
// Make newform 1185.2.a.j in Magma, downloaded from the LMFDB on 02 June 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_1185_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_1185_2_a_j();".
// 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_1185_2_a_j();".
// 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 := [-1, -6, 11, 5, -7, -1, 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], [-3, 0, 1, 0, 0, 0], [2, -4, -1, 1, 0, 0], [3, 3, -5, -1, 1, 0], [-3, 7, 4, -6, -1, 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_1185_a();"
function MakeCharacter_1185_a()
    N := 1185;
    order := 1;
    char_gens := [791, 712, 556];
    v := [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_1185_a_Hecke( : Kf := Kf)
    return MakeCharacter_1185_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, -1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [2, 0, 1, 0, 0, -1], [-1, 0, 0, -1, -1, 0], [2, 1, 1, 1, -1, -1], [1, -1, 1, -1, 0, 1], [2, -1, 1, 1, -1, -1], [2, -1, 1, 1, 1, 1], [0, -2, 1, 1, 0, -1], [2, 0, 0, 0, 0, -1], [1, 0, -2, -1, -1, 1], [0, 0, 1, 1, 0, -2], [3, -1, -2, -1, 0, 2], [1, 2, -1, 0, -1, 0], [0, 1, 0, 1, -1, -3], [0, 1, 0, 1, 1, 2], [1, 0, -2, -2, 1, 0], [3, 0, 1, -1, 1, -2], [1, 2, -2, 4, 1, 2], [5, 3, -1, 1, -2, -1], [1, 0, 0, 0, 0, 0], [0, 1, -4, 1, -1, 0], [-2, -1, -1, -1, 3, 0], [2, 0, -1, 0, 2, 3], [1, -1, 2, -3, 2, 1], [5, -2, -2, 0, 1, 2], [0, 6, 2, 2, -2, -5], [0, 2, 5, 2, -2, -1], [3, 2, 0, 4, -3, -3], [9, -1, 1, -1, 2, 2], [2, 1, 0, 0, 1, 4], [1, 8, 2, 2, -3, -3], [-5, 0, 0, 4, -3, 0], [-5, 2, 4, 3, -3, 1], [2, 7, 0, -1, -1, 1], [0, -1, -2, -4, 1, 4], [3, 0, -1, 1, 3, 3], [3, 2, 2, -4, -1, -1], [-5, 1, -5, 1, -2, 0], [-3, 3, 0, 0, -6, -3], [-2, 5, -2, -1, -5, 2], [-1, 5, 0, -1, -4, -7], [6, -1, 0, -6, -1, 4], [-6, 5, 2, 5, 3, 0], [4, -4, 0, -4, 2, 0], [2, 5, 4, -1, -1, -1], [6, -4, 2, 3, 0, 1], [9, -1, 2, 1, 4, 2], [-4, -5, -2, 3, 1, 0], [-2, -3, -3, -3, 1, -3], [0, 1, 1, 2, -1, -8], [1, 10, 0, 0, 1, -2], [2, -3, -1, 5, 3, 0], [4, -1, 6, -3, 3, -1], [-4, 8, 0, 2, 2, 2], [-6, 0, -9, 0, 2, 1], [14, -5, -1, -1, -5, -4], [1, 0, -2, 4, -3, -2], [-3, -2, -1, -4, 3, 0], [-1, -5, -1, 4, 0, -4], [0, -5, 6, -5, -1, 0], [9, -5, 8, -1, 0, -1], [10, -4, 4, -2, -4, 3], [8, 2, -1, 2, 0, -2], [-7, 4, -4, -2, -1, 1], [-6, -1, -3, -5, 5, 6], [7, -10, 6, -2, -5, -1], [1, 5, 6, 3, 2, -2], [7, -2, 7, 8, 