
// Make newform 1152.3.g.c in Magma, downloaded from the LMFDB on 16 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_c();".
// 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_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 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, 2, -4, 2, 0, -2, 2, 0], [0, 4, 0, 4, 0, 4, 0, -8], [0, -6, 0, 6, 0, 2, -2, -4], [-4, 0, 0, 0, 8, 0, 0, 0], [0, 4, 8, 4, 0, -4, -4, 0], [0, 2, 0, -2, 0, -6, -2, -4], [0, 0, 0, 0, 0, 0, -8, 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_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], [-2, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 1, 0, 0, 1, -1], [-6, 0, 1, 0, 0, -1, 0, 0], [-2, 0, 2, 0, 0, 1, 0, 0], [0, 0, 0, -2, 1, 0, 0, -1], [0, 0, 0, 2, 0, 0, 0, 0], [-10, -5, -2, 0, 0, 0, 0, 0], [0, 0, 0, -2, 2, 0, -3, 2], [2, -6, 3, 0, 0, 1, 0, 0], [-10, 0, 2, 0, 0, -5, 0, 0], [0, 0, 0, -4, -3, 0, -2, 5], [0, 0, 0, 4, 2, 0, 2, 0], [22, 3, -2, 0, 0, -4, 0, 0], [0, 0, 0, -2, -3, 0, 2, 8], [34, -2, -1, 0, 0, -7, 0, 0], [0, 0, 0, -6, 1, 0, 6, 0], [0, 0, 0, 2, -6, 0, 0, -8], [-2, -20, 2, 0, 0, -2, 0, 0], [0, 0, 0, 10, -2, 0, 1, -4], [0, 0, 0, -5, 0, 0, -9, -5], [30, 8, -4, 0, 0, -2, 0, 0], [50, -24, 0, 0, 0, -10, 0, 0], [-66, -5, 2, 0, 0, -10, 0, 0], [0, 0, 0, 12, 16, 0, 1, -10], [0, 0, 0, -6, 5, 0, -6, 10], [-70, -4, -3, 0, 0, -9, 0, 0], [-42, -8, -8, 0, 0, -6, 0, 0], [0, 0, 0, 10, 2, 0, -9, 10], [0, 0, 0, -12, -3, 0, 12, -8], [22, -8, -2, 0, 0, 1, 0, 0], [0, 0, 0, 2, 11, 0, 14, -4], [78, -15, 8, 0, 0, 0, 0, 0], [0, 0, 0, 4, -16, 0, 7, -18], [42, -6, 3, 0, 0, 5, 0, 0], [0, 0, 0, 8, -9, 0, 18, -15], [0, 0, 0, 2, -32, 0, -10, 0], [-74, 9, 4, 0, 0, -10, 0, 0], [0, 0, 0, 10, -5, 0, -10, -16], [34, 28, 13, 0, 0, 3, 0, 0], [0, 0, 0, 12, -18, 0, -4, 12], [-18, -44, -2, 0, 0, 2, 0, 0], [-74, 7, -6, 0, 0, 20, 0, 0], [0, 0, 0, -12, 28, 0, -11, 6], [0, 0, 0, -10, -7, 0, -14, 0], [0, 0, 0, 2, 18, 0, 15, 0], [0, 0, 0, 17, 2, 0, 5, -15], [-94, 16, 9, 0, 0, -9, 0, 0], [38, -16, -8, 0, 0, 18, 0, 0], [0, 0, 0, 8, 30, 0, 28, 0], [70, 12, -26, 0, 0, 12, 0, 0], [0, 0, 0, 25, 4, 0, -7, 15], [62, 8, 8, 0, 0, -16, 0, 0], [0, 0, 0, 6, -26, 0, 18, -40], [-98, 27, -22, 0, 0, 2, 0, 0], [0, 0, 0, -34, -2, 0, -13, 0], [210, 12, 5, 0, 0, -5, 0, 0], [118, -16, 12, 0, 0, 4, 0, 0], [0, 0, 0, 16, -3, 0, -24, 0], [-218, -37, -2, 0, 0, -8, 0, 0], [0, 0, 0, 2, 21, 0, -2, 0], [0, 0, 0, 42, 22, 0, -14, -24], [142, 36, -2, 0, 0, 10, 0, 0], [222, 23, -2, 0, 0, -2, 0, 0], [0, 0, 0, 18, 11, 0, -30, 22], [-114, -4, -6, 0, 0, 6, 0, 0], [0, 0, 0, 7, -30, 0, -13, 15], [-30, 46, -1, 0, 0, 21, 0, 0], [-74, -16, -16, 0, 0, -6, 0, 0], [0, 0, 0, -38, -38, 0, 16, 4], [0, 0, 