
// Make newform 1232.2.q.n in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1232_q();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1232_q_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_1232_2_q_n();".
// 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_1232_2_q_n();".
// 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 := [225, 15, 136, -9, 66, -2, 9, 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, 1, 0, 0, 0, 0, 0, 0], [-44550, 3122, -21978, 2112, -2474, 198, -330, 27], [14514, 225, 15, 704, -9, 66, -110, 9], [-29700, 2897, -14652, 1408, -2465, 132, -220, 18], [112320, -247959, -21914, -63074, -6917, -11266, -1615, -424], [1215, 1650, 110, 4347, -66, 484, 9, 66], [-51705, 87207, -102833, -55298, -12689, -10537, -2830, -1993]];
    Rf_basisdens := [1, 1, 36705, 7341, 7341, 110115, 7341, 110115];
    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_1232_q();"
function MakeCharacter_1232_q()
    N := 1232;
    order := 3;
    char_gens := [463, 309, 353, 673];
    v := [3, 3, 1, 3];
    // 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_1232_q_Hecke();"
function MakeCharacter_1232_q_Hecke(Kf)
    N := 1232;
    order := 3;
    char_gens := [463, 309, 353, 673];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 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 := 2;
    raw_aps := [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -1, 0, 0, 0], [1, -1, 1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, -2, 1, 0, 0, 1, 0, -1], [-5, 0, -3, -2, -1, 2, 0, 1], [2, -1, 3, -1, -1, 0, -1, 0], [0, 0, 0, -2, 0, 0, 1, 0], [0, 0, 1, 0, -1, 1, 0, -1], [2, 2, 2, 0, 0, 0, 2, 0], [4, 0, 0, 2, 1, -1, 3, -2], [3, 0, 0, -1, 0, 0, 0, 0], [-3, -2, -1, -2, -3, -2, -2, -1], [0, 1, 0, 0, 0, 1, 0, -1], [0, 1, 9, 0, -2, -1, 0, 1], [2, 3, 1, 1, 2, 2, 3, 1], [0, 3, -7, 0, 1, -1, 0, 1], [1, 0, 0, 2, 1, -1, 2, -2], [0, -2, 0, 0, -1, -2, 0, 2], [8, 3, 6, 2, 2, 0, 3, 0], [-3, 0, 0, -2, -1, 1, -4, 2], [-2, -4, -1, -1, 0, 2, -4, 1], [2, 0, 0, -3, -2, 2, 0, 4], [0, 2, 2, 0, -4, -1, 0, 1], [-6, 5, -5, -1, -1, 0, 5, 0], [1, 1, -3, 4, 2, -4, 1, -2], [0, 3, 1, 0, -2, -4, 0, 4], [1, 0, 0, -3, -2, 2, 1, 4], [-1, 0, 0, -4, -1, 1, -3, 2], [0, 4, -1, 