
// Make newform 1792.2.m.d in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1792_m();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1792_m_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_2_m_d();".
// 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_2_m_d();".
// 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 := [2, -12, 30, -44, 43, -28, 14, -4, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [4, -12, 19, -15, 10, -3, 1, 0], [-3, 13, -19, 26, -17, 11, -3, 1], [-8, 29, -43, 43, -28, 14, -4, 1], [-14, 65, -120, 146, -102, 59, -17, 5], [19, -71, 127, -148, 103, -59, 17, -5], [31, -126, 223, -256, 175, -98, 28, -8], [42, -166, 285, -325, 220, -123, 35, -10]];
    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_1792_m();"
function MakeCharacter_1792_m()
    N := 1792;
    order := 4;
    char_gens := [1023, 1541, 1025];
    v := [4, 1, 4];
    // 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_m_Hecke();"
function MakeCharacter_1792_m_Hecke(Kf)
    N := 1792;
    order := 4;
    char_gens := [1023, 1541, 1025];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 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 := 2;
    raw_aps := [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, -1, -1], [0, 0, 0, 0, 0, 0, -1, 0], [0, -1, 0, 0, 2, 0, 0, -1], [-1, -1, 0, -1, 0, 0, -1, -1], [1, 0, -1, 1, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 3, 2, 1], [-2, 1, 1, 1, -1, 1, -2, 1], [1, -2, 0, -2, 0, 0, 1, -2], [1, -1, -2, 2, 1, 1, 0, 0], [-1, 3, 2, 0, -2, 0, -1, -1], [-3, 2, 1, 1, -2, 2, 4, 0], [-2, -2, -2, 0, 0, 0, 4, 2], [5, 0, -1, 1, 0, 0, 0, 0], [-1, -1, -2, 0, 0, 0, 3, 1], [-8, 0, 2, 0, -1, 0, 6, 1], [2, -1, 0, -2, 0, 3, 5, -1], [6, 2, 0, -4, 0, 0, 6, 2], [4, -3, -1, -1, 3, -3, -6, 0], [4, 0, -4, -4, 0, 0, 6, 2], [0, -1, 5, -5, 1, 1, 0, 0], [-2, 0, 0, 3, 0, -2, -4, 0], [6, -3, -3, -3, 3, -3, -2, -8], [9, -3, 2, -2, 1, 1, 0, 0], [0, 1, 1, 0, 4, 0, -1, -5], [3, -2, -1, -1, 2, -2, -8, -2], [2, -3, -8, 0, 0, 0, 6, 3], [-3, 3, 0, 0, 0, 4, 1, 3], [-7, 1, 1, -1, 2, 2, 0, 0], [-4, -4, 1, -1, -3, -3, 0, 0], [4, 0, 0, -5, 0, -4, 0, 0], [6, -2, -4, -4, 2, -2, -2, -4], [2, 4, -4, 0, 1, 0, 2, -5], [-5, 6, 6, 0, -6, 0, -1, 0], [4, -1, -3, -3, 1, -1, 