
// Make newform 9240.2.a.cb in Magma, downloaded from the LMFDB on 17 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_9240_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_9240_2_a_cb();".
// 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_9240_2_a_cb();".
// 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 := [14, 8, -7, -2, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0], [3, 2, -1, 0], [-4, -5, 0, 1], [-8, 3, 3, -1]];
    Rf_basisdens := [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_9240_a();"
function MakeCharacter_9240_a()
    N := 9240;
    order := 1;
    char_gens := [2311, 4621, 6161, 3697, 5281, 2521];
    v := [1, 1, 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_9240_a_Hecke(Kf)
    return MakeCharacter_9240_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], [-1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [0, -1, 0, 0], [-2, 1, 0, 0], [1, 2, 1, 1], [-2, -1, -1, 0], [-1, -1, 0, -1], [1, 1, 2, -1], [0, -2, 1, 0], [-5, -2, 0, 1], [0, 0, 1, -2], [-3, 0, -1, -1], [-2, 1, 1, 2], [-2, 1, 2, 2], [-4, -2, 0, 0], [0, 2, -1, -2], [1, 1, -1, 1], [-3, -1, 2, 1], [-6, 1, -2, 0], [4, 3, -1, -2], [-3, -2, 2, 1], [2, 4, 0, 0], [-5, 2, 2, 1], [-5, -1, -2, -1], [1, 1, -2, -1], [-4, -3, 0, 0], [-5, 0, -2, -3], [0, 0, 1, 2], [3, -1, -1, 3], [-9, -3, 1, 1], [-7, -5, -1, 1], [-5, -3, -3, 1], [1, 4, 0, 1], [-6, -2, -1, -4], [0, -2, 0, 4], [4, 0, 2, -2], [-4, 2, -1, -2], [-5, 1, -1, -5], [2, -2, 2, -2], [2, 0, 2, 0], [9, 1, -1, 1], [3, -1, -3, 1], [-12, -2, 2, 0], [3, 4, 2, -3], [-4, -7, -2, -2], [-5, 3, -2, 1], [1, 7, 2, 3], [-10, 1, -3, 2], [1, -7, -1, -3], [5, 1, 3, 3], [10, -4, 1, -2], [3, -1, -5, 1], [3, 0, 2, 3], [-8, -5, -2, 2], [10, 2, 2, 0], [-4, 4, 0, -2], [-9, 3, -4, -1], [3, 4, 1, -3], [5, -1, 5, -1], [0, -4, -2, 0], [7, 4, 2, 3], [8, 8, 0, -2], [-1, 2, -3, 3], [1, 2, -2, 1], [-7, 5, -3, -1], [-12, 1, -4, 0], [-2, 0, 2, 0], [-10, 3, 7, 2], [-1, 8, 0, 5], [-11, -8, -4, 1], [-11, 2, 3, 1], [-4, -2, 3, 2], [4, -4, -3, 0], [0, 4, 4, 6], [-4, 2, -1, 4], [3, -1, -3, -5], [6, 1, -1, -2], [-11, 2, 1, -1], [7, 7, 3, -3], [-10, -4, -2, 0], [-4, 3, -4, -6], [-9, -3, 1, 5], [-18, -4, -1, -2], [11, 4, 4, -1], [6, -4, 6, 0], [-3, -1, -3, -1], [0, -4, 6, 0], [-8, 4, 1, -2], [5, 3, 1, 7], [-15, 2, 2, -1], [-25, -2, -1, -1], [-19, 0, -1, 1], [-5, -8, 0, -1], [-4, -9, -3, -6], [-19, -7, -3, 3], [-19, 5, -2, 3], [-27, 0, 0, 3], [17, -9, -1, -3], [5, -1, 