
// Make newform 1792.3.d.f in Magma, downloaded from the LMFDB on 30 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1792_d();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1792_d_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_1792_3_d_f();".
// 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_1792_3_d_f();".
// 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 := [49, 0, -49, 0, 42, 0, -7, 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, 7, 0, -42, 0, 6, 0, -1], [0, 91, 0, -42, 0, 6, 0, -1], [-49, 0, 70, 0, -14, 0, 2, 0], [196, 0, 0, 0, 0, 0, 2, 0], [0, 238, 0, -112, 0, 20, 0, -2], [0, 70, 0, -336, 0, 60, 0, -10], [-56, 0, 84, 0, -12, 0, 2, 0]];
    Rf_basisdens := [1, 21, 21, 21, 21, 21, 21, 3];
    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_1792_d();"
function MakeCharacter_1792_d()
    N := 1792;
    order := 2;
    char_gens := [1023, 1541, 1025];
    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_1792_d_Hecke();"
function MakeCharacter_1792_d_Hecke(Kf)
    N := 1792;
    order := 2;
    char_gens := [1023, 1541, 1025];
    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, -1, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, -2, 0, 0], [-6, 0, 0, 0, 2, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 0, -1], [0, 0, 2, 0, 0, -4, 0, 0], [0, 0, 0, -4, 0, 0, 0, 2], [0, 0, 6, 0, 0, 0, 0, 0], [2, 0, 0, 0, 2, 0, 0, 0], [0, 6, 0, 0, 0, 0, 3, 0], [0, 0, 0, 8, 0, 0, 0, 0], [0, 0, -4, 0, 0, -8, 0, 0], [0, 9, 0, 0, 0, 0, -2, 0], [0, 0, 3, 0, 0, 4, 0, 0], [0, -8, 0, 0, 0, 0, -1, 0], [0, 0, 0, -28, 0, 0, 0, -2], [-50, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 20, 0, 0, 0, -2], [0, 13, 0, 0, 0, 0, 6, 0], [-46, 0, 0, 0, 4, 0, 0, 0], [30, 0, 0, 0, -4, 0, 0, 0], [0, 0, -1, 0, 0, -10, 0, 0], [0, 0, 0, -52, 0, 0, 0, -2], [0, 12, 0, 0, 0, 0, -3, 0], [0, 0, -6, 0, 0, -4, 0, 0], [-12, 0, 0, 0, -15, 0, 0, 0], [0, 0, 0, -14, 0, 0, 0, 1], [0, -7, 0, 0, 0, 0, 14, 0], [118, 0, 0, 0, -4, 0, 0, 0], [0, -37, 0, 0, 0, 0, 12, 0], [0, 0, 20, 0, 0, 4, 0, 0], [0, 0, 0, -22, 0, 0, 0, -3], [0, 0, 21, 0, 0, 18, 0, 0], [0, 62, 0, 0, 0, 0, 9, 0], [0, 0, 0, -32, 0, 0, 0, 0], [0, 0, -11, 0, 0, -6, 0, 0], [0, -20, 0, 0, 0, 0, -9, 0], [0, 0, 25, 0, 0, 8, 0, 0], [0, 0, 0, -96, 0, 0, 0, 4], [20, 0, 0, 0, -13, 0, 0, 0], [0, 0, 0, 0, 0, 12, 0, 0], [0, 0, 0, -28, 0, 0, 0, -6], [0, -48, 0, 0, 0, 0, -1, 0], [0, 0, 0, 4, 0, 0, 0, -14], [0, -75, 0, 0, 0, 0, -8, 0], [0, 0, -27, 0, 0, 18, 0, 0], [-150, 0, 0, 0, -20, 0, 0, 0], [0, 0, 0, -98, 0, 0, 0, 7], [358, 0, 0, 0, 8, 0, 0, 0], [0, -1, 0, 0, 0, 0, -10, 0], [10, 0, 0, 0, -4, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 