2, -1], [1, -5, 0, -3, 0, -4, -3, -5], [4, 3, 0, 0, 0, 2, 6, 3], [1, 0, -1, -1, 0, 0, 4, 0], [5, 3, 0, 1, 0, -4, 1, 3], [-2, 4, 0, -4, 0, 4, 2, 4], [-9, -2, 10, 0, 1, 0, -1, 1], [-6, -12, 2, -2, 0, 0, 0, 0], [7, -7, 1, -1, 2, 2, 0, 0], [3, 9, 4, 0, -2, 0, -7, -7], [5, -3, -2, -2, 3, -3, -4, -8], [0, 0, 0, 4, 0, 0, 0, 0], [-8, 11, -1, 1, 1, 1, 0, 0], [-9, 1, 0, 0, 0, -1, -10, 1], [4, -3, -5, 0, 6, 0, 1, -3], [-10, 2, 8, 8, -2, 2, -10, 2], [6, -8, 1, -1, 3, 3, 0, 0], [7, 4, -1, 1, 2, 2, 0, 0], [5, 6, -5, 0, 4, 0, 0, -10], [-6, 1, -7, 7, -1, -1, 0, 0], [-4, -1, 5, 5, 1, -1, 2, -6], [-3, 11, 0, -3, 0, 4, 1, 11], [-6, -7, -5, 5, 3, 3, 0, 0], [1, -10, 2, 0, 6, 0, -3, 4], [-6, 6, 0, 0, -6, 6, 8, 6], [3, 0, 1, 0, -6, 0, -4, 6], [-6, 7, -5, 0, -6, 0, 11, -1], [2, 6, 0, 5, 0, 2, 4, 6], [12, -5, -7, -7, 5, -5, 8, -2], [-1, 0, 1, 1, 0, 0, 0, 8], [5, 1, 0, -6, 0, 4, 9, 1], [10, -4, -6, 0, -4, 0, -4, 8], [-5, 1, -7, 7, 4, 4, 0, 0], [8, 6, -2, 0, 0, 0, -6, -6], [-16, 5, 0, 2, 0, 3, -13, 5], [0, 1, 5, -5, -3, -3, 0, 0], [-4, 5, -1, -1, -5, 5, 22, 3], [-14, 6, -2, 2, 8, 8, 0, 0], [7, -4, -2, 0, -2, 0, -5, 6], [0, -6, -4, 0, 2, 0, 4, 4], [3, -3, 0, 0, -3, -3, 0, 0], [-9, 7, 4, 0, 4, 0, 5, -11], [12, 5, 0, -6, 0, -3, 9, 5], [-1, 13, -5, 5, 0, 0, 0, 0], [-1, 3, -2, -2, -3, 3, 4, -2], [-12, 8, 0, 1, 0, 4, -8, 8], [-17, 0, 14, 0, -10, 0, 3, 10], [-2, -4, -5, 5, -3, -3, 0, 0], [13, -1, 6, -6, -7, -7, 0, 0], [2, -6, 4, 4, 6, -6, -4, -6], [-6, -8, 6, 0, 2, 0, 0, 6], [-8, 14, 2, -2, -2, -2, 0, 0], [-1, 4, -3, -3, -4, 4, 2, 15], [-12, 9, 0, -2, 0, -1, -13, 9], [-8, -12, 0, 0, -4, -4, 0, 0], [-13, 3, 0, 0, 0, -1, -14, 3], [21, 0, 5, -5, -2, -2, 0, 0], [-2, 1, 1, 1, -1, 1, 2, 5], [-4, -10, 6, 0, -2, 0, -2, 12], [8, -11, 0, -2, 0, -14, -6, -11], [6, 0, -6, -6, 0, 0, 8, -10], [4, 1, 0, 6, 0, 5, 9, 1], [11, -6, -5, -5, 6, -6, -16, -6], [10, 6, 4, 0, -3, 0, -14, -3], [9, -2, 0, 4, 0, 0, 9, -2], [4, -1, 0, -10, 0, 4, 8, -1], [-11, 1, 0, 16, 0, -2, -13, 1], [9, 1, 0, 0, 0, 5, 14, 1], [11, -6, -5, -5, 6, -6, -10, -3], [-4, 2, -12, 0, 2, 0, 16, -4], [14, 3, -3, 3, -5, -5, 0, 0], [-4, 4, -2, 0, 3, 0, 6, -7], [-14, 3, 7, -7, 5, 5, 0, 0], [8, -6, -2, -2, 6, -6, -4, -18], [14, -11, -3, -3, 11, -11, -6, -12], [-8, -7, 