0, -22, -14, 0, 25, 30], [106, 22, -41, 0, 0, 1, 0, 0], [0, 0, 0, 26, -9, 0, -12, -21], [0, 0, 0, -20, 14, 0, -36, 0], [-298, 25, 4, 0, 0, 10, 0, 0], [154, -26, -9, 0, 0, 13, 0, 0], [46, -80, -10, 0, 0, -5, 0, 0], [-14, 24, 16, 0, 0, 34, 0, 0], [0, 0, 0, -19, 62, 0, -15, -19], [-206, -52, -3, 0, 0, 23, 0, 0], [0, 0, 0, -28, 2, 0, 46, -12], [66, 8, 44, 0, 0, -8, 0, 0], [0, 0, 0, -8, -16, 0, 5, -22], [0, 0, 0, -61, 14, 0, -41, 15], [-66, 88, -14, 0, 0, 53, 0, 0], [-142, 24, 32, 0, 0, 6, 0, 0], [-74, -71, 4, 0, 0, 34, 0, 0], [0, 0, 0, 54, -10, 0, 23, -30], [0, 0, 0, 29, 18, 0, -15, 45], [0, 0, 0, 4, -28, 0, -2, 0], [0, 0, 0, 0, 20, 0, 31, 0], [0, 0, 0, -12, 43, 0, 24, -34], [0, 0, 0, 40, 35, 0, 0, 0], [0, 0, 0, -66, 18, 0, -28, 20], [102, -105, -22, 0, 0, -40, 0, 0], [158, 72, 22, 0, 0, -13, 0, 0], [0, 0, 0, 6, 71, 0, 16, -45], [98, 36, -19, 0, 0, -49, 0, 0], [0, 0, 0, -4, -69, 0, -14, -25], [-50, 53, -60, 0, 0, 12, 0, 0], [0, 0, 0, -63, -10, 0, 33, 15], [-58, -112, -38, 0, 0, -37, 0, 0], [0, 0, 0, -60, 9, 0, -72, -6], [-90, 52, -50, 0, 0, -6, 0, 0], [0, 0, 0, -8, -49, 0, 28, -30], [374, -24, -24, 0, 0, 26, 0, 0], [0, 0, 0, 82, -20, 0, 52, -44], [-26, -108, -26, 0, 0, 22, 0, 0], [0, 0, 0, -22, -2, 0, -41, -10], [-54, -114, -41, 0, 0, -43, 0, 0], [-154, -104, 4, 0, 0, -48, 0, 0], [0, 0, 0, -8, -47, 0, -32, -20], [0, 0, 0, -4, 44, 0, -61, 64], [-106, -56, 38, 0, 0, -11, 0, 0], [0, 0, 0, -20, 83, 0, 50, 35], [0, 0, 0, 14, 32, 0, 76, 20], [-90, -123, 40, 0, 0, -54, 0, 0], [0, 0, 0, 20, 33, 0, 16, 18], [362, -150, 67, 0, 0, 5, 0, 0], [-270, -8, 60, 0, 0, -44, 0, 0], [-450, -107, -60, 0, 0, 16, 0, 0], [0, 0, 0, 17, 64, 0, -59, 25], [0, 0, 0, -108, 47, 0, 6, 1], [126, 47, -34, 0, 0, 62, 0, 0], [-414, 112, 25, 0, 0, -13, 0, 0], [0, 0, 0, -8, -4, 0, 54, -64], [0, 0, 0, -12, 16, 0, -89, 50], [386, -120, 9, 0, 0, -21, 0, 0], [0, 0, 0, -44, -37, 0, -8, 90], [0, 0, 0, 2, 56, 0, -118, 80], [0, 0, 0, 18, 70, 0, -7, -52], [290, 0, -15, 0, 0, -81, 0, 0], [-258, -56, 66, 0, 0, -51, 0, 0], [-274, 36, 22, 0, 0, 46, 0, 0], [-1090, -9, 30, 0, 0, 10, 0, 0], [0, 0, 0, -50, -23, 0, -28, 5], [62, 29, 28, 0, 0, -64, 0, 0], [-42, -80, -10, 0, 0, 105, 0, 0], [0, 0, 0, -14, -133, 0, -40, -55], [334, -41, -2, 0, 0, -66, 0, 0], [0, 0, 0, 108, 64, 0, -9, -20], [0, 0, 0, 22, 5, 0, -10, -90], [138, 12, -3, 0, 0, 47, 0, 0], [0, 0, 0, -14, 58, 0, -68, 64], [202, -78, -77, 0, 0, -59, 0, 0], [550, -216, 50, 0, 0, 27, 0, 0], [0, 0, 0, 24, 5, 0, -106, 3], [0, 0, 0, -100, 82, 0, -36, -20], [-670, -58, -65, 0, 0, 5, 0, 0], [30, -8, -32, 0, 0, 52, 0, 0], [0, 0, 0, 28, 95, 0, 78, 5], [0, 0, 0, 106, -106, 0, -18, 40], [0, 0, 0, -12, 125, 0, -94, 95], [0, 0, 0, 0, -2, 0, -44, -92], [0, 