 0, -95], [0, 0, 0, 199, 15, 0, 0, 0], [0, 0, -120, 0, 0, 40, 0, 0], [0, 0, 0, -273, 0, 0, 0, 0], [0, 0, 0, 186, -70, 0, 0, 0], [0, 0, -153, 0, 0, 38, 0, 0], [0, 0, 0, -5, 80, 0, 0, 0], [-110, 0, 0, 0, 0, 0, 0, -183], [0, 0, 146, 0, 0, 4, 0, 0], [-1026, 0, 0, 0, 0, 0, 0, -88], [0, 0, -158, 0, 0, 211, 0, 0], [1470, 0, 0, 0, 0, 0, 0, -56], [0, 0, 252, 0, 0, -231, 0, 0], [0, 71, 0, 0, 0, 0, -36, 0], [682, 0, 0, 0, 0, 0, 0, 9], [-1146, 0, 0, 0, 0, 0, 0, -150], [0, 10, 0, 0, 0, 0, -90, 0], [0, 20, 0, 0, 0, 0, 98, 0], [0, 0, -26, 0, 0, -139, 0, 0], [0, 186, 0, 0, 0, 0, 21, 0], [-22, 0, 0, 0, 0, 0, 0, -79], [0, 0, 59, 0, 0, -98, 0, 0], [0, 136, 0, 0, 0, 0, 84, 0], [-46, 0, 0, 0, 0, 0, 0, 6], [0, 0, 0, 251, 204, 0, 0, 0], [0, 0, -140, 0, 0, 159, 0, 0], [0, 0, 0, 302, -122, 0, 0, 0], [0, 0, 0, -155, 30, 0, 0, 0], [0, 66, 0, 0, 0, 0, 14, 0], [0, 0, 0, -158, 290, 0, 0, 0], [0, -78, 0, 0, 0, 0, -42, 0], [146, 0, 0, 0, 0, 0, 0, -191], [0, 0, 0, 73, -62, 0, 0, 0], [0, 0, 364, 0, 0, -127, 0, 0], [0, 0, 0, -7, 204, 0, 0, 0], [0, 143, 0, 0, 0, 0, 8, 0], [0, 0, -189, 0, 0, -66, 0, 0], [-434, 0, 0, 0, 0, 0, 0, -110], [0, 0, 0, 69, 170, 0, 0, 0], [0, 0, -160, 0, 0, -193, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1152_g_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1152_3_g_e();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
function MakeNewformModFrm_1152_3_g_e(:prec:=8)
    chi := MakeCharacter_1152_g();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 3));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(1999) - 1;
    while true do
        trunc_vec := Vector(Kf, [0] cat [f_vec[i]: i in [1..prec]]);
        B := Basis(S, prec + 1);
        S_basismat := Matrix([AbsEltseq(g): g in B]);
        if Rank(S_basismat) eq Min(NumberOfRows(S_basismat), NumberOfColumns(S_basismat)) then
            S_basismat := ChangeRing(S_basismat,Kf);
            f_lincom := Solution(S_basismat,trunc_vec);
            f := &+[f_lincom[i]*Basis(S)[i] : i in [1..#Basis(S)]];
            return f;
        end if;
        error if prec eq maxprec, "Unable to distinguish newform within newspace";
        prec := Min(Ceiling(1.25 * prec), maxprec);
    end while;
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1152_3_g_e();".
// 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_1152_3_g_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1152_g();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<5,R![400, 0, -72, 0, 1]>,<13,R![-188, -12, 1]>],Snew);
    return Vf;
end function;