11, -11, -3, -3, 0, 0], [5, -2, -8, 0, -6, 0, 3, 8], [7, -2, -5, -5, 2, -2, 8, -5], [-3, 12, -1, 0, -6, 0, 4, -6], [10, 4, -14, -14, -4, 4, 12, 6], [17, 9, -5, 5, -2, -2, 0, 0], [15, 1, 0, -2, 0, 3, 18, 1], [-9, 5, 4, 4, -5, 5, -4, -16], [9, -4, 0, 4, 0, -10, -1, -4], [-20, 7, 0, -2, 0, 0, -20, 7], [-14, 5, 7, 0, -10, 0, 7, 5], [-8, -8, 10, -10, 0, 0, 0, 0], [1, 10, 4, 0, -1, 0, -5, -9], [-4, 13, -2, 0, -10, 0, 6, -3], [16, -8, 0, -7, 0, 0, 16, -8], [25, 2, 0, -18, 0, -8, 17, 2], [9, -3, -10, 0, 6, 0, 1, -3], [23, 3, 2, -2, -1, -1, 0, 0], [9, -6, -3, -3, 6, -6, -16, -12], [-12, -7, 0, 8, 0, 9, -3, -7], [-8, -7, 0, -4, 0, -6, -14, -7], [-12, 7, 5, 5, -7, 7, -14, 7], [2, 0, -9, 9, 9, 9, 0, 0], [7, -12, -12, 0, 2, 0, 5, 10], [-9, 7, 2, 2, -7, 7, 24, 8], [15, -4, -1, 1, -6, -6, 0, 0], [-7, 14, 12, 0, -7, 0, -5, -7], [-7, -9, 0, 12, 0, 5, -2, -9], [-9, -1, 0, -17, 0, 2, -7, -1], [-9, 0, 9, 9, 0, 0, -10, -21], [-5, -8, 1, 0, 14, 0, 4, -6], [-3, -4, -12, 0, 4, 0, 15, 0], [-22, 7, 15, 15, -7, 7, -22, -4], [-20, 5, 6, 0, -2, 0, 14, -3], [-10, -3, 0, -6, 0, 1, -9, -3], [3, 5, -8, -8, -5, 5, 4, 12], [10, 1, -27, 0, -4, 0, 17, 3], [-15, 10, 5, 5, -10, 10, 0, 6], [7, -6, -3, 0, 6, 0, -4, 0], [10, -18, -6, 6, -8, -8, 0, 0], [11, -7, 0, -16, 0, 4, 15, -7], [14, -3, 7, -7, 1, 1, 0, 0], [14, -3, 0, 2, 0, 6, 20, -3], [-5, 4, 1, 1, -4, 4, 8, 24], [16, -6, -6, 0, 10, 0, -10, -4], [0, -8, 1, -1, 5, 5, 0, 0], [-6, 7, -1, -1, -7, 7, 2, 14], [-5, 27, 0, 0, 5, 5, 0, 0], [-2, -3, 5, 5, 3, -3, 2, -2], [7, -7, 0, 1, 0, -6, 1, -7], [4, -1, 0, -2, 0, 16, 20, -1], [0, -6, 6, 6, 6, -6, -12, -12], [-6, 5, 1, 1, -5, 5, -10, 15], [14, -12, -16, 0, 13, 0, 2, -1], [2, -20, 6, -6, 4, 4, 0, 0], [-13, 3, 10, 10, -3, 3, -24, 12], [-18, 3, 9, -9, -1, -1, 0, 0], [5, 2, -4, 0, -7, 0, -1, 5], [-1, 9, -3, 3, 14, 14, 0, 0], [22, 3, -3, 0, -8, 0, -19, 5], [-12, 6, -2, 0, 6, 0, 14, -12], [-8, -7, 0, 10, 0, 1, -7, -7], [8, -5, -3, -3, 5, -5, 6, -18], [4, -4, 0, 0, 4, -4, -12, -12], [3, 10, -1, 1, -10, -10, 0, 0], [14, -4, -10, -10, 4, -4, 14, 0], [-6, 15, 8, 0, -16, 0, -2, 1], [1, 0, 12, 0, 10, 0, -13, -10], [-2, -1, 3, 3, 1, -1, -20, -10], [1, 3, 0, 15, 0, 0, 1, 3], [-6, 0, -5, 5, 1, 1, 0, 0], [15, 7, 0, -4, 0, -5, 10, 7], [-13, -9, 4, 0, -12, 