1, -4], [10, -3, 5, 3, 3, 2], [-1, 5, -7, -3, -2, 2], [0, 10, -6, 1, -4, -5], [-1, 5, 0, 0, -4, -4], [5, -6, -1, -4, 1, 1], [-1, -5, -3, 1, 8, -1], [4, 0, 7, 2, 6, 0], [2, -14, -3, -6, 4, 9], [3, -2, 3, 3, 9, 1], [-2, -1, -7, -5, 1, 9], [3, 8, 5, 6, -3, -4], [-21, 5, -4, 1, 4, 3], [15, -7, -4, -8, -4, 0], [16, -3, 7, 7, 1, -1], [-1, -3, -4, -5, -6, 0], [3, 4, -4, 0, -3, -8], [2, -9, -1, 2, -1, -3], [6, -4, 4, 6, -2, 3], [-11, 2, -3, -9, -3, -4], [4, 11, 5, 7, -1, -6], [4, 9, -8, -5, -3, 3], [12, 10, -3, -3, -4, 6], [13, -3, -2, 8, 8, 6], [-6, 6, 6, 4, -2, -5], [-13, -6, -1, -8, 9, 9], [8, -3, -4, -11, 1, 4], [3, 6, 0, -9, 5, 9], [-4, 14, 5, 11, -2, -10], [5, 1, 11, 8, 0, -4], [-12, 6, -12, -2, 4, 3], [9, -1, 0, 6, 0, 1], [-12, 1, -2, 1, -5, 2], [-8, 4, -9, -2, 2, 4], [-12, 12, -12, -8, -4, 1], [-3, 8, 12, 0, -1, -6], [0, -6, -3, -1, 4, -2], [16, 5, 8, -1, -1, -3], [-2, 2, -2, 4, -10, -9], [-7, 2, -2, -7, 3, 2], [-12, 5, -7, -5, -1, 10], [12, -17, -4, -3, 7, 8], [-20, -1, -7, 2, 5, 10], [-26, -5, -4, 1, -1, 3], [-14, 12, -8, -6, 0, -1], [-9, 1, -2, 11, 6, -1], [-1, -11, -5, 1, 4, 6], [4, 9, -5, 0, 1, -6], [9, 0, -7, 0, -1, 1], [-6, -3, 1, -3, -5, 0], [-5, -16, -9, -2, 5, 10], [-8, 5, -7, 5, 1, -1], [-5, 12, -7, -5, -5, -4], [5, -12, -3, 0, 3, -2], [-3, -7, -3, 1, 14, 4], [5, 7, 2, -3, -12, -3], [-13, -7, -3, 4, 0, 7], [-3, -6, 8, 4, 5, 9], [6, 5, -4, 10, 5, 2], [4, -1, 6, 0, 1, -3], [-21, 6, -11, -4, 1, 0], [-12, -2, -7, -8, 2, -3], [6, -7, 7, 5, -3, -8], [1, -3, -7, 11, 4, 8], [-18, -11, 6, -1, 7, -3], [-9, -8, -1, -8, 1, 5], [13, -3, 0, -7, 8, 5], [1, -11, 11, 1, 0, 4], [20, 4, 7, 3, 0, -8], [-23, -7, -4, -7, 12, 10], [-2, -5, 0, -3, 7, 0], [6, -14, 7, 2, 6, 5], [-7, -5, 2, -1, 0, -4], [0, -12, 1, -8, 0, -4], [28, -8, 9, 4, -4, -2], [1, -5, 6, 3, -2, -1], [22, 4, 8, 5, -12, -10], [21, 8, -2, 5, 1, -2], [-12, 0, 3, 6, -6, -3], [-13, -2, -11, 2, -3, 4], [14, 2, -3, -10, -2, 2], [-9, 5, -7, 3, 2, 1], [-5, 12, 0, 9, -1, -7], [-3, 1, 5, 3, -4, -10], [13, -11, 5, 1, -4, -9], [7, 11, 11, -6, 2, -5], [18, -14, 13, 9, 6, -2], [17, -13, 8, -3, -2, 0], [0, -10, 1, -1, 0, -7], [3, 17, 4, 10, -4, -2], [-6, 11, 12, 1, 3, -6], [3, -13, 1, 3, 0, 5], [-10, -9, 5, -7, -3, -3], [0, -11, -3, 6, 5, -2], [-19, 5, -2, 2, 8, 17], [-21, -1, -7, -7, 8, 14], [12, 18, 8, 8, -8, -15], [-14, 14, 0, -8, 4, 5], [-7, 17, -18, -5, 0, 1], [9, -9, -5, -3, 2, -1], [-7, -4, 8, 10, -7, 1], [17, -10, 