
// Make newform 9464.2.a.bf in Magma, downloaded from the LMFDB on 11 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_9464_a();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_9464_2_a_bf();".
// 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_9464_2_a_bf();".
// 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, -6, 7, 8, -5, -2, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [-2, -1, 1, 0, 0, 0], [1, -3, -1, 1, 0, 0], [2, 2, -4, -1, 1, 0], [-2, 4, 6, -4, -2, 1]];
    Rf_basisdens := [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_9464_a();"
function MakeCharacter_9464_a()
    N := 9464;
    order := 1;
    char_gens := [2367, 4733, 2705, 9297];
    v := [1, 1, 1, 1];
    // 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;

function MakeCharacter_9464_a_Hecke( : Kf := Kf)
    return MakeCharacter_9464_a();
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]];
    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, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, -1], [-1, 0, 0, 0, 0, 0], [2, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, -1], [3, -1, 0, -1, 1, 1], [-1, -1, -3, -1, 2, -1], [-3, -1, 1, 0, -2, 0], [-2, 2, -1, 0, -2, -2], [-1, 2, -1, 0, 1, 1], [2, -1, -4, -1, 1, 0], [-1, -2, 0, -1, 0, 1], [-1, -1, 0, 1, 2, -1], [3, -2, 0, 0, 0, 2], [-2, 2, 3, 0, -2, 0], [1, 0, 1, 0, 1, 1], [-2, -1, 0, 0, -1, 2], [2, 0, -2, -2, 0, 0], [2, -1, 2, 1, 3, -2], [-1, -3, -1, 3, -2, -1], [6, 0, 1, 0, 0, 4], [-1, 1, -2, 3, -3, 1], [0, 4, 4, 2, -5, 0], [-2, -4, -4, -3, 3, 2], [-5, -2, -3, 3, 2, -4], [1, -4, 5, -1, 3, 4], [3, -8, -1, 1, -1, 3], [1, 4, 4, 2, 0, 4], [-6, 1, -3, 2, -6, -2], [4, -2, 0, -2, 2, -3], [-2, -5, 1, -7, 3, 3], [-1, 3, -1, -1, -2, -8], [-12, 5, -1, -1, 1, -1], [5, -4, 5, 1, 3, 3], [-5, 0, 3, 0, -5, -2], [5, -7, 1, -1, 0, 1], [6, -6, -5, 4, 0, 4], [-3, 2, 3, -5, 6, 2], [-1, 1, 8, 1, 3, 2], [-5, 4, 7, 0, 1, 1], [-10, 9, 6, 0, -3, -1], [5, 0, -7, 6, -3, -1], [-1, 5, 6, 5, -8, 0], [-15, 4, -3, 1, 0, -2], [-6, 0, 1, -4, 5, 3], [2, -4, -2, -4, -3, -2], [6, -2, -7, -4, 2, -4], [-8, 2, 0, 0, 6, 0], [-3, 0, -1, -9, 1, -2], [-2, 3, -6, -4, 5, 2], [-4, 9, 4, 5, -2, 2], [2, -4, -6, 2, -4, 4], [-3, 2, 5, -2, -3, 0], [-8, 0, 1, 6, -7, -1], [-6, 2, -2, 8, 2, -1], [-6, 2, 1, 4, 0, -6], [-9, 6, 10, -2, 6, 2], [-7, -2, 5, 6, 1, 5], [-5, 5, 5, 5, -4, -1], [-10, 5, -12, -3, -5, -10], [1, 7, 5, 3, 1, -3], [-7, 1, -1, 1, 4, 2], [2, 4, 2, -6, -2, 2], [2, -6, 8, 1, 2, 0], [2, 6, 9, -4, -4, 