0, 9, 21], [-4, -3, 7, 7, 3, -3, -2, -30], [4, -6, 5, -5, 5, 5, 0, 0], [12, 11, -15, 0, 2, 0, 3, -13], [1, 9, 0, 18, 0, 12, 13, 9], [5, 17, 0, -2, 0, -3, 2, 17], [2, -2, 0, 0, 2, -2, -2, -20], [-3, -18, 15, -15, 0, 0, 0, 0], [-12, -20, 8, -8, -6, -6, 0, 0], [2, -9, 6, 0, 6, 0, -8, 3], [0, -3, 0, -16, 0, 4, 4, -3], [-33, 5, 0, 11, 0, 12, -21, 5], [0, -1, 0, -20, 0, 4, 4, -1], [-2, 6, -4, -4, -6, 6, 18, 0], [3, -13, -5, 5, 6, 6, 0, 0], [-3, 6, 0, 2, 0, -8, -11, 6], [-16, 19, 3, -3, -5, -5, 0, 0], [-6, 1, 5, 5, -1, 1, -4, 20], [1, 17, 0, 8, 0, 14, 15, 17], [-9, -4, -1, 1, -14, -14, 0, 0], [-17, 12, 4, 0, -5, 0, 13, -7], [-6, 17, 7, -7, -3, -3, 0, 0], [-8, -4, 2, 0, 1, 0, 6, 3], [-3, -11, 0, 7, 0, -10, -13, -11], [37, 2, -9, 9, 8, 8, 0, 0], [16, -4, 0, -16, 0, -14, 2, -4], [3, -2, -1, -1, 2, -2, 12, -13], [1, 0, -9, 0, 6, 0, 8, -6], [7, 1, 15, -15, 4, 4, 0, 0], [-1, -12, 8, 0, 11, 0, -7, 1], [-4, 3, 1, 1, -3, 3, 30, -13], [-9, 12, 21, 0, -20, 0, -12, 8], [12, -8, -4, -4, 8, -8, 4, -30], [-7, 11, -4, -4, -11, 11, -4, 16], [32, 4, -2, 2, 10, 10, 0, 0], [7, -4, 3, -3, -10, -10, 0, 0], [8, 0, -8, -8, 0, 0, 12, 4], [-5, -6, 0, 24, 0, -18, -23, -6], [11, -4, -18, 0, -16, 0, 7, 20], [8, 4, -12, -12, -4, 4, 16, -2], [-2, 24, -4, 4, -4, -4, 0, 0], [-22, 16, 1, -1, -9, -9, 0, 0], [-29, 7, 0, 14, 0, 19, -10, 7], [-23, 12, 4, 0, -6, 0, 19, -6], [0, 2, -2, -2, -2, 2, 30, 24], [6, 8, 17, -17, 3, 3, 0, 0], [-4, 5, -1, -1, -5, 5, 20, -20], [18, 15, -8, 0, -6, 0, -10, -9], [7, 0, 0, 2, 0, 16, 23, 0], [-8, -12, 0, 1, 0, -8, -16, -12], [-28, 12, 6, -6, 6, 6, 0, 0], [0, -6, 6, 6, 6, -6, -16, -4], [21, -4, 3, 0, -8, 0, -24, 12], [2, 1, -9, 9, 7, 7, 0, 0], [-1, 3, 8, -8, -3, -3, 0, 0], [-3, -6, 0, 0, -4, 0, 3, 10], [14, -2, -8, 0, 8, 0, -6, -6], [-10, 2, 8, 8, -2, 2, 16, 32], [24, -22, 0, -4, 0, -18, 6, -22], [-6, 14, 8, 0, -15, 0, -2, 1], [12, -1, -11, -11, 1, -1, 12, 8], [-17, 3, 0, 12, 0, 2, -15, 3], [-18, -12, 14, -14, 2, 2, 0, 0], [17, -10, -7, -7, 10, -10, 12, 6], [-16, -15, -1, 1, 1, 1, 0, 0], [-12, -8, 0, 17, 0, -4, -16, -8], [-14, -7, 8, 0, -10, 0, 6, 17], [-10, -9, 1, -1, -9, -9, 0, 0], [-5, 8, 0, -18, 0, 18, 13, 8], [-12, -6, -2, 2, 4, 4, 0, 0], [-30, 10, 20, 20, -10, 10, -4, 12], [-8, 4, 4, 4, -4, 