
// Make newform 1152.3.b.j in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1152_b();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1152_b_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_b_j();".
// 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_b_j();".
// 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 := [1, 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], [0, 0, 0, 0, 0, 0, 4, 0], [0, 2, 0, -2, 0, -2, 0, 0], [0, 0, 8, 0, 0, 0, -4, 0], [0, -2, 0, 2, 0, -2, 0, -4], [0, 8, 0, 8, 0, -8, 0, 0], [0, 8, 0, 8, 0, 8, 0, -16], [-16, 0, 0, 0, 32, 0, 0, 0]];
    Rf_basisdens := [1, 1, 1, 1, 1, 1, 1, 1];
    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_b();"
function MakeCharacter_1152_b()
    N := 1152;
    order := 2;
    char_gens := [127, 901, 641];
    v := [1, 1, 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_b_Hecke();"
function MakeCharacter_1152_b_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, 1, 0, 0, -1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 2, 0, 0, 0], [2, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 2, 0, 0, 0, 0, -1], [0, -5, 0, 0, -5, 0, 0, 0], [0, 0, -9, 0, 0, 0, 0, -1], [0, -1, 0, 0, 8, 0, 0, 0], [-18, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 5, 0, 0], [0, 0, -6, 0, 0, 0, 0, 2], [0, 9, 0, 0, -7, 0, 0, 0], [0, 0, 0, -5, 0, 0, 0, 0], [0, -11, 0, 0, 4, 0, 0, 0], [0, 0, 0, -7, 0, 4, 0, 0], [0, 0, -34, 0, 0, 0, 0, -1], [-10, 0, 0, 0, 0, 0, 0, 0], [0, 0, -17, 0, 0, 0, 0, -3], [0, 0, 0, -11, 0, 3, 0, 0], [34, 0, 0, 0, 0, 0, -2, 0], [-66, 0, 0, 0, 0, 0, 2, 0], [0, 13, 0, 0, 21, 0, 0, 0], [0, 0, -33, 0, 0, 0, 0, 2], [0, 0, 0, 7, 0, 6, 0, 0], [0, -11, 0, 0, -18, 0, 0, 0], [-82, 0, 0, 0, 0, 0, -6, 0], [0, 0, -55, 0, 0, 0, 0, 1], [0, 0, 0, 19, 0, 4, 0, 0], [-50, 0, 0, 0, 0, 0, -5, 0], [0, 0, 0, -3, 0, 12, 0, 0], [0, 61, 0, 0, 3, 0, 0, 0], [0, 0, 21, 0, 0, 0, 0, -6], [0, -19, 0, 0, -8, 0, 0, 0], [0, 0, 0, -31, 0, 3, 0, 0], [0, 0, 52, 0, 0, 0, 0, -1], [0, -53, 0, 0, -11, 0, 0, 0], [0, 0, 0, -13, 0, 12, 0, 0], [0, 39, 0, 0, -22, 0, 0, 0], [0, 0, -4, 0, 0, 0, 0, -6], [-26, 0, 0, 0, 0, 0, -8, 0], [0, 41, 0, 0, -3, 0, 0, 0], [0, 0, -33, 0, 0, 0, 0, -2], [0, 0, 0, 29, 0, -16, 0, 0], [0, 0, 85, 0, 0, 0, 0, 1], [0, 0, 0, 33, 0, -11, 0, 0], [0, -13, 0, 0, 54, 0, 0, 0], [-238, 0, 0, 0, 0, 0, 6, 0], [0, 0, 24, 0, 0, 0, 0, -4], [86, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, -27, 0, 13, 0, 0], [-290, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 9], [0, -25, 0, 0, -41, 0, 0, 0], [0, 0, 29, 0, 0, 0, 0, 11], [0, 51, 0, 0, 2, 0, 0, 0], [-46, 0, 0, 0, 0, 0, -8, 