3], [1, -1, 9, 2, 0, 8], [-5, 3, 1, -5, 2, 3], [-13, -1, -6, 3, 4, -7], [5, 6, -4, 0, 0, 1], [8, -9, -5, 4, -3, -1], [-9, -3, 1, -3, 6, 5], [-4, 0, -11, 1, 5, -6], [-4, -2, 5, -2, 2, -3], [-1, -5, 9, -3, -7, 1], [0, 3, -10, -7, -3, -4], [2, -8, 0, -2, -4, 4], [-4, 3, 3, 1, 7, -5], [-3, 0, -2, -8, 2, -3], [-6, -1, 4, 0, 4, -1], [-13, 6, -7, -4, 1, -5], [6, -13, -3, 2, 3, -3], [-6, 2, -12, 1, -3, -3], [-5, -7, 1, -1, 0, -4], [10, 6, 2, 10, -4, 2], [-8, 8, 6, -2, -4, -6], [5, 2, 1, -2, 3, -5], [-7, -8, -4, -10, 10, 3], [-2, -1, 0, 8, -13, -2], [-10, -5, -8, 12, -8, -3], [6, -6, -1, 14, -1, -2], [16, -7, -3, -4, 9, -3], [10, 5, -3, -2, 4, 2], [7, 0, 0, 5, -1, 0], [0, -3, 0, -4, -4, 6], [-11, 0, 8, 2, -1, 1], [13, -6, -3, 0, 11, 3], [-22, 0, 4, -10, -2, -6], [10, -3, -5, 5, -3, 3], [0, 10, 11, 6, -3, 11], [-13, 1, -2, 10, 0, 2], [-11, 9, -9, -1, -4, -7], [-2, 6, 10, 6, -10, 0], [-3, 14, -3, -1, -7, 4], [-1, 0, -10, -8, 13, 1], [-4, 12, 6, -2, 1, 6], [-22, 5, 0, -1, -12, 0], [-2, 7, -5, 2, -8, -6], [-8, 2, 0, 1, -5, 2], [3, -4, -15, -9, 2, -6], [11, -3, 10, -4, -4, 2], [-18, 10, 4, 1, -8, -2], [3, 13, -1, 15, -12, -7], [7, 15, 0, 3, -6, 4], [-10, -10, -1, -7, 13, -4], [1, 13, 0, 7, -4, -11], [-8, -2, 2, 4, -14, 6], [2, 7, 9, 14, -2, 0], [8, -10, 2, -4, -6, 4], [-10, 5, 2, -3, -3, 2], [7, 2, 0, -10, -6, 8], [-19, 16, -1, -3, -4, -11], [-7, -12, -7, 1, -1, -7], [-27, 9, -6, 5, -5, -9], [-6, 4, -4, 6, 0, 6], [-8, -7, 3, -1, -3, 11], [6, -5, -6, 12, 8, 7], [-1, -4, 1, 11, 6, -6], [0, -11, 14, -5, 4, 10], [22, 2, -2, -2, 2, -2], [-4, 3, 13, -4, 9, 11], [-12, 0, -13, -2, 13, 5], [4, -20, -2, -8, 6, 12], [20, -16, -4, 2, -7, -2], [7, -1, -2, -7, 6, -1], [5, 7, 0, 7, 6, 11], [-1, 3, -11, -9, -2, -9], [-12, 12, -2, -2, -10, 0], [-1, -10, 12, 8, 2, 8], [6, 8, 3, 6, -1, 8], [7, -6, -1, 3, 15, 3], [5, 5, 14, -9, 11, 0], [-7, 10, -6, -13, -3, 0], [-2, 6, -12, 5, 1, -6], [-5, 17, 4, -5, -1, -5], [1, -6, -18, 0, -1, 1], [1, 6, -1, -20, 1, -6], [-7, -9, -9, 7, -6, 3], [5, 7, 19, 3, -10, 5], [-2, -12, 0, 3, -2, -10], [0, 0, -10, -9, 1, -7], [-4, -2, -9, 10, -3, 5], [-14, 6, 0, -10, -8, -10], [1, -5, -7, 1, 12, 3], [13, 16, -9, -1, 3, 0], [-8, -2, 6, 0, -4, 10], [-19, 12, 18, 12, 1, 11], [-14, 8, 2, -3, 9, -3], [-1, 17, -4, 5, -8, -1], [24, 8, -19, 6, -8, -1], [1, -7, -2, -5, -5, 0], [12, 7, 2, -6, 9, 8], [-13, 20, 11, -1, -2, 4], [12, -14, -6, 3, -12, -6], [24, 0, 8, 2, 3, 10], [-2, 11, 4, 4, -9, -5], [8, 10, 22, 3, -9, 3], [-20, 3, 7, 6, 13, -3], [-2, 