0, 0, 76, 76, 0, 103, 12], [1230, 8, -10, 0, 0, -17, 0, 0], [242, 96, 48, 0, 0, 8, 0, 0], [-42, -127, -44, 0, 0, -2, 0, 0], [0, 0, 0, -94, 3, 0, -114, 80], [-386, 168, -74, 0, 0, 43, 0, 0], [0, 0, 0, 52, -52, 0, 21, -60], [0, 0, 0, 81, -80, 0, -99, -43], [302, 56, -42, 0, 0, -113, 0, 0], [0, 0, 0, -6, -66, 0, -106, -40], [0, 0, 0, 30, -46, 0, 13, -136], [-350, 54, 55, 0, 0, -7, 0, 0], [-558, 88, 48, 0, 0, 18, 0, 0], [982, -163, 8, 0, 0, -18, 0, 0], [0, 0, 0, 40, 19, 0, -52, 74], [394, -46, -53, 0, 0, -71, 0, 0], [0, 0, 0, -38, 108, 0, -22, 44], [530, -48, 0, 0, 0, -80, 0, 0], [0, 0, 0, -118, -38, 0, -19, 56], [-570, -48, -60, 0, 0, -68, 0, 0], [0, 0, 0, -88, 37, 0, 96, 80], [126, 137, -96, 0, 0, 72, 0, 0], [0, 0, 0, 28, -104, 0, 25, 130], [306, -6, -29, 0, 0, 69, 0, 0], [0, 0, 0, 86, -22, 0, 93, 20], [0, 0, 0, 47, -16, 0, 75, -105], [-214, 56, -31, 0, 0, 11, 0, 0], [758, -192, 12, 0, 0, 44, 0, 0], [0, 0, 0, 56, -118, 0, -16, 120], [630, 149, 8, 0, 0, 74, 0, 0], [-622, 0, 97, 0, 0, 95, 0, 0], [0, 0, 0, -16, -113, 0, -96, -20], [-666, -20, -42, 0, 0, -20, 0, 0], [0, 0, 0, 72, 28, 0, 128, -20], [-254, -192, -16, 0, 0, -36, 0, 0], [0, 0, 0, -42, -175, 0, 2, 60], [0, 0, 0, 24, -53, 0, 48, 24], [246, -123, -88, 0, 0, 22, 0, 0], [0, 0, 0, 120, 153, 0, -24, -80], [-954, -56, 84, 0, 0, -88, 0, 0], [-442, 292, -34, 0, 0, 2, 0, 0], [-334, 32, -71, 0, 0, -29, 0, 0], [-938, -64, 68, 0, 0, 64, 0, 0], [0, 0, 0, -10, 6, 0, -10, -20], [-306, -23, -96, 0, 0, -28, 0, 0], [0, 0, 0, -58, 78, 0, 63, 34], [106, 188, 109, 0, 0, 19, 0, 0], [702, 156, -94, 0, 0, 86, 0, 0], [0, 0, 0, 143, 110, 0, 23, -27], [182, 111, -22, 0, 0, 72, 0, 0], [0, 0, 0, -230, 46, 0, -53, 40], [0, 0, 0, -35, -162, 0, -51, -85], [-90, 280, 72, 0, 0, -10, 0, 0], [0, 0, 0, -76, 205, 0, -6, 23], [398, 84, 22, 0, 0, 62, 0, 0], [-226, 189, 12, 0, 0, -96, 0, 0], [0, 0, 0, 8, 60, 0, 21, -250], [0, 0, 0, 94, 5, 0, -22, -60], [0, 0, 0, 42, 78, 0, 68, -64], [146, -216, -84, 0, 0, 64, 0, 0], [0, 0, 0, -134, 46, 0, -83, 10], [-138, -96, 78, 0, 0, 109, 0, 0], [0, 0, 0, -42, 32, 0, -150, -20], [414, -127, 56, 0, 0, 12, 0, 0], [-470, -188, -11, 0, 0, 27, 0, 0], [0, 0, 0, -56, -68, 0, 153, 20], [-586, -24, -134, 0, 0, 11, 0, 0], [0, 0, 0, 174, 62, 0, 139, -80], [0, 0, 0, -53, 56, 0, 71, -45], [186, 58, 19, 0, 0, 73, 0, 0], [110, -176, 20, 0, 0, 10, 0, 0], [0, 0, 0, -124, -40, 0, 166, 44], [0, 0, 0, 76, 0, 0, 33, -240], [0, 0, 0, -64, -9, 0, -132, 166], [266, -244, -91, 0, 0, 19, 0, 0], [0, 0, 0, -8, -13, 0, -74, 111], [0, 0, 0, 2, -22, 0, -37, 74], [998, -32, 60, 0, 0, -72, 0, 0], [0, 0, 0, 132, -59, 0, -38, 175], [0, 0, 0, -72, 8, 0, 170, 100], [-558, 104, -24, 0, 0, 34, 0, 0], [686, -31, 