0], [0, 0, 0, -3, 0, -12, 0, 0], [0, 1, 0, 0, -23, 0, 0, 0], [0, 0, 0, 17, 0, -12, 0, 0], [0, 0, 132, 0, 0, 0, 0, 3], [58, 0, 0, 0, 0, 0, -16, 0], [0, -5, 0, 0, 15, 0, 0, 0], [0, 0, 0, 1, 0, -14, 0, 0], [-54, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 9, 0, -35, 0, 0], [0, 65, 0, 0, -60, 0, 0, 0], [46, 0, 0, 0, 0, 0, 18, 0], [0, 0, -10, 0, 0, 0, 0, -5], [0, 0, 63, 0, 0, 0, 0, -7], [0, -45, 0, 0, 20, 0, 0, 0], [0, 0, 0, 61, 0, -9, 0, 0], [0, 0, 196, 0, 0, 0, 0, -2], [0, 45, 0, 0, 11, 0, 0, 0], [0, -43, 0, 0, -36, 0, 0, 0], [34, 0, 0, 0, 0, 0, -37, 0], [290, 0, 0, 0, 0, 0, 10, 0], [0, 0, 0, 77, 0, -3, 0, 0], [0, -101, 0, 0, -78, 0, 0, 0], [0, 0, -162, 0, 0, 0, 0, 2], [62, 0, 0, 0, 0, 0, -4, 0], [0, 0, 3, 0, 0, 0, 0, 12], [0, 0, 0, -27, 0, -3, 0, 0], [-318, 0, 0, 0, 0, 0, -19, 0], [-190, 0, 0, 0, 0, 0, 30, 0], [0, -9, 0, 0, 137, 0, 0, 0], [0, 0, 141, 0, 0, 0, 0, -17], [0, 0, 0, -43, 0, 33, 0, 0], [0, 0, 130, 0, 0, 0, 0, 10], [0, 0, 69, 0, 0, 0, 0, 12], [0, 0, 0, 23, 0, -22, 0, 0], [0, 0, 0, -7, 0, 28, 0, 0], [0, 0, -114, 0, 0, 0, 0, -15], [0, -9, 0, 0, 27, 0, 0, 0], [-258, 0, 0, 0, 0, 0, -3, 0], [0, 0, 0, 33, 0, 19, 0, 0], [0, 53, 0, 0, -154, 0, 0, 0], [0, 0, 0, -59, 0, -15, 0, 0], [0, 139, 0, 0, -7, 0, 0, 0], [0, 0, 0, 45, 0, -69, 0, 0], [686, 0, 0, 0, 0, 0, -7, 0], [0, 0, 0, 29, 0, -6, 0, 0], [-422, 0, 0, 0, 0, 0, -16, 0], [0, 0, 0, -29, 0, 2, 0, 0], [-82, 0, 0, 0, 0, 0, 34, 0], [0, 0, -18, 0, 0, 0, 0, 3], [230, 0, 0, 0, 0, 0, 20, 0], [0, 0, -95, 0, 0, 0, 0, -11], [0, 75, 0, 0, 140, 0, 0, 0], [-526, 0, 0, 0, 0, 0, 12, 0], [0, 0, 0, -19, 0, 36, 0, 0], [0, 0, 117, 0, 0, 0, 0, -22], [-142, 0, 0, 0, 0, 0, 9, 0], [0, 0, 0, 69, 0, -15, 0, 0], [0, 0, -158, 0, 0, 0, 0, -23], [0, 135, 0, 0, -115, 0, 0, 0], [0, 0, 0, 23, 0, 58, 0, 0], [0, -1, 0, 0, 24, 0, 0, 0], [-386, 0, 0, 0, 0, 0, -48, 0], [0, -195, 0, 0, -25, 0, 0, 0], [0, 0, 0, -11, 0, 75, 0, 0], [0, 0, 0, -175, 0, -5, 0, 0], [0, 7, 0, 0, 115, 0, 0, 0], [0, -145, 0, 0, -130, 0, 0, 0], [0, 0, -386, 0, 0, 0, 0, -4], [0, 0, 49, 0, 0, 0, 0, 2], [0, 177, 0, 0, 74, 0, 0, 0], [0, 0, 0, 73, 0, 78, 0, 0], [0, 0, 264, 0, 0, 0, 0, -5], [0, 0, -149, 0, 0, 0, 0, 29], [0, 15, 0, 0, 30, 0, 0, 0], [862, 0, 0, 0, 0, 0, -5, 0], [-122, 0, 0, 0, 0, 0, 20, 0], [0, -35, 0, 0, -255, 0, 0, 0], [0, 0, 0, 53, 0, 79, 0, 0], [0, 191, 0, 0, 77, 0, 0, 0], [-1042, 0, 0, 0, 0, 0, -5, 0], [0, 0, 0, 65, 0, 45, 0, 0], [0, 41, 0, 0, 221, 0, 0, 0], [0, 0, -15, 0, 0, 0, 0, -26], [0, 0, 0, -1, 0, 110, 0, 0], [0, -99, 0, 0, 78, 0, 0, 0], [0, 0, 34, 0, 0, 0, 0, -9], [0, -237, 0, 0, 16, 0, 0, 0], [590, 0, 0, 0, 0, 0, -15, 0], [0, 0, 0, -127, 