4, 2, 5, -2], [1, 3, 4, -7, 2, 6], [0, -2, -6, -3, 4, 4], [-5, 7, -3, 4, 6, 0], [3, 4, -12, 2, -5, 5], [-3, 16, 4, -2, -9, 5], [-31, -1, 0, -11, 0, 1], [1, 10, -7, -1, -5, 5], [-1, 4, 0, 5, -5, -15], [7, -8, -1, -12, 3, 9], [-12, 4, 1, -6, 8, 8], [-30, -1, -7, 2, 9, 1], [-7, -15, -7, -2, 10, 14], [-13, -17, -4, -3, 6, 7], [-18, 2, -1, 8, 4, 7], [2, 15, 7, -2, -5, -13], [-2, 9, -13, -1, 3, -1], [-9, -2, -1, -2, 3, -8], [-11, 0, -2, -6, 3, 2], [-1, -13, 3, 10, 0, -7], [16, -19, 13, 4, 3, 4], [-1, -14, 0, -10, -1, 0], [1, 3, 5, 9, -8, 1], [-15, -4, 3, 1, -1, 0], [-7, 10, -7, 6, 13, -1], [-15, -12, 2, 4, 9, -12], [-3, 10, 6, 12, 1, -13], [15, -2, 4, -9, 5, 0], [-29, -2, -15, -6, 5, 6], [15, -5, -8, -3, 6, 10], [1, -12, 4, -4, 1, -10], [-1, -4, -1, 6, 11, 5], [15, 11, 10, -9, -2, -6], [18, 17, 5, 13, -11, -8], [10, -9, 4, -1, 3, -9], [-18, 14, 1, 10, 4, -6], [-16, -11, -8, 5, 5, 6], [-19, -11, -2, -5, 2, 6], [-7, -19, 0, -9, 8, 11], [-10, 0, 3, -10, -10, -13], [19, -16, 6, 1, -5, -8], [12, -13, 10, 8, 1, -11], [11, 13, 14, -1, -14, -8], [24, 2, 4, 4, 0, 0], [16, 20, -1, -1, 0, -3], [-1, 17, 3, 11, 4, -6], [2, 2, 8, -4, 6, 7], [-9, 4, -10, 0, -11, 5], [3, 0, 1, -20, 5, 4], [-16, -4, -17, -2, 12, 4], [42, -4, 1, 2, -2, -5], [-2, 19, -15, 1, 3, 5], [13, 15, -13, 6, -6, 0], [16, -18, 1, -9, -4, 7], [-15, -1, -11, -15, -8, 6], [23, -11, 13, 7, 14, -3], [-11, 28, -4, -2, 1, 1], [1, -11, -5, -3, 2, 9], [-18, 6, 2, 11, 12, -2], [-2, 3, -14, -7, -7, 14], [10, -1, 15, -3, 1, -1], [5, -8, 5, 4, 9, 0], [10, 3, 0, -1, -3, 6], [21, 6, 15, -5, -11, -10], [9, -15, -20, -1, 0, 8], [14, 8, 0, -6, -4, -12], [25, -2, 15, -4, -3, 2], [-12, -7, -3, 5, 1, 16], [-26, -2, -7, 2, 2, -7], [18, 13, 5, -8, -1, 7], [-11, 13, 2, 3, 2, -8], [8, -19, -6, 3, 19, 5], [-6, 21, -19, 2, -1, 0], [21, -9, -8, -11, -4, 8], [4, 3, 7, -3, -5, 1], [8, 16, -2, -2, -6, 3], [-16, -1, -3, 3, 5, -1], [-7, -21, 10, -7, -8, -3], [-5, -21, -9, -3, 6, 13], [-19, 2, 0, 0, -9, 9], [-6, 10, 15, 11, -8, -5], [21, -17, 6, 11, 4, 2], [-10, -5, 6, 13, -9, 1], [4, 15, -17, 7, -5, -1], [-13, -26, -1, -10, 13, 19], [20, 10, -10, 2, -8, -5], [9, 4, -8, -16, -1, -3], [-13, -1, -6, -3, 8, -6], [23, 1, 10, -9, 2, -10], [2, -3, 1, 0, -3, -16], [-12, 23, -12, -12, -5, 4], [7, 3, 4, 5, 16, 5], [22, -8, 7, -8, 4, 6], [-3, 16, 5, 11, -11, -14], [14, 17, -6, 7, -15, -5], [14, -28, 7, 0, 14, 14], [-9, 8, -4, 