1, 0, -2, 4, -1], [0, -1, 5, 0, -6, -1, 0, 1], [-1, 0, 0, 1, -1, 1, 5, 2], [-5, -1, 0, -5, -2, 6, -1, 3], [0, 0, 5, 0, 1, 0, 0, 0], [0, -1, -10, 0, 1, -1, 0, 1], [-7, -6, -7, 0, 0, 0, -6, 0], [12, 0, 0, 4, 4, -4, 5, -8], [14, 4, 13, 1, 1, 0, 4, 0], [0, -3, -3, 0, -6, -1, 0, 1], [7, 0, 0, -1, 2, -2, 0, -4], [1, 5, -4, 5, 2, -6, 5, -3], [0, -5, 4, 0, 4, 1, 0, -1], [-10, 0, 0, 2, 1, -1, 4, -2], [0, -8, 9, 0, -1, 1, 0, -1], [2, 0, 0, -2, 0, 0, -4, 0], [7, 0, 0, -3, -1, 1, -3, 2], [0, 1, 19, 0, -2, 0, 0, 0], [1, -1, 6, -5, -6, -2, -1, -1], [3, 1, 6, -3, -6, -6, 1, -3], [8, 0, 0, 2, 4, -4, 3, -8], [0, 2, 18, 0, 1, 0, 0, 0], [7, 0, 0, 2, -1, 1, 0, 2], [6, 1, 10, -4, 0, 8, 1, 4], [0, -4, 0, 0, 4, 1, 0, -1], [0, 0, -5, 0, -1, -1, 0, 1], [-11, 2, -5, -6, -4, 4, 2, 2], [0, -3, -1, 0, 10, 1, 0, -1], [3, 0, 0, 4, 2, -2, -3, -4], [0, 1, -7, 0, 5, 0, 0, 0], [-9, 0, 0, -3, -3, 3, -3, 6], [-1, 0, 0, 8, 0, 0, 5, 0], [0, 1, 15, 0, 2, 0, 0, 0], [-1, 1, -4, 3, 3, 0, 1, 0], [9, 0, 10, -1, -3, -4, 0, -2], [3, 4, 7, -4, -6, -4, 4, -2], [3, 0, 0, 4, 1, -1, -4, -2], [0, -2, -3, 0, -11, -3, 0, 3], [-5, 0, 0, -1, 1, -1, -9, -2], [0, -7, 6, 0, 4, 3, 0, -3], [-10, 4, -10, 0, -1, -2, 4, -1], [0, 4, 5, 0, -5, -7, 0, 7], [-11, 6, -13, 2, 0, -4, 6, -2], [-5, 0, 0, -1, 0, 0, 1, 0], [4, -3, 8, -4, -3, 2, -3, 1], [0, 8, 5, 0, -5, -1, 0, 1], [2, 0, 0, 2, 0, -4, 0, -2], [3, 9, -1, 4, 5, 2, 9, 1], [0, 0, 19, 0, -3, -3, 0, 3], [3, 0, 0, 7, -1, 1, -5, 2], [-8, 0, 0, 1, -2, 2, -7, 4], [0, 0, 1, 0, 6, 4, 0, -4], [14, 0, 0, 8, 2, -2, 2, -4], [-8, -6, -8, 0, 1, 2, -6, 1], [-1, 1, -11, 10, 10, 0, 1, 0], [1, 0, 0, -1, -3, 3, 5, 6], [-1, 4, -1, 0, -3, -6, 4, -3], [-1, 0, 0, -11, 0, 0, -3, 0], [18, 0, 0, 7, 5, -5, 6, -10], [-4, -5, -11, 7, 9, 4, -5, 2], [0, -5, 12, 0, -4, -2, 0, 2], [0, 2, 0, 0, 5, 2, 0, -2], [3, 0, 0, 3, -1, 1, 13, 2], [-14, -6, -5, -9, -4, 10, -6, 5], [14, 0, 0, 13, 6, -6, 4, -12], [-14, -3, -19, 5, 7, 4, -3, 2], [0, -7, 7, 0, 1, 0, 0, 0], [23, 0, 15, 8, 5, -6, 0, -3], [-18, 3, -4, -14, -14, 0, 3, 0], [-17, 0, 0, 1, 1, -1, 5, -2], [0, 3, -13, 0, 2, 2, 0, -2], [0, -7, 3, 0, 2, 2, 0, -2], [-2, -1, 5, -7, -5, 4, -1, 2], [0, -8, 17, 0, 8, -1, 0, 1], [0, 1, 2, 0, 7, 0, 0, 0], [7, 0, 0, 4, -3, 3, -1, 