0, 63, 0, 0], [0, 0, -212, 0, 0, 0, 0, -22], [0, 29, 0, 0, -212, 0, 0, 0], [702, 0, 0, 0, 0, 0, -44, 0], [0, 0, 0, -155, 0, -21, 0, 0], [0, 0, 64, 0, 0, 0, 0, 15], [0, 0, 0, -55, 0, -69, 0, 0], [0, 0, 136, 0, 0, 0, 0, -36], [0, 0, -407, 0, 0, 0, 0, 2], [-670, 0, 0, 0, 0, 0, -25, 0], [-610, 0, 0, 0, 0, 0, 40, 0], [0, 7, 0, 0, 129, 0, 0, 0], [0, 0, 0, 183, 0, -28, 0, 0], [1310, 0, 0, 0, 0, 0, 5, 0], [0, 0, 11, 0, 0, 0, 0, 18], [0, 0, 0, -179, 0, 11, 0, 0], [-318, 0, 0, 0, 0, 0, -9, 0], [0, 0, 96, 0, 0, 0, 0, 3], [0, 0, -53, 0, 0, 0, 0, 63], [0, -305, 0, 0, 20, 0, 0, 0], [-802, 0, 0, 0, 0, 0, -10, 0], [0, -75, 0, 0, -105, 0, 0, 0], [0, 0, 0, -173, 0, -18, 0, 0], [0, -319, 0, 0, -48, 0, 0, 0], [0, 0, 168, 0, 0, 0, 0, 47], [670, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, -19], [-654, 0, 0, 0, 0, 0, -48, 0], [0, 0, 0, -63, 0, 52, 0, 0], [0, 5, 0, 0, 115, 0, 0, 0], [0, 0, 555, 0, 0, 0, 0, -6], [0, 257, 0, 0, 88, 0, 0, 0], [0, 0, 111, 0, 0, 0, 0, -25], [0, 0, 0, -123, 0, -73, 0, 0], [0, -85, 0, 0, 190, 0, 0, 0], [114, 0, 0, 0, 0, 0, 32, 0], [0, 0, 36, 0, 0, 0, 0, 20], [0, 101, 0, 0, -273, 0, 0, 0], [0, -419, 0, 0, 42, 0, 0, 0], [0, 0, 0, 73, 0, -56, 0, 0], [-598, 0, 0, 0, 0, 0, 66, 0], [0, 0, 176, 0, 0, 0, 0, -36], [322, 0, 0, 0, 0, 0, -84, 0], [0, 0, 0, -5, 0, -36, 0, 0], [0, 0, 0, 101, 0, -4, 0, 0], [0, 35, 0, 0, -239, 0, 0, 0], [0, 0, 0, -17, 0, -28, 0, 0], [-910, 0, 0, 0, 0, 0, 60, 0], [-262, 0, 0, 0, 0, 0, -56, 0], [0, 309, 0, 0, 58, 0, 0, 0], [-850, 0, 0, 0, 0, 0, -60, 0], [0, 0, -68, 0, 0, 0, 0, -11], [0, -29, 0, 0, -163, 0, 0, 0], [0, 0, 521, 0, 0, 0, 0, -21], [0, 179, 0, 0, 18, 0, 0, 0], [-310, 0, 0, 0, 0, 0, -64, 0], [0, 0, 0, 149, 0, 119, 0, 0], [0, -501, 0, 0, -57, 0, 0, 0], [0, 0, -127, 0, 0, 0, 0, -23], [0, 0, 0, -119, 0, -105, 0, 0], [498, 0, 0, 0, 0, 0, 58, 0], [0, 0, 0, -51, 0, -121, 0, 0], [-1050, 0, 0, 0, 0, 0, 20, 0], [0, 293, 0, 0, 7, 0, 0, 0], [0, 0, 659, 0, 0, 0, 0, 12], [0, 0, 0, 135, 0, -4, 0, 0], [0, 0, 210, 0, 0, 0, 0, -65], [-894, 0, 0, 0, 0, 0, -52, 0], [0, 0, 443, 0, 0, 0, 0, -27], [-2126, 0, 0, 0, 0, 0, -7, 0], [0, 0, -804, 0, 0, 0, 0, -15], [0, -197, 0, 0, -99, 0, 0, 0], [0, 59, 0, 0, -86, 0, 0, 0], [0, 0, -209, 0, 0, 0, 0, 64], [370, 0, 0, 0, 0, 0, -9, 0], [0, 0, 57, 0, 0, 0, 0, 19], [0, 0, 0, -95, 0, -21, 0, 0], [0, -229, 0, 0, -232, 0, 0, 0], [-414, 0, 0, 0, 0, 0, 58, 0], [0, 0, -406, 0, 0, 0, 0, 26], [0, 0, -201, 0, 0, 0, 0, 50], [0, 0, 0, -25, 0, -30, 0, 0], [0, -115, 0, 0, 190, 0, 0, 0], [0, 0, 0, -275, 0, -55, 0, 0], [0, 0, 253, 0, 0, 0, 0, 17], [-430, 0, 0, 0, 0, 0, -100, 0], [0, 0, 0, 249, 0, -57, 0, 0], [0, 