0, -7, -3], [7, -2, -6, -2, -3, -2], [-19, 16, -8, -7, 5, 15], [-14, 8, -17, 0, -8, 3], [3, -10, 1, 8, 7, 1], [-24, 0, -2, 5, -12, 2], [1, -27, -14, 4, 10, 16], [-15, 9, -23, -1, -6, 9], [0, 13, -15, 2, -1, -2], [5, 0, 1, -3, -3, 11], [7, -4, 0, 0, 3, -4], [37, -19, -9, -9, 0, 4], [21, -22, 1, 12, 11, 0], [16, -3, -1, 6, 11, 2], [-9, -15, -4, -3, 10, 10], [12, -17, 3, 5, -5, -3], [3, -2, -15, -24, 5, 1], [4, 7, 4, 11, 1, -10], [10, -14, 13, 7, 0, 14], [23, 7, -1, -1, -12, 4], [1, 24, -12, -9, -7, 4], [-6, -16, -10, 10, 6, 12], [5, -7, -3, -11, -6, 7], [0, -2, 4, -10, -2, 7], [-18, -17, 5, -1, 9, -3], [19, 7, -6, -13, -2, 2], [-17, -2, 5, 4, 7, -16], [9, 14, 1, 16, 7, -3], [4, -1, 4, 4, -1, 15], [26, 0, 8, -7, 16, 1], [-20, -4, -3, -2, -8, -4], [1, 3, 7, -13, 2, 6], [-11, -5, 9, -2, -8, -16], [-10, -13, -4, -9, 5, 2], [-2, -1, 9, 17, 11, 0], [17, 5, 10, -3, -8, -6], [-8, -5, 22, 13, 9, -5], [-14, -26, 2, -6, -8, 9], [-8, -15, 4, 3, 9, -10], [29, -5, -10, -9, 2, -7], [-11, -15, -19, -1, 14, 14], [10, -6, -17, -2, -10, -2], [-37, -8, 8, -1, 7, 2], [21, 2, 2, 1, -5, -14], [-4, -1, 7, -7, -1, -7], [25, -13, -11, -8, -2, 14], [13, -29, -3, -10, 6, 14], [0, 36, 6, 4, -4, -6], [7, -23, 7, 3, -12, -13], [-12, -4, -6, 0, -2, -10], [8, 8, 2, 1, -4, -9], [-23, 5, -11, -11, -2, 15], [7, 14, -8, 9, 7, 13], [17, -15, -9, -20, 8, 14], [-10, -2, 3, 14, -8, -16], [21, 3, 6, 5, 4, 12], [-10, 15, 1, -3, -17, -10], [-1, -19, -2, -12, 0, 15], [-15, -16, -13, -4, -3, 10], [5, 10, -8, -6, 3, 16], [-30, 11, -19, -25, -1, 1], [-3, -8, 13, 4, -3, -11], [24, -7, 25, 7, -1, -6], [14, -7, -7, -7, -7, -18], [11, -32, 13, -2, -3, 4], [8, -10, 23, 2, -4, -10], [-30, -5, 3, 1, 3, -1], [-41, -15, 0, 1, -6, 7], [-10, -11, -2, 11, -1, 15], [2, 19, -1, 5, -13, -12], [2, 32, -7, 6, 10, -7], [0, -34, 4, -4, 6, 14], [-30, -21, -15, -11, 9, 15], [0, -31, -1, -19, 15, 21], [5, 28, -5, 2, -9, -5], [10, -22, 3, 6, 2, 13], [-5, -12, -4, -26, 17, 17], [-21, -18, 2, -26, 9, 7], [-1, 6, -22, -6, -5, 16], [12, -21, 9, 9, -3, -9], [-9, 16, 14, 24, -5, -2], [-19, -15, 7, -7, 6, -7], [14, -23, 18, 3, -1, -12], [36, -10, 16, 20, 0, -1], [13, 1, -10, 7, 0, 8], [-5, -8, 18, 3, -9, -4], [-8, 1, 9, -3, 1, -15], [0, 8, -9, 3, -2, 7], [1, 5, 5, 21, -14, -15], [-17, 4, 1, -4, -21, -6], [5, 6, 3, 12, 5, -6], [-3, 7, -9, 11, -18, -14], [15, 0, 18, 16, 13, -10], [21, 6, 3, -4, -5, -3], [11, -15, -4, 7, 4, 0], [-22, 10, -18, 