4, -2, 4], [0, -5, 0, -8, 0, -15, -15, -5], [-24, -4, 0, 10, 0, 6, -18, -4], [27, 0, -8, 0, -2, 0, -19, 2], [24, -16, 14, 0, 11, 0, -38, 5], [17, 0, -2, 0, -3, 0, -15, 3], [-13, 5, 8, 8, -5, 5, -12, 22], [-6, 4, -21, 21, -3, -3, 0, 0], [-2, -4, 0, -4, 0, 2, 0, -4], [5, -4, 6, 0, 17, 0, -11, -13], [24, 7, 0, -24, 0, -7, 17, 7], [-9, 2, -7, 7, -8, -8, 0, 0], [-37, 11, 0, 4, 0, 19, -18, 11], [-21, 4, 0, 2, 0, -2, -23, 4], [-14, 0, 14, 14, 0, 0, -18, 16], [-8, 23, -8, 0, -4, 0, 16, -19], [-9, -15, -18, 0, 14, 0, 27, 1], [-1, -13, 0, 7, 0, 2, 1, -13], [-10, 10, 0, -8, 0, 10, 0, 10], [-4, -1, 5, 5, 1, -1, 18, 24], [12, -10, 13, -13, 5, 5, 0, 0], [0, 3, -3, 3, -15, -15, 0, 0], [-2, -10, 12, 12, 10, -10, -12, -24], [14, 13, -30, 0, -8, 0, 16, -5], [-15, 23, 0, 10, 0, 0, -15, 23], [-25, 4, 21, 21, -4, 4, 8, 15], [-38, 4, 0, 3, 0, 2, -36, 4], [-24, -20, -18, 18, 2, 2, 0, 0], [2, 9, -11, -11, -9, 9, 6, 24], [9, 9, -18, -18, -9, 9, 12, 14], [12, -3, 5, 0, -16, 0, -17, 19], [-21, -2, 25, 0, 14, 0, -4, -12], [-36, 12, -3, 3, -3, -3, 0, 0], [-30, -18, -6, 6, 6, 6, 0, 0], [13, -3, -12, 0, -6, 0, -1, 9], [-21, 11, 10, 10, -11, 11, 20, 30], [-2, 39, 1, -1, 7, 7, 0, 0], [21, -21, 0, 0, 0, -30, -9, -21], [16, -28, 0, -1, 0, 0, 16, -28], [-9, 8, 1, 1, -8, 8, -4, 23], [-7, -2, 15, 0, -12, 0, -8, 14], [-11, 4, 0, -4, 0, 8, -3, 4], [16, 7, 0, -10, 0, 15, 31, 7], [-26, -3, -1, 1, -9, -9, 0, 0], [-14, -17, 7, 0, -16, 0, 7, 33], [19, -18, -11, 0, 26, 0, -8, -8], [-12, -20, 0, 13, 0, -8, -20, -20], [19, -12, -7, -7, 12, -12, -8, -6], [-11, -7, 0, 26, 0, -10, -21, -7], [16, -18, 2, -2, 2, 2, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1792_m_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1792_2_m_d();".
// 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_2_m_d(:prec:=8)
    chi := MakeCharacter_1792_m();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    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_2_m_d();".
// 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_2_m_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1792_m();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![4, 16, 32, -8, 0, 0, 8, -4, 1]>,<5,R![4, 0, 0, 8, 32, 24, 8, -4, 1]>],Snew);
    return Vf;
end function;