6], [10, -12, 11, -1, 0, 2, -12, 1], [0, 8, -10, 0, 7, -2, 0, 2], [13, 0, 0, -4, 0, 0, -5, 0], [-8, -1, 4, -12, -11, 2, -1, 1], [0, 0, -4, 0, -4, -2, 0, 2], [30, 0, 0, -1, -1, 1, -3, 2], [0, 6, -4, 0, 8, 2, 0, -2], [3, 0, 0, -5, -2, 2, 0, 4], [0, 3, -32, 0, 8, 0, 0, 0], [22, 0, 0, 1, 3, -3, 7, -6], [0, -6, 0, 0, -6, 0, 0, 0], [-6, -11, 4, -10, -11, -2, -11, -1], [18, 0, 0, 7, 0, 0, -1, 0], [0, -1, -3, 0, 14, 4, 0, -4], [24, 0, 0, 16, 6, -6, -4, -12], [17, 4, 7, 10, 11, 2, 4, 1], [0, -2, 19, 0, -1, 6, 0, -6], [18, 1, 3, 15, 8, -14, 1, -7], [3, 0, 0, 5, 2, -2, 5, -4], [2, 12, 5, -3, -2, 2, 12, 1], [3, -5, 3, 0, 2, 4, -5, 2], [2, 0, 0, 3, -1, 1, 12, 2], [-3, -1, -10, 7, 1, -12, -1, -6], [0, 16, 8, 0, -5, -2, 0, 2], [-14, 0, 0, -1, -1, 1, -10, 2], [19, 7, 23, -4, -4, 0, 7, 0], [-17, 0, 0, 10, 2, -2, 9, -4], [-12, 3, -3, -9, -9, 0, 3, 0], [11, 0, 0, -1, -5, 5, 5, 10], [0, 6, -5, 0, -2, 1, 0, -1], [0, -3, -22, 0, 6, 1, 0, -1], [-24, 0, 0, 5, 2, -2, 7, -4], [0, 13, 26, 0, -3, -3, 0, 3], [15, 0, 0, 2, 0, 0, -7, 0], [13, -6, 10, 3, 4, 2, -6, 1], [0, -4, 1, 0, 7, 3, 0, -3], [0, 0, 0, 2, 3, -3, -11, -6], [0, 12, 0, 0, 1, -6, 0, 6], [-1, 0, 0, -14, -4, 4, -17, 8], [28, 0, 0, 8, 4, -4, 6, -8], [0, -9, -15, 0, 9, 6, 0, -6], [-8, 4, -19, 11, 11, 0, 4, 0], [3, -1, 9, -6, -4, 4, -1, 2], [15, 1, 9, 6, 3, -6, 1, -3], [2, 0, 0, 7, 6, -6, 0, -12], [-4, 0, 0, 7, 6, -6, 2, -12], [-15, -1, -10, -5, -7, -4, -1, -2], [0, -7, 20, 0, 5, -1, 0, 1], [1, 0, 0, 4, 2, -2, 17, -4], [-17, -9, -22, 5, 4, -2, -9, -1], [5, 2, -4, 9, 2, -14, 2, -7], [2, 0, 0, -1, 1, -1, -10, -2], [0, 7, 1, 0, 6, -1, 0, 1], [5, 3, 1, 4, -2, -12, 3, -6], [0, 0, 0, -1, -4, 4, -1, 8], [-17, 0, 0, -3, -4, 4, -14, 8], [-30, 2, -24, -6, -5, 2, 2, 1], [0, -15, -11, 0, 9, 6, 0, -6], [0, 6, 2, 0, 9, 6, 0, -6], [0, 10, 5, 0, 12, 5, 0, -5], [0, -7, 26, 0, 0, 7, 0, -7], [6, 0, 0, 9, 3, -3, 12, -6], [20, -5, 17, 3, -1, -8, -5, -4], [0, 15, -14, 0, 2, -3, 0, 3], [20, 0, 0, -7, 0, 0, -9, 0], [-25, -16, -18, -7, -4, 6, -16, 3], [0, -6, -5, 0, 2, 7, 0, -7], [0, 1, -17, 0, -1, 2, 0, -2], [-15, 0, 0, -16, -5, 5, -5, 10], [2, 0, 0, -5, 4, -4, -7, -8], [0, 6, 0, 0, -5, 0, 0, 0], [-10, 0, 0, -12, -3, 3, -9, 6], [3, -5, 2, 1, 2, 2, -5, 1], [21, 13, 