1, 12, 6], [12, 2, -5, -2, -6, -6], [16, 28, 22, -1, -6, -18], [-7, 3, -13, 8, -4, 1], [-28, 16, -7, -21, -6, 0], [-6, -10, 6, 10, 6, 15], [23, 6, -3, -12, -9, -6], [-35, 22, -24, -14, -1, 7], [-35, -1, 1, 9, -10, 4], [-13, 7, 6, 11, 2, 5], [18, -7, 29, 5, 7, -11], [-5, -29, -20, 3, 8, 17], [-24, 19, -2, -7, -13, -12], [32, -3, -3, 2, 13, 13], [19, 8, 12, -11, -7, -7], [35, -11, -21, -13, 0, 3], [-8, 4, 0, 2, -2, 0], [30, -23, 20, -1, -7, 0], [-15, 11, 3, 25, -8, -16], [12, -28, -10, 5, 10, 1], [-24, 13, 1, -5, 1, -1], [-22, 15, -25, -14, -9, 7], [-13, -26, -6, -12, 19, 7], [-17, 16, 5, -2, 7, 13], [12, 23, -5, 7, 11, 0], [-16, 3, -1, 13, -9, 12], [-16, 16, -7, -1, 10, -2], [9, 21, 8, -16, -2, -7], [-1, 18, -19, 8, 9, 6], [-17, -20, -21, -8, 1, 23], [-33, 10, -10, -6, -11, 1], [-54, -9, -17, -14, 15, 10], [-26, -17, 15, 4, 11, 1], [-6, -14, 1, 19, 2, 2], [12, 1, 26, 12, 9, -13], [-26, -4, -3, 18, 6, -3], [-31, 31, -4, -10, 6, 10], [10, -17, -5, -3, 19, 5], [1, -13, 4, -3, 20, 12], [12, 7, 12, -5, -15, -4], [-33, 17, -14, 11, 22, 5], [-33, -22, 9, -17, 1, -1], [30, 9, 9, 1, -17, -8], [46, 4, 29, 3, -16, -15], [-14, -29, 17, -9, 3, -1], [-30, 20, 23, 16, 2, -5], [29, -15, 26, 17, 0, 3], [38, -17, -4, -20, -1, 13], [2, -8, 8, 4, 6, -6], [15, 7, -2, -14, -6, -8], [-25, -6, -17, -8, 5, 5], [30, 2, 9, -6, 8, 1], [13, -18, 11, 6, -3, 4], [-24, -9, 6, -21, -5, -5], [30, 2, -4, -3, 0, 0], [-47, 8, 1, 2, 5, 15], [-20, 20, -6, -2, -8, 2], [-14, 12, -14, 12, -10, -6], [47, -6, -2, -14, -5, 4], [2, 17, 2, 19, -9, -5], [31, -26, -19, -22, -3, 12], [38, -6, 7, -12, 2, 0], [-4, -15, 17, -4, -7, -9], [-12, 15, -10, -4, -11, 14], [18, -17, 0, 3, -7, -6], [-17, -10, -7, 2, -1, 27], [7, 18, 8, 32, -9, -11], [18, 33, 18, 13, -3, -30], [-29, -2, 0, 3, -15, -20]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1185_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1185_2_a_j();".
// 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_1185_2_a_j(:prec:=6)
    chi := MakeCharacter_1185_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_1185_2_a_j();".
// 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_1185_2_a_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1185_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-1, 6, 11, -5, -7, 1, 1]>,<7,R![344, -100, -161, 64, 14, -9, 1]>,<11,R![46, 170, -167, -134, -5, 8, 1]>],Snew);
    return Vf;
end function;