1, -1], [-21, 2, -2, 3], [8, 6, 1, -2], [14, -4, -4, -4], [14, 4, -1, 0], [-1, -1, 1, 3], [-6, -12, 0, -2], [4, 9, -2, 0], [-2, -4, 0, -6], [8, 2, 6, 2], [15, 7, 1, 3], [-22, -4, -2, 2], [-31, -2, -1, 1], [-6, 0, -4, 0], [-15, 6, 0, 3], [4, 4, -6, -8], [-3, -2, -5, -5], [-7, 6, 8, 3], [-25, -1, 2, -3], [3, -8, -6, -5], [11, -2, -7, 1], [-5, -9, 1, -3], [-14, 12, -6, 2], [-6, 5, 5, 4], [-5, -2, -1, -3], [-1, -2, -4, 5], [-1, -2, -2, -3], [16, 2, 4, -6], [6, -4, 4, -2], [-3, -1, -7, 3], [1, 0, 3, -3], [-9, -7, 1, -5], [-4, -10, -6, 2], [-10, -1, -2, 2], [-10, 8, -6, -4], [-17, -1, 5, 5], [18, 0, -2, 0], [20, 10, 4, 2], [-29, -1, 5, 1], [-24, 5, 3, 2], [-13, -1, -4, -5], [9, -7, 1, -1], [-3, 15, 3, 5], [5, -10, -6, -5], [-4, 2, 7, 8], [11, 5, 3, 7], [10, -6, 3, 4], [9, 8, 3, -7], [-7, -8, 0, 5], [4, -1, -7, 2], [6, 2, 8, -2], [13, 14, 1, 1], [-2, -2, -9, 0], [-14, -2, 4, 2], [11, 13, 1, 1], [27, 11, 1, -1], [15, -11, -2, -3], [-14, 2, 3, 6], [12, -3, 4, 6], [-17, -7, 3, 7], [-17, 2, -4, 1], [-2, 11, -1, 2], [-12, -9, 0, -4], [26, 0, 4, -2], [19, 4, -1, -5], [10, 0, 0, -4], [-8, 10, 5, 4], [6, 8, -1, 2], [17, 6, 4, 3], [-13, 11, -6, 1], [-26, 1, -5, -2], [29, 10, 2, -3], [9, -1, 9, -5], [35, 5, 1, 3], [-34, -4, -1, -8], [-18, -6, -4, -4], [-8, 2, 10, 8], [25, -7, 3, 1], [-3, -3, 3, 7], [24, 8, -6, -8], [-9, 9, 5, 3], [16, -1, -4, -8], [15, 2, -3, 3], [-23, -2, 6, 1], [21, -6, -2, -7], [15, 2, -8, -3], [-20, 4, 5, -4], [2, -4, -9, 8], [10, 8, 0, 0], [5, -1, 3, -5], [-24, -10, -4, 0], [19, -10, 6, -1], [19, 5, 4, -1], [2, 6, 4, -4], [6, -2, -8, 8], [-3, -3, -2, -5], [22, -1, -6, -2], [24, -10, -4, -4], [2, 1, 7, -8], [0, -9, -2, 2], [11, -6, -8, 3], [-17, -21, -5, -5], [32, -7, -1, -4], [8, 4, 2, 2], [-11, -15, -2, 1], [-1, -3, 5, 1], [13, -10, -8, -3], [-4, 8, -3, 2], [5, -4, 0, 5], [5, -10, 8, 1], [-7, 5, 5, 7], [-4, -2, -3, 10], [8, -4, -4, 0], [8, 6, 8, 6], [-7, -10, 0, -1], [-6, 12, 2, 0], [6, -4, -2, 10], [-17, 2, 7, 1], [-39, 5, 5, 1], [9, 11, -3, 7], [-4, -10, 3, 4], [23, 3, 4, 7], [30, -3, 2, -4], [5, -5, 6, 7], [-10, 2, 3, 2], [22, 12, 3, 4], [-8, 8, -2, 4], [3, -6, -6, -3], [-17, -1, -4, 1], [1, 11, -7, -5], [-15, 3, 8, 1], [15, 6, 6, -9], [13, -2, -10, -5], [15, -8, 3, 7], [24, 10, 1, -4], [-21, -1, 1, 7], [-2, -16, 0, -10], [22, -10, -12, -6], [9, -1, -7, -1], [-16, -3, 12, 6], [12, 6, 0, -8], [-7, 2, -1, 7], [30, -1, 4, -6], [-16, 0, -9, 2], [24, 0, -12, 0], [38, -1, -5, 