6], [0, 0, 9, 0, 0, -18, 0, 0], [0, 0, 0, -60, 0, 0, 0, 10], [0, 0, -8, 0, 0, -52, 0, 0], [226, 0, 0, 0, -32, 0, 0, 0], [0, -3, 0, 0, 0, 0, -4, 0], [0, 0, -1, 0, 0, -30, 0, 0], [0, 9, 0, 0, 0, 0, 26, 0], [0, 0, 0, 184, 0, 0, 0, 0], [74, 0, 0, 0, -42, 0, 0, 0], [0, 0, -16, 0, 0, 24, 0, 0], [0, 78, 0, 0, 0, 0, 7, 0], [-432, 0, 0, 0, -17, 0, 0, 0], [0, -26, 0, 0, 0, 0, 7, 0], [0, 0, 25, 0, 0, -36, 0, 0], [454, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 94, 0, 0, 0, -1], [0, 0, 0, 172, 0, 0, 0, -10], [0, 0, -28, 0, 0, -52, 0, 0], [0, 10, 0, 0, 0, 0, 27, 0], [0, 0, 0, -112, 0, 0, 0, 12], [0, 0, 70, 0, 0, 4, 0, 0], [0, 0, -59, 0, 0, -16, 0, 0], [-32, 0, 0, 0, 49, 0, 0, 0], [-202, 0, 0, 0, -52, 0, 0, 0], [0, 59, 0, 0, 0, 0, -8, 0], [0, 0, 40, 0, 0, -52, 0, 0], [0, 0, 0, 58, 0, 0, 0, 13], [2, 0, 0, 0, 54, 0, 0, 0], [0, 0, 0, 28, 0, 0, 0, 10], [0, -24, 0, 0, 0, 0, 49, 0], [-282, 0, 0, 0, -36, 0, 0, 0], [-228, 0, 0, 0, -49, 0, 0, 0], [0, 0, 97, 0, 0, 4, 0, 0], [0, 0, 0, 88, 0, 0, 0, 24], [0, -159, 0, 0, 0, 0, 4, 0], [0, 0, 0, 124, 0, 0, 0, -6], [0, 0, 0, -226, 0, 0, 0, -9], [0, -160, 0, 0, 0, 0, -31, 0], [0, 88, 0, 0, 0, 0, -1, 0], [0, 0, 0, 164, 0, 0, 0, 22], [0, 0, 53, 0, 0, -52, 0, 0], [-202, 0, 0, 0, -76, 0, 0, 0], [0, 157, 0, 0, 0, 0, 10, 0], [0, 0, -4, 0, 0, -96, 0, 0], [0, 66, 0, 0, 0, 0, 33, 0], [0, 0, -56, 0, 0, -60, 0, 0], [0, 59, 0, 0, 0, 0, -14, 0], [-592, 0, 0, 0, 9, 0, 0, 0], [0, -6, 0, 0, 0, 0, -1, 0], [454, 0, 0, 0, 42, 0, 0, 0], [0, 107, 0, 0, 0, 0, 20, 0], [-214, 0, 0, 0, 20, 0, 0, 0], [0, 0, 0, 184, 0, 0, 0, 24], [26, 0, 0, 0, 120, 0, 0, 0], [0, 0, 0, 296, 0, 0, 0, 12], [0, 0, 2, 0, 0, 48, 0, 0], [16, 0, 0, 0, -1, 0, 0, 0], [0, -15, 0, 0, 0, 0, -68, 0], [0, 0, 0, -24, 0, 0, 0, 0], [328, 0, 0, 0, -43, 0, 0, 0], [0, 91, 0, 0, 0, 0, -42, 0], [0, 0, 0, -68, 0, 0, 0, -18], [0, 0, -34, 0, 0, 144, 0, 0], [0, 242, 0, 0, 0, 0, 13, 0], [0, 0, -13, 0, 0, -70, 0, 0], [-674, 0, 0, 0, 8, 0, 0, 0], [0, 0, 113, 0, 0, 4, 0, 0], [0, -8, 0, 0, 0, 0, 9, 0], [0, -191, 0, 0, 0, 0, 10, 0], [0, 0, -90, 0, 0, -28, 0, 0], [0, 0, -10, 0, 0, 32, 0, 0], [0, 0, 0, -64, 0, 0, 0, 36], [0, 0, 0, -248, 0, 0, 0, -4], [0, 0, 127, 0, 0, 48, 0, 0], [0, 102, 0, 0, 0, 0, -23, 0], [0, 0, 0, -26, 0, 0, 0, 27], [0, 0, 0, 154, 0, 0, 0, 5], [0, 0, 122, 0, 0, 0, 0, 0], [130, 0, 0, 0, -110, 0, 0, 0], [702, 0, 0, 0, 84, 0, 0, 0], [0, 0, -145, 0, 0, -28, 0, 0], [0, 113, 0, 0, 0, 0, -60, 0], [0, 0, 1, 0, 0, -78, 0, 0], [692, 0, 0, 0, 75, 0, 0, 0], [0, 69, 0, 0, 0, 0, 36, 0], [0, 0, 192, 0, 0, 80, 0, 0], [0, 0, 0, 100, 0, 0, 0, -10], [0, 60, 0, 0, 0, 0, 17, 0], [0, 0, 115, 0, 0, -72, 0, 0], [0, 0, 0, 348, 0, 0, 0, -10], [0, 0, 45, 0, 