6, -8, 9, 15, 1], [7, -10, 6, -7, 17, 8], [-16, 15, -2, 5, 0, -12], [8, 11, 13, 8, -8, -6], [21, -11, 8, -8, 16, 8], [6, -5, 16, -14, 14, 12], [-14, 6, -8, 9, 7, -11], [-4, 4, 14, -12, 6, 4], [11, -11, 2, 0, 4, -4], [-4, 6, -2, -10, 6, -1], [14, 2, 8, -6, -4, 5], [8, -7, -12, 2, 19, -2], [1, 8, -5, 15, -6, -7], [-15, -8, 6, -8, 12, -8], [3, -9, -4, 3, 13, 9], [-3, 27, 8, 1, -8, -2], [8, -4, -10, -13, 3, -15], [0, -2, 4, -8, -10, 6], [0, 18, 16, -6, 3, -4], [23, -16, -11, -18, 1, -3], [9, -1, -16, -15, 3, -5], [4, 12, 4, 21, -9, -1], [-3, 20, 4, 11, -5, -6], [-25, 4, 3, -3, -13, -10], [-29, -3, 6, -3, -3, -1], [0, 3, 0, -6, 13, -5], [25, -8, -13, -3, -8, 4], [15, -11, -16, -12, -4, -10], [18, 8, -13, -15, 5, -10], [-6, 5, 4, -7, 5, 4], [3, -2, 3, 11, -18, -8], [-33, -11, -4, 2, 2, 0], [-11, 18, 11, -9, 0, -5], [-27, -8, -2, 6, -1, -3], [-22, -8, 14, 1, -1, 0], [-11, 13, 16, 7, -20, 5], [18, -10, 4, 3, 7, -3], [-7, -17, -11, -11, 8, -9], [30, -8, 1, 0, 5, 7], [-9, 3, -8, 0, -4, 6], [6, -20, -12, 2, 2, 2], [13, -5, 15, -2, 6, 14], [-2, 14, 20, -2, -4, -1], [27, -5, 2, 5, -11, -2], [31, 3, 10, -7, 6, 5], [12, 12, 18, -2, -5, -8], [-49, -4, -4, 6, 1, 1], [-20, -6, -5, 2, -3, 15], [7, 12, -7, 14, -9, -10], [-8, 19, -11, 4, -3, -9], [-11, -9, 12, -11, 20, 4], [-9, 7, -7, 10, -8, -12], [-11, -11, 2, 3, 2, -13], [21, -4, -5, 12, -1, -5], [16, -21, -13, 8, -3, 11], [25, -36, -13, 3, 2, -1], [-11, -19, -9, 10, 0, -14], [16, -16, -6, -11, 17, -5], [2, -1, -13, -6, 2, -10], [-24, 2, -2, -2, 10, -5], [3, 24, 15, -1, -5, -15], [0, -23, -8, 13, -1, 6], [-19, -14, -15, 5, -2, -12], [-11, 8, 0, 7, 3, -4], [-6, 5, 2, -17, -5, 4], [-11, -9, -13, 7, 6, 7], [19, 1, 2, 9, 10, 9], [2, -2, -12, 10, -9, -12], [-26, 0, -10, -5, -6, -18], [8, 20, 0, 16, -12, 0], [16, 1, -14, -14, -6, -9], [14, 2, -3, -12, 12, -11], [-14, 1, 24, -4, 0, 3], [8, 12, 2, -2, 2, 1], [-4, 10, 12, -1, -12, -6], [2, 15, 2, 3, 3, -6], [31, -11, 9, 17, 8, -1], [-1, 25, 13, 11, -6, 5], [9, 7, 0, 1, 7, -11], [-5, 5, -1, 9, 0, -13], [14, 13, 13, 6, -16, -2], [-26, 3, -23, -8, -3, -1], [-8, -18, 6, 2, 3, 2], [21, 4, 17, -11, -3, 1], [-24, 8, 8, -5, -19, -1], [-13, -4, 19, 5, -2, 0], [9, -18, 11, 5, 7, 13], [-15, 16, -17, -3, -1, -2], [-15, 15, -12, 3, 0, -19], [23, -14, 1, 17, 6, 8], [-14, -19, -2, 7, -2, -8], [-11, 9, -10, 3, -1, -24], [21, 9, 14, -9, 3, 4], [3, -2, 18, 14, -7, 15], [18, -16, 10, -5, 3, 9], [-4, -5, -22, -5, 19, -4], [1, -1, -17, -21, -2, -1], [9, -18, -5, -5, 19, 