64, 0, 0, 12, 0, 0], [0, 0, 0, -7, 44, 0, -59, -59], [0, 0, 0, -114, -148, 0, -100, 68], [0, 0, 0, -71, -122, 0, 73, -105], [0, 0, 0, 10, -241, 0, 18, -2], [0, 0, 0, 8, 24, 0, -29, 50], [458, 114, -109, 0, 0, 109, 0, 0], [118, -88, -108, 0, 0, 68, 0, 0], [0, 0, 0, 54, -114, 0, -24, 76], [0, 0, 0, -98, 94, 0, 97, -160], [0, 0, 0, 46, 91, 0, -122, -22], [0, 0, 0, 114, -141, 0, 42, 38], [0, 0, 0, 60, -28, 0, -208, 100], [634, 60, 21, 0, 0, 55, 0, 0], [-2026, 24, 56, 0, 0, -6, 0, 0], [0, 0, 0, -2, 8, 0, 20, -260], [594, 256, 32, 0, 0, 116, 0, 0], [726, -117, -66, 0, 0, 12, 0, 0], [0, 0, 0, -106, 135, 0, -66, -30], [634, 236, -19, 0, 0, 71, 0, 0], [0, 0, 0, -12, 49, 0, 0, 170], [-122, 7, 122, 0, 0, 16, 0, 0], [-1038, 56, -12, 0, 0, -136, 0, 0], [0, 0, 0, 18, -18, 0, 55, 170], [0, 0, 0, -110, -121, 0, -18, -40], [1306, -28, -3, 0, 0, 107, 0, 0], [-1126, -78, -109, 0, 0, -59, 0, 0], [1766, 208, 114, 0, 0, -25, 0, 0], [0, 0, 0, 18, -95, 0, -62, -150], [702, -139, 124, 0, 0, -4, 0, 0], [-650, -184, -48, 0, 0, -154, 0, 0], [0, 0, 0, -194, 99, 0, -12, 85], [-354, -103, 64, 0, 0, 120, 0, 0], [-1886, 6, 111, 0, 0, -39, 0, 0], [0, 0, 0, 12, -17, 0, 16, 110], [-174, -192, 24, 0, 0, -136, 0, 0], [0, 0, 0, 134, 210, 0, 9, -66], [306, -192, 64, 0, 0, 112, 0, 0], [0, 0, 0, 136, -172, 0, -95, 100], [0, 0, 0, -89, 218, 0, -89, -15], [490, -242, 47, 0, 0, 133, 0, 0], [822, -332, 30, 0, 0, -122, 0, 0], [0, 0, 0, 62, 15, 0, 182, 18], [0, 0, 0, 68, -8, 0, -26, 140], [0, 0, 0, -76, 204, 0, -23, 6], [0, 0, 0, 2, 200, 0, 20, -40], [-214, 22, 15, 0, 0, 117, 0, 0], [0, 0, 0, -154, -89, 0, 180, -95], [0, 0, 0, -76, 28, 0, -40, 96], [518, -388, -18, 0, 0, 200, 0, 0], [-1346, 157, -44, 0, 0, 48, 0, 0], [0, 0, 0, -12, -4, 0, -45, -284], [438, 400, -16, 0, 0, 90, 0, 0], [182, 5, 40, 0, 0, -150, 0, 0], [0, 0, 0, 38, -257, 0, 82, -60], [-1122, -368, 12, 0, 0, -46, 0, 0], [0, 0, 0, 98, -83, 0, -58, -244], [-190, -102, -5, 0, 0, -107, 0, 0], [-1466, 321, -20, 0, 0, 106, 0, 0], [0, 0, 0, 90, -14, 0, -133, 160], [190, 67, 50, 0, 0, 66, 0, 0], [0, 0, 0, 63, -166, 0, 71, -123], [0, 0, 0, -130, -155, 0, -52, 65], [238, -172, -58, 0, 0, -234, 0, 0], [454, 269, 16, 0, 0, -82, 0, 0], [0, 0, 0, -118, -254, 0, 109, 4]];
    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_c();".
// 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_c(: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_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_1152_3_g_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1152_g();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<5,R![-128, -128, -16, 8, 1]>,<13,R![-35696, -6432, -136, 24, 1]>],Snew);
    return Vf;
end function;