0, -26, 0, 0], [-370, 0, 0, 0, 112, 0, 0, 0], [0, -13, 0, 0, 0, 0, 22, 0], [0, 0, 0, -64, 0, 0, 0, 4], [0, 0, 110, 0, 0, -52, 0, 0], [446, 0, 0, 0, -42, 0, 0, 0], [0, 124, 0, 0, 0, 0, 51, 0], [0, 0, 0, 160, 0, 0, 0, 32], [0, 108, 0, 0, 0, 0, -3, 0], [0, 0, 0, -202, 0, 0, 0, -5], [0, 0, 0, -156, 0, 0, 0, 46], [-542, 0, 0, 0, 94, 0, 0, 0], [838, 0, 0, 0, -58, 0, 0, 0], [0, 0, 7, 0, 0, -86, 0, 0], [0, -54, 0, 0, 0, 0, 9, 0], [-506, 0, 0, 0, 28, 0, 0, 0], [0, 0, 0, -458, 0, 0, 0, -5], [0, 225, 0, 0, 0, 0, 50, 0], [-442, 0, 0, 0, 148, 0, 0, 0], [0, 0, 0, 252, 0, 0, 0, 14], [0, 0, 0, -340, 0, 0, 0, 26], [0, 0, -25, 0, 0, 132, 0, 0], [-660, 0, 0, 0, -49, 0, 0, 0], [0, 0, 1, 0, 0, 66, 0, 0], [0, 360, 0, 0, 0, 0, -11, 0], [0, 0, -115, 0, 0, -112, 0, 0], [0, 0, 0, -156, 0, 0, 0, 54], [274, 0, 0, 0, -40, 0, 0, 0], [0, 0, 0, -200, 0, 0, 0, -24], [642, 0, 0, 0, 60, 0, 0, 0], [0, 364, 0, 0, 0, 0, -15, 0], [0, 0, 186, 0, 0, -16, 0, 0], [0, 0, 0, 96, 0, 0, 0, -52], [0, 0, 19, 0, 0, -138, 0, 0], [0, 0, 0, -102, 0, 0, 0, -43], [0, -81, 0, 0, 0, 0, 70, 0], [0, 0, 210, 0, 0, 116, 0, 0], [-634, 0, 0, 0, -42, 0, 0, 0], [0, 0, 0, -82, 0, 0, 0, -65], [0, 0, -11, 0, 0, -146, 0, 0], [0, 0, 204, 0, 0, -72, 0, 0], [0, 153, 0, 0, 0, 0, -144, 0], [38, 0, 0, 0, -28, 0, 0, 0], [0, 0, 0, 52, 0, 0, 0, -58], [-634, 0, 0, 0, -110, 0, 0, 0], [0, -208, 0, 0, 0, 0, -75, 0], [0, 180, 0, 0, 0, 0, -49, 0], [0, 0, 49, 0, 0, -78, 0, 0], [0, -84, 0, 0, 0, 0, 123, 0], [650, 0, 0, 0, -96, 0, 0, 0], [512, 0, 0, 0, -41, 0, 0, 0], [0, 0, -158, 0, 0, 228, 0, 0], [390, 0, 0, 0, 98, 0, 0, 0], [0, 0, 0, -92, 0, 0, 0, -10], [0, 0, -260, 0, 0, -108, 0, 0], [0, 0, 0, -396, 0, 0, 0, 30], [0, 0, -13, 0, 0, -152, 0, 0], [-778, 0, 0, 0, -94, 0, 0, 0], [0, -203, 0, 0, 0, 0, 62, 0], [0, 0, -45, 0, 0, 102, 0, 0], [0, 0, 0, -524, 0, 0, 0, 14], [0, -66, 0, 0, 0, 0, 57, 0], [-1636, 0, 0, 0, 61, 0, 0, 0], [0, 23, 0, 0, 0, 0, 86, 0], [-760, 0, 0, 0, 5, 0, 0, 0], [0, 0, 107, 0, 0, -180, 0, 0], [0, 0, 0, -638, 0, 0, 0, 25], [0, -211, 0, 0, 0, 0, -32, 0], [0, 0, 0, 484, 0, 0, 0, -18], [802, 0, 0, 0, -70, 0, 0, 0], [0, 0, 0, 152, 0, 0, 0, 32], [1030, 0, 0, 0, -96, 0, 0, 0], [0, 0, 0, -288, 0, 0, 0, -68], [0, 0, -82, 0, 0, 184, 0, 0], [0, 0, -274, 0, 0, -20, 0, 0], [0, 0, 0, -180, 0, 0, 0, 82], [-186, 0, 0, 0, -140, 0, 0, 0], [0, 0, 0, 86, 0, 0, 0, -77], [0, 33, 0, 0, 0, 0, -132, 0], [0, 0, 262, 0, 0, 48, 0, 0], [-662, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 542, 0, 0, 0, 39], [0, 0, 0, -284, 0, 0, 0, -26], [0, -270, 0, 0, 0, 0, -97, 0], [0, 0, -162, 0, 0, -12, 0, 0], [0, -129, 0, 0, 0, 0, 100, 0], [0, 0, 0, -168, 0, 0, 0, -56], [-454, 0, 0, 0, 116, 0, 0, 0], [0, -387, 