2], [-20, -2, -3, 10], [17, -7, -7, -5], [24, -10, -6, -6], [26, 4, -3, -6], [14, 2, 10, -10], [6, -6, -3, -2], [1, 4, -11, -1], [11, 0, -8, 5], [-25, 10, 3, 1], [13, 7, 8, -7], [0, -8, 11, 8], [23, 1, -3, 7], [55, 4, 0, -3], [19, 7, 9, 1], [-24, -9, -4, 0], [16, -2, 1, -8], [-32, -10, -5, 0], [14, 12, -5, 4], [34, 14, 0, 0], [28, 13, 7, 2], [-47, -10, 0, 3], [-19, -1, 4, -1], [-7, -13, 1, -11], [-18, 4, 10, -2], [7, -14, -14, -1], [-3, -7, 6, -3], [45, 13, 4, 3], [12, -10, 8, -8], [38, 13, 6, -8], [19, -5, -1, 7], [-44, 4, 7, 0], [-14, -2, -2, -14], [-15, -2, 11, 9], [20, -10, 4, 0], [0, -4, 8, 0], [-16, -1, 4, 8], [-29, -5, 0, 3], [-12, -12, -9, -2], [14, 16, 7, -2], [-27, 5, -11, 9], [-13, -7, 1, 5], [14, -4, -1, 10], [-8, 16, 2, 2], [34, 8, 1, 0], [-23, -13, 8, 7], [16, -8, 0, 4], [22, -4, -12, -4], [-16, 4, 2, 6], [-15, 1, -3, -9], [26, -4, -7, 2], [-8, 4, 8, -12], [-21, -17, -7, 1], [25, 3, -5, -3], [-1, -7, 0, 1], [21, -9, -4, -3], [-8, -11, 2, -2], [11, -8, 7, -9], [10, -4, 9, -2], [-34, 1, -4, -4], [7, -3, 14, -7], [10, 0, -13, -8], [-23, 4, -6, -7], [16, -6, -6, -8], [2, 16, 7, -2], [9, -14, 6, -11], [18, 4, -13, -8], [23, -9, 2, -9], [-2, 1, -4, -6], [71, -1, -5, -3], [-16, -7, -7, 0], [22, -4, 10, -8], [-19, -8, 4, 1], [-17, -17, 1, -3], [16, 10, -7, -4], [2, -12, -8, -8], [11, 3, -8, 3], [-25, -5, -3, -1], [0, 0, -4, 2], [30, 0, -8, -2], [-3, -4, -14, 7], [-19, -7, -4, -7], [25, 3, 8, -5], [41, 1, -8, 3], [10, 6, -4, 8], [32, 1, 2, -2], [21, 1, 7, -9], [-12, 6, 18, 0], [28, 4, -4, 8], [7, 14, -9, -7], [21, 5, 7, 5], [12, -6, -1, 12], [10, -4, 1, 12], [21, -1, -14, -1], [-20, 11, 8, -4], [-20, 14, 1, 0], [-18, 0, -4, 10], [-13, -4, 9, -3], [19, 4, 0, 13], [-35, -1, 8, -5], [-4, -10, 9, 14], [4, 20, 12, 4], [-24, -4, 9, -4], [-24, -5, 2, -2], [12, -4, -4, -10], [-2, 2, 3, 6], [14, -14, -1, -8], [7, 7, 11, -5], [-16, 1, 10, -8], [8, 10, 4, 8], [24, 0, 1, 2], [19, 5, 5, -1], [-17, 16, 1, 7], [15, 2, -14, -1], [34, -8, 8, 4], [44, 2, -4, 4], [19, 18, 6, 13], [-51, 6, 4, 7], [10, -8, 0, 8], [13, 10, -11, -9], [-19, -4, -10, 3], [6, -6, -7, -2], [12, 0, -14, -4], [-4, 12, 6, 0], [7, 15, -1, -3], [-22, -15, 3, -8], [26, 15, -2, -8], [7, 7, 4, 9], [19, -23, 1, -7], [18, -3, 1, 6], [7, 3, 7, -1], [22, 14, 5, 10], [13, -7, -4, -5], [-25, 10, -6, -5], [-8, 19, -4, 8], [-20, 0, 8, -4], [-5, -5, -12, 13], [-6, -3, -8, -4], [14, 2, -5, 16], [9, 0, 1, 1], [-11, -8, 8, -3], [6, 2, 0, -6], [-2, 