5], [28, -23, 0, -3, 8, 6], [5, 0, -3, 13, 3, -11], [3, 12, 6, -4, -8, -2], [3, 14, -5, 28, -11, -4], [20, 3, 7, 0, -13, -9], [26, -3, 4, -23, -9, 4], [3, -29, -10, -15, 11, -4], [2, 0, -16, -4, -4, 2], [-34, -2, -5, -22, 5, 6], [10, 17, -16, -8, 7, -8], [35, -18, 9, 2, 19, 13], [15, -10, -15, 2, 3, -5], [37, -22, 7, 9, 14, 2], [-36, 22, 12, 2, 0, -1], [-10, -1, -7, -22, -1, -5], [6, -13, 28, 2, 8, 14], [2, -9, 12, -1, 1, 0], [-41, 11, 16, 1, 14, 11], [20, 6, 18, -8, -6, 14], [-6, -18, 1, 1, 13, -8], [-19, 3, 20, -4, 8, 6], [-14, 8, 8, 2, 0, 16], [4, 10, -14, 5, 11, 6], [-11, 5, -6, 21, -9, -10], [-24, -6, -2, 6, 8, -5], [25, -20, -15, 0, 7, -3], [-1, -1, -1, 21, -15, -15], [18, 10, 6, -6, 12, -8], [3, -2, 1, 12, -13, -4], [3, -10, 19, -15, 2, 13], [29, 10, -1, 16, -7, 4], [19, -14, -3, -19, -8, -5], [-20, 10, -1, -20, -9, -2], [3, 4, -3, 18, -1, -15], [34, -11, 9, -5, -1, 5], [6, -12, 16, 14, -18, -4], [-17, -1, 16, -11, -19, -12], [-9, 9, 0, 1, -3, -12], [16, 2, 0, 3, -18, -6], [15, -3, 2, -11, -13, -8], [-26, -6, -22, -9, 7, 1], [20, -17, 10, -14, 9, 12], [-32, 27, 24, -3, -11, -4], [7, 20, 3, -1, -12, -4], [-11, -8, -23, -1, 15, 1], [-17, 10, -2, 24, -2, -4], [26, 3, 4, 20, -5, -13], [22, -1, -7, 14, -21, -9], [39, -8, 7, -6, 19, 12], [-6, -26, -17, -8, 10, 8], [21, 3, -17, 23, -6, 1], [25, 7, -4, 19, 2, -3], [4, -11, 6, -23, 11, 14], [-4, 15, 4, -10, -10, -3], [6, 5, 9, 2, 3, -1], [4, -14, 4, -23, 5, 15], [5, -3, 14, -19, -2, 8], [38, -20, -10, -6, -6, 8], [-1, 14, 3, -20, -11, 2], [19, -3, 14, 3, 0, 14], [2, -12, -1, -6, 13, 18], [-2, -17, -26, 4, 19, 5], [14, -9, -2, -17, -3, -14], [-16, -16, -6, -33, 18, 10], [35, 7, -1, 6, 0, -12], [8, -6, 4, 0, -4, 10], [-3, 9, 0, 7, -22, -11], [-24, 29, 23, 12, -5, 3], [-20, 2, -2, 4, 4, -2], [6, -16, -24, -9, 12, -2], [-6, 24, 12, 2, -10, -8], [-4, -3, -18, 3, -22, -6], [14, -7, -24, 24, 4, 5], [16, 11, 15, 2, -3, -11], [-16, 33, 20, 1, -3, -8], [-16, 3, 12, -5, -16, 12], [-3, 15, -9, -15, 8, -3], [-14, 6, 6, 24, -8, -2], [-17, 15, -15, 11, 4, -19], [-30, -6, 10, 3, 9, 18], [-12, -8, -14, -8, 4, 14], [8, -6, 7, -18, 16, 2], [-5, 24, -11, 7, -6, -28], [7, -1, -2, 5, -2, 29], [20, 0, -10, -14, 0, -22], [-38, 2, -20, 3, 14, -6], [-17, 23, -23, 7, -4, -16], [1, 8, -14, 30, -10, -8], [33, 26, -3, 12, -11, 2], [31, -5, -4, 3, -19, -5], [24, -4, 22, -4, 0, 4], [11, 1, 17, -28, 24, 8], [-10, 0, 30, 14, -10, 18], [-23, 31, 34, 16, -20, 6], [-1, 22, 3, -26, -7, 7], [12, -12, -2, 0, 18, 8], [14, 