0, -54, 0, 0, 0, 0, 68], [1502, 0, 0, 0, 0, 0, 46, 0], [0, 5, 0, 0, 315, 0, 0, 0], [0, 0, 0, -31, 0, -81, 0, 0], [0, 0, 34, 0, 0, 0, 0, 21], [0, 0, 0, -175, 0, -101, 0, 0], [0, 0, 0, -39, 0, -194, 0, 0], [0, 0, 585, 0, 0, 0, 0, 36], [0, -399, 0, 0, -288, 0, 0, 0], [-402, 0, 0, 0, 0, 0, 24, 0], [0, 0, -566, 0, 0, 0, 0, 41], [0, 0, 103, 0, 0, 0, 0, -37], [0, 0, 0, 159, 0, -86, 0, 0], [0, 0, 0, -59, 0, 126, 0, 0], [0, 0, -60, 0, 0, 0, 0, 26], [0, 73, 0, 0, -314, 0, 0, 0], [974, 0, 0, 0, 0, 0, 26, 0], [0, 0, 450, 0, 0, 0, 0, 9], [-34, 0, 0, 0, 0, 0, 28, 0], [0, -185, 0, 0, 295, 0, 0, 0], [0, 0, 0, -269, 0, -34, 0, 0], [0, 431, 0, 0, 122, 0, 0, 0], [0, 0, 0, -103, 0, -34, 0, 0], [0, 269, 0, 0, 113, 0, 0, 0], [162, 0, 0, 0, 0, 0, -4, 0], [0, 0, -99, 0, 0, 0, 0, 93], [0, 0, 0, -69, 0, -48, 0, 0], [0, 511, 0, 0, -78, 0, 0, 0], [0, -551, 0, 0, -192, 0, 0, 0], [946, 0, 0, 0, 0, 0, 3, 0], [0, 0, 0, -39, 0, 246, 0, 0], [0, 127, 0, 0, -171, 0, 0, 0], [50, 0, 0, 0, 0, 0, -86, 0], [0, 0, 0, -67, 0, 9, 0, 0], [0, -355, 0, 0, 75, 0, 0, 0], [0, -271, 0, 0, 28, 0, 0, 0], [0, 0, 0, 125, 0, 14, 0, 0], [-1410, 0, 0, 0, 0, 0, 0, 0], [0, 0, -585, 0, 0, 0, 0, -5], [2018, 0, 0, 0, 0, 0, 64, 0], [0, 0, 111, 0, 0, 0, 0, -40], [0, 0, 0, -131, 0, 123, 0, 0], [0, 197, 0, 0, 4, 0, 0, 0], [422, 0, 0, 0, 0, 0, 76, 0], [0, 0, 0, -217, 0, -42, 0, 0], [0, 0, -54, 0, 0, 0, 0, -10], [0, 0, -141, 0, 0, 0, 0, -94], [0, 0, 222, 0, 0, 0, 0, -81], [0, -301, 0, 0, 148, 0, 0, 0], [0, 0, 0, 109, 0, 93, 0, 0], [0, 0, -324, 0, 0, 0, 0, -86], [-2090, 0, 0, 0, 0, 0, -70, 0], [0, 129, 0, 0, 283, 0, 0, 0], [0, 0, -671, 0, 0, 0, 0, 26], [1774, 0, 0, 0, 0, 0, 42, 0], [0, -561, 0, 0, -203, 0, 0, 0], [0, 0, 0, -145, 0, 104, 0, 0], [962, 0, 0, 0, 0, 0, -94, 0], [0, 0, 0, 127, 0, -48, 0, 0], [0, 565, 0, 0, 40, 0, 0, 0], [0, -113, 0, 0, -247, 0, 0, 0], [0, 0, 21, 0, 0, 0, 0, 89], [0, -371, 0, 0, 13, 0, 0, 0], [0, 0, 0, -59, 0, 91, 0, 0], [0, 0, 0, -383, 0, -69, 0, 0], [1658, 0, 0, 0, 0, 0, -76, 0], [0, -277, 0, 0, 81, 0, 0, 0], [0, 0, -353, 0, 0, 0, 0, 53]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1152_b_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1152_3_b_j();".
// 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_b_j(:prec:=8)
    chi := MakeCharacter_1152_b();
    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_b_j();".
// 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_b_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1152_b();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<5,R![64, 0, 80, 0, 1]>,<7,R![8, 0, 1]>,<17,R![-380, -4, 1]>],Snew);
    return Vf;
end function;