10, 8, -10], [-3, -2, -9, -1], [-26, -4, -6, 4], [44, -10, -1, -2], [-25, 4, 4, -7], [-8, -6, 8, 12], [13, -2, 2, 5], [35, -7, -15, -7], [3, 1, -7, 3], [-19, 4, -5, 5], [-46, 1, -3, -4], [16, -9, 10, 12], [-38, -1, 2, -6], [-1, -8, -14, -7], [2, -12, -1, 2], [-22, 10, -9, -10], [-42, 7, -8, 0], [-15, -17, -2, 3], [-30, 0, 4, 8], [13, 2, 2, 11], [-20, 3, 19, 4], [-19, -15, 9, 1], [37, -11, 0, -5], [13, 19, -3, -5], [2, -12, -7, -8], [26, 20, 2, 0], [-11, -16, -8, 5], [-48, 5, 5, 0], [27, 4, -12, -15], [56, 2, -1, -8], [-66, 0, -2, -2], [-24, 18, 1, 8], [2, 8, 6, -8], [7, 8, -5, -13], [34, -4, 3, 12], [43, 4, 2, -1], [-38, -28, -7, -6], [16, -9, 4, 14], [-15, -20, 12, 13], [66, 8, 6, -6], [2, -26, 1, -8], [40, -8, 6, -2], [18, 0, 6, -2], [-35, 4, 5, 1], [14, -14, -15, -12], [-3, 12, -8, 5], [22, 7, 1, 8], [54, 14, -1, 2], [-53, 0, 11, 9], [-48, 10, 0, -4], [13, 19, 5, 3], [-34, -4, -9, 0], [0, 20, -7, 0], [-3, -5, 8, -5], [8, 7, 1, -4], [-60, -7, 4, -4], [51, -5, -2, 9], [5, -15, 7, -1], [3, -2, -13, -1], [0, 8, 3, 12], [-50, 3, 0, -6], [20, 8, 4, -8], [1, 2, 0, -13], [27, -11, -5, 1], [14, 18, 1, 10], [36, 6, 7, -12], [-8, 20, 10, 2], [-45, -3, 11, 3], [38, 12, 3, 0], [-4, -8, -14, -2], [6, -3, -4, -2], [37, 12, 3, 5], [16, 6, -8, 4], [-29, -12, -4, 13], [-39, -14, 9, 11], [-39, 3, 14, 1], [-1, 6, 14, 3], [-37, -9, -4, 7], [18, 10, -1, 8], [0, -18, 12, -2], [36, 4, 4, -12], [39, 20, 6, 9], [18, 13, 6, 4], [44, -2, 8, 4], [-38, -8, 10, -4], [24, -12, -13, -10], [26, -2, -2, 4], [-44, 6, 9, 4], [13, 9, -3, 11], [-55, -10, -3, 5], [-73, -20, -3, 1], [-7, 4, -4, 5], [18, 6, 14, -12], [-8, -6, -10, 2], [-32, -12, 12, 10], [-17, 0, 12, 13], [39, 5, 8, -5], [35, -22, -3, -7], [-28, 11, -15, 0], [44, -12, -17, -10], [35, -1, -4, 15], [-28, 2, -4, 6], [-5, 2, 5, 11], [5, -10, -5, 7], [-56, 0, -4, -2], [16, -8, -8, -12], [-11, -5, -15, -3], [11, -12, 2, 1], [-7, -10, 7, -9], [0, -1, 2, 10], [-76, 4, 2, 4], [-6, -11, 11, 0], [-16, 0, -3, -10], [-65, 15, 5, 7], [-1, -4, 4, -3], [3, 23, 8, 5], [20, 4, 7, 0], [19, 12, 15, -17], [9, -7, -13, 11], [-1, 18, -14, -1], [63, 3, -2, -5], [-4, -18, -8, -12], [-10, 6, 7, -16], [17, 13, -7, 5], [-55, -10, 9, 11], [20, 14, 6, 16], [-38, -18, -6, 0], [4, -2, -18, -6], [-9, -7, -1, -5], [20, -2, -5, -14], [-12, -16, 0, 4], [27, 11, 3, -17], [-26, -8, 10, -6], [66, 28, 4, -8], [6, -8, -14, 10], [13, 15, 5, 1], [28, -16, -2, 4], [19, 14, -4, -1], [-60, 0, -8, 