3, -8, 12, -15, -20], [-38, 4, -16, -6, 8, -6], [29, -9, 4, 7, -9, -6], [-16, -12, 2, -14, -4, 8], [-20, 6, -7, 6, 2, 9], [4, 2, -21, 1, 19, 0], [16, -6, -2, 20, -14, 0], [-10, 29, -4, 12, 0, -3], [13, -9, 6, 5, -20, -12], [12, 4, 15, -13, 15, 8], [-29, 7, 21, 17, 0, 3], [1, 19, -7, -12, -2, -14], [-5, 3, 4, -3, -12, -5], [27, -7, 19, 7, 8, 29], [32, 20, -20, 26, -17, -6], [8, -32, -14, -23, 15, 7], [-24, 10, -2, 9, 5, -13], [22, -12, -18, -22, 15, -10], [-4, 16, 4, 9, 2, 0], [-28, 1, 8, 18, -31, 6], [25, 2, 15, -1, 7, 21], [29, -47, -19, -5, 21, -3], [2, 4, -12, 18, 2, 4], [-4, 1, -32, 6, 3, 0], [1, -16, -15, -17, 0, -14], [6, -15, -28, -16, 3, 4], [-27, 9, 15, 27, -22, 7], [22, 9, -23, 11, 3, 3], [-47, 4, 6, 0, -11, 5], [-25, 12, -24, -7, -13, -30], [-38, 3, 8, 12, 6, -9], [-7, 6, 32, -13, -9, 0], [18, -38, 2, -2, 8, 14], [9, -13, 17, -17, 11, 25], [24, -12, -10, -14, -8, 6], [-37, 24, 16, 15, -8, 7], [-8, 15, 7, 23, -9, -5], [-7, -5, -4, -5, 26, 9], [-10, 19, -11, -6, -8, -32], [6, 16, 22, 6, -6, 12], [-20, -3, -20, -19, 4, 4], [-2, 33, 34, 23, -20, 16], [28, -13, -4, 2, 2, 1], [-8, 6, -28, -14, -10, -6], [17, -2, -15, 0, -11, 7], [-9, -33, -13, 23, -2, -11], [-2, -30, -14, -22, 20, 14], [19, -18, -9, 22, 13, 16], [26, 5, -2, 11, -11, 22], [23, -19, 8, 17, 9, -2], [-62, -6, -16, -10, 4, -4], [-17, -12, -12, -16, -6, -26], [-21, 30, 31, 12, -9, 5], [-12, -16, -12, -8, -2, 8], [-16, 21, -22, 8, -8, -32], [15, -13, 6, 17, -2, -1], [-32, -5, -8, 10, -22, -13], [27, -16, -14, 10, 12, 24], [-23, -16, -14, -4, 7, -25], [43, -8, 3, -1, 5, 7], [14, -13, -22, 4, -14, 5], [20, 4, 18, -4, -12, 10], [-2, -27, 18, 7, 2, -2], [33, 3, 27, -11, -8, 13], [0, 3, 19, -3, -13, -13], [-45, -11, -6, -15, 16, 19], [0, -13, -12, 14, -10, 9]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_9464_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_9464_2_a_bf();".
// 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_9464_2_a_bf(:prec:=6)
    chi := MakeCharacter_9464_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(2999) - 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_9464_2_a_bf();".
// 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_9464_2_a_bf( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_9464_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-2, -6, 7, 8, -5, -2, 1]>,<5,R![1, 26, 14, -24, -6, 4, 1]>,<11,R![-74, 214, -153, 6, 29, -10, 1]>,<17,R![49, -70, -37, 72, -21, -2, 1]>],Snew);
    return Vf;
end function;