20, 1, -2, -6, 13, -3], [-21, 0, 0, -2, 0, 0, 3, 0], [2, 0, 0, -10, -3, 3, -11, 6], [21, -5, 1, 20, 10, -20, -5, -10], [0, 13, 14, 0, -9, -5, 0, 5], [0, -14, 4, 0, -6, -2, 0, 2], [0, 8, 24, 0, -1, -5, 0, 5], [0, 2, 19, 0, 3, -4, 0, 4], [28, 2, 15, 13, 12, -2, 2, -1], [0, 3, -6, 0, -7, 4, 0, -4], [-22, 0, -14, -8, -8, 0, 0, 0], [-15, 0, 0, 9, 8, -8, -2, -16], [25, 13, 20, 5, 3, -4, 13, -2], [18, -8, 18, 0, -4, -8, -8, -4], [0, -15, -20, 0, 10, 7, 0, -7], [0, 7, -11, 0, -1, -9, 0, 9], [0, 12, 5, 0, 15, 1, 0, -1], [-16, 5, 3, -19, -17, 4, 5, 2], [22, 0, 0, 11, 1, -1, 8, -2], [26, 3, 22, 4, -2, -12, 3, -6], [0, -5, 17, 0, -4, -7, 0, 7], [38, 0, 0, 8, 1, -1, -4, -2], [17, 2, 17, 0, 5, 10, 2, 5], [0, -3, 20, 0, -3, 3, 0, -3], [28, 0, 0, 5, 1, -1, 11, -2], [0, -14, -23, 0, 4, 3, 0, -3], [-18, 7, -18, 0, 3, 6, 7, 3], [15, 0, 18, -3, -1, 4, 0, 2], [15, 0, 0, 4, 0, 0, 9, 0], [0, -9, -6, 0, 5, 0, 0, 0], [-5, -2, 7, -12, -7, 10, -2, 5], [-38, 0, 0, -8, 1, -1, -7, -2], [8, 0, 0, -20, -3, 3, -3, 6], [-19, -3, -11, -8, 0, 16, -3, 8], [0, 3, 12, 0, -17, -10, 0, 10], [-36, -3, -30, -6, -8, -4, -3, -2], [0, 4, 26, 0, -5, -3, 0, 3], [0, 8, -12, 0, -8, 2, 0, -2], [14, 4, 3, 11, 2, -18, 4, -9], [-15, 0, 0, -6, -3, 3, -14, 6], [31, -3, 9, 22, 19, -6, -3, -3], [-20, 0, 0, -9, 0, 0, -12, 0], [28, 14, 20, 8, 1, -14, 14, -7], [2, 12, 3, -1, 6, 14, 12, 7], [31, 0, 0, -11, -5, 5, -5, 10], [-7, 0, 0, -16, -10, 10, -14, 20], [19, 2, 7, 12, 10, -4, 2, -2], [0, 4, -5, 0, -10, -7, 0, 7], [15, -6, 4, 11, 14, 6, -6, 3], [14, 4, 24, -10, -8, 4, 4, 2], [0, -10, -17, 0, 15, 9, 0, -9], [0, -1, 2, 0, 0, 9, 0, -9], [-12, 0, 0, -7, -1, 1, -5, 2], [0, -1, 4, 0, -3, -1, 0, 1], [7, 0, 0, -5, 5, -5, 0, -10], [0, -1, 27, 0, -3, -3, 0, 3], [-25, 18, -37, 12, 7, -10, 18, -5], [-14, 8, -10, -4, -5, -2, 8, -1], [7, 0, 0, -1, 0, 0, -13, 0], [1, 0, 0, 14, 4, -4, 1, -8], [0, -9, 20, 0, 2, 5, 0, -5], [-30, -3, -17, -13, -11, 4, -3, 2], [0, 3, -11, 0, 3, 6, 0, -6], [-14, -14, -6, -8, -4, 8, -14, 4], [-38, 0, 0, -8, -4, 4, -6, 8], [-8, -9, -14, 6, 5, -2, -9, -1], [17, 0, 0, 10, -1, 1, -2, 2], [0, 1, 7, 0, 0, 1, 0, -1], [0, -9, -6, 0, 0, 3, 0, -3], [-29, 0, 0, -1, 2, -2, 9, -4], [18, 0, 0, 6, 4, -4, -1, -8], [-15, -12, -7, -8, -3, 