10], [-29, 21, -12, 7], [30, 10, 2, 0], [-8, 4, -2, -4], [-33, -21, -9, -9], [29, 10, 10, -9], [48, -10, -1, 2], [-20, 10, 16, -2], [-19, -2, -9, -11], [5, 2, 0, 17], [16, -1, 15, 10], [36, 0, -16, -2], [9, 18, 14, 15], [-6, -16, 7, 8], [-46, 2, 12, 0], [1, 3, 2, 17], [16, 5, 4, 6], [-63, -12, 0, 5], [33, -4, 5, -11], [45, -17, -8, -7], [38, -4, 2, -6], [-6, 2, -1, 4], [-64, -6, -3, 4], [-15, 8, -14, -7], [-51, -19, 4, 13], [-34, -10, 5, -4], [-58, -4, -12, 8], [42, 10, -1, -8], [-74, 5, 16, 6], [24, 30, 13, 2], [5, -3, -17, -11], [18, 8, -2, -6], [30, -8, -11, 2], [-18, 8, 17, 10], [4, 0, 2, -12], [48, -6, -7, 6], [-9, 6, -10, -21], [0, 12, -18, -16], [35, -3, -7, 9], [5, -11, 6, -3], [8, -10, 17, -4], [-24, -28, -10, 2], [-8, 14, 16, -8], [-42, 6, -10, 0], [53, 8, 5, 11], [45, -10, -15, -7], [-3, 11, 1, -3], [52, 14, -5, -4], [50, -6, -5, 0], [24, 32, 12, 2], [24, 11, 14, -10], [6, -8, -10, 12], [-26, -5, -6, 4], [22, 16, -9, 2], [9, 12, -10, 11], [-81, 1, 3, 3], [38, -4, 0, -10], [-65, -19, -3, 3], [-6, -2, 9, 16], [36, -10, -10, -2], [14, 6, 3, 12], [28, 8, -13, -4], [61, 9, 9, 1], [-35, -5, 14, -3], [-58, 13, -8, 6], [50, 8, 2, -6], [18, 2, -2, -4], [-47, 10, -6, 1], [18, 18, -8, -2], [-27, -8, 1, 3], [-43, 19, -1, 7], [3, -15, -15, 11], [-42, -11, -7, -4], [-30, -1, -9, -4], [-26, 10, -10, -14], [-30, -1, 6, 6], [29, -3, 3, -9], [-36, -12, 10, 12], [30, 5, -4, 22], [-19, -5, 16, -3], [22, -16, 12, 4], [33, -7, -1, -13], [34, -12, -15, 2], [-5, 11, -8, 3], [23, -8, -12, -1], [-7, 21, 7, 1], [58, 18, 2, -10], [-5, -19, 19, 9], [14, 7, 4, -8], [-9, 23, -1, 7], [-22, -28, 2, 4], [-18, -24, -9, -4], [-7, 14, 11, 1], [-57, -17, -12, 7], [8, 8, 4, -10], [46, -12, -19, -8]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_9240_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_9240_2_a_cb();".
// 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_9240_2_a_cb(:prec:=4)
    chi := MakeCharacter_9240_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(4603) - 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_9240_2_a_cb();".
// 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_9240_2_a_cb( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_9240_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<13,R![8, 24, -26, 0, 1]>,<17,R![4, 4, -11, -2, 1]>,<19,R![-16, 8, 25, 10, 1]>,<23,R![1168, 8, -79, -2, 1]>,<37,R![5128, -72, -154, 0, 1]>],Snew);
    return Vf;
end function;