0, 0, 0, 0, -120, 0], [0, 0, 0, 300, 0, 0, 0, 14], [-654, 0, 0, 0, 126, 0, 0, 0], [0, 0, -172, 0, 0, 120, 0, 0], [0, 504, 0, 0, 0, 0, 65, 0], [0, 0, 0, -88, 0, 0, 0, 8], [0, -350, 0, 0, 0, 0, -35, 0], [0, 117, 0, 0, 0, 0, -66, 0], [0, 0, 0, -180, 0, 0, 0, -14], [0, 0, 68, 0, 0, 36, 0, 0], [166, 0, 0, 0, -38, 0, 0, 0], [0, 0, 0, 572, 0, 0, 0, -34], [0, 0, 0, 400, 0, 0, 0, 56], [0, -459, 0, 0, 0, 0, -38, 0], [0, -186, 0, 0, 0, 0, 115, 0], [0, 0, 0, 308, 0, 0, 0, -2], [0, 0, 124, 0, 0, -156, 0, 0], [-2146, 0, 0, 0, 110, 0, 0, 0], [0, 0, 0, -448, 0, 0, 0, -12], [-310, 0, 0, 0, -160, 0, 0, 0], [0, 0, 27, 0, 0, -112, 0, 0], [0, 68, 0, 0, 0, 0, 67, 0], [0, 0, -202, 0, 0, -8, 0, 0], [0, 395, 0, 0, 0, 0, 60, 0], [0, 0, -13, 0, 0, 288, 0, 0], [1614, 0, 0, 0, -40, 0, 0, 0], [0, 0, 0, -642, 0, 0, 0, 15], [0, -106, 0, 0, 0, 0, -99, 0], [0, 0, 267, 0, 0, 112, 0, 0], [0, 0, -209, 0, 0, 168, 0, 0], [-1938, 0, 0, 0, -116, 0, 0, 0], [0, 215, 0, 0, 0, 0, 6, 0], [0, 0, -140, 0, 0, -180, 0, 0], [138, 0, 0, 0, 0, 0, 0, 0], [0, -28, 0, 0, 0, 0, 85, 0], [0, 0, -142, 0, 0, 0, 0, 0], [0, 0, -115, 0, 0, 106, 0, 0], [0, 546, 0, 0, 0, 0, 37, 0], [1266, 0, 0, 0, 60, 0, 0, 0], [0, 0, 0, -78, 0, 0, 0, 65], [586, 0, 0, 0, 276, 0, 0, 0], [0, 0, 0, 8, 0, 0, 0, 32], [0, -290, 0, 0, 0, 0, -73, 0], [0, 0, -152, 0, 0, 0, 0, 0], [844, 0, 0, 0, -91, 0, 0, 0], [0, 585, 0, 0, 0, 0, -78, 0], [0, 0, 0, 780, 0, 0, 0, -26], [0, 0, 0, 636, 0, 0, 0, 58], [0, 0, 0, 184, 0, 0, 0, -36], [0, 0, -169, 0, 0, -78, 0, 0], [0, 333, 0, 0, 0, 0, 0, 0], [0, 0, 0, 398, 0, 0, 0, -33], [1350, 0, 0, 0, 68, 0, 0, 0], [0, 0, 144, 0, 0, -212, 0, 0], [0, 0, 0, 120, 0, 0, 0, 76], [-338, 0, 0, 0, 206, 0, 0, 0], [0, 0, -212, 0, 0, 76, 0, 0], [0, -303, 0, 0, 0, 0, 46, 0], [256, 0, 0, 0, -57, 0, 0, 0], [0, 489, 0, 0, 0, 0, -44, 0], [0, 0, 264, 0, 0, 24, 0, 0], [0, 0, -51, 0, 0, 304, 0, 0], [0, 0, 0, 44, 0, 0, 0, -18], [0, 0, -51, 0, 0, -26, 0, 0], [0, 147, 0, 0, 0, 0, 130, 0], [0, -373, 0, 0, 0, 0, 148, 0], [998, 0, 0, 0, 172, 0, 0, 0], [0, 0, -126, 0, 0, -208, 0, 0], [0, 0, 0, -720, 0, 0, 0, 36]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1792_d_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1792_3_d_f();".
// 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_1792_3_d_f(:prec:=8)
    chi := MakeCharacter_1792_d();
    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_1792_3_d_f();".
// 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_1792_3_d_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1792_d();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<3,R![112, 0, 28, 0, 1]>,<5,R![1008, 0, -84, 0, 1]>],Snew);
    return Vf;
end function;