10, -12, 5], [0, -17, -27, 0, -16, -6, 0, 6], [11, 0, 0, -6, -4, 4, -1, 8], [0, 10, -30, 0, 0, 1, 0, -1], [-34, 13, -20, -14, -13, 2, 13, 1], [0, -2, 13, 0, -4, -7, 0, 7], [0, -9, -16, 0, -3, 1, 0, -1], [15, 0, 0, 4, 0, 0, 15, 0], [-38, -5, -36, -2, 5, 14, -5, 7], [0, -12, 16, 0, 0, -4, 0, 4], [12, 0, 0, -7, -4, 4, -5, 8], [0, 20, -4, 0, -5, 2, 0, -2], [-32, 0, 0, 1, -3, 3, 7, 6], [0, 21, -3, 0, -4, -5, 0, 5], [-17, -14, -4, -13, -12, 2, -14, 1], [-18, 0, 0, -18, 0, 0, -4, 0], [-16, 0, 0, -8, 3, -3, 2, -6], [3, 0, 0, 4, -9, 9, -2, 18], [0, -12, 27, 0, -16, 1, 0, -1], [9, -15, 32, -23, -14, 18, -15, 9], [0, -13, -5, 0, 1, 0, 0, 0], [0, -10, 19, 0, 0, 8, 0, -8], [10, 4, 2, 8, 6, -4, 4, -2], [40, 0, 0, 3, 0, 0, 3, 0], [-25, 5, -16, -9, -4, 10, 5, 5], [-26, -22, -19, -7, -5, 4, -22, 2], [0, -4, 57, 0, -7, 2, 0, -2], [-1, -4, -6, 5, 3, -4, -4, -2], [11, -8, 29, -18, -17, 2, -8, 1], [0, -20, -9, 0, 9, 4, 0, -4], [0, -13, 7, 0, 7, 10, 0, -10], [7, 0, 0, -12, 0, 0, 2, 0], [7, 0, 0, 14, 6, -6, -2, -12], [-1, 6, 9, -10, -1, 18, 6, 9], [-15, -12, -12, -3, 3, 12, -12, 6], [0, 18, -36, 0, 1, -5, 0, 5], [16, 0, 0, -13, -4, 4, -5, 8], [0, 1, -47, 0, 4, -4, 0, 4], [-3, 0, 0, -5, -8, 8, -10, 16], [0, 1, 21, 0, 14, 6, 0, -6], [0, -10, 8, 0, 4, 1, 0, -1], [14, 12, 22, -8, -4, 8, 12, 4], [0, 0, 0, -7, -7, 7, 6, 14], [-22, 0, 0, 6, 2, -2, 1, -4], [0, 1, -36, 0, -6, 6, 0, -6], [-6, 14, -13, 7, 8, 2, 14, 1], [-56, 0, 0, 1, 1, -1, 8, -2], [-18, 10, -3, -15, -18, -6, 10, -3], [-3, 0, 0, -20, -5, 5, 8, 10], [17, 14, 16, 1, -7, -16, 14, -8], [22, 4, 18, 4, 3, -2, 4, -1], [0, -3, 47, 0, -9, 3, 0, -3]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1232_q_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1232_2_q_n();".
// 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_1232_2_q_n(:prec:=8)
    chi := MakeCharacter_1232_q();
    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_1232_2_q_n();".
// 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_1232_2_q_n( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1232_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![441, -189, 270, -3, 78, 0, 13, 2, 1]>,<13,R![21, -9, -9, 2, 1]>],Snew);
    return Vf;
end function;