
// Make newform 9025.2.a.bs in Magma, downloaded from the LMFDB on 13 January 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_9025_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_9025_2_a_bs();".
// 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_9025_2_a_bs();".
// 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 := [-5, -25, 18, 21, -8, -3, 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], [-4, -1, 1, 0, 0, 0], [-5, 20, 6, -10, -1, 1], [-5, 15, 7, -15, -2, 2], [20, 25, -28, -20, 3, 2]];
    Rf_basisdens := [1, 1, 1, 5, 5, 5];
    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_9025_a();"
function MakeCharacter_9025_a()
    N := 9025;
    order := 1;
    char_gens := [5777, 3251];
    v := [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_9025_a_Hecke( : Kf := Kf)
    return MakeCharacter_9025_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, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 1, 0, -1, 0], [0, -1, 0, -2, 1, 1], [0, -1, 0, -1, -1, -1], [0, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0], [-1, 0, 0, -3, 0, 1], [-1, -1, -2, -1, 1, -1], [-1, 1, -1, 0, 2, 1], [0, 2, 0, 2, 0, 0], [-2, 1, -1, 2, -2, 0], [1, 1, -1, 0, 1, 0], [0, 0, 2, 2, -1, 1], [-6, 4, -1, 2, 2, 1], [0, -2, 2, -2, 3, -1], [3, 1, -1, -1, 1, -2], [-1, 2, 0, 5, -3, 0], [-6, 4, -1, -1, 2, 2], [2, -1, 0, 2, -4, 1], [0, 1, -1, -3, -4, 0], [-5, 1, 0, -1, 2, -3], [-3, -2, -1, 3, 5, -1], [-1, 3, 1, 6, -2, -2], [-7, 2, 0, -1, 3, -2], [-8, 0, 1, -3, 1, 1], [-1, -1, 0, -3, 0, 3], [8, 0, 0, -1, 1, 0], [-2, -3, 1, 0, -4, 2], [-6, -1, -1, -1, 6, -2], [2, 3, 1, 1, -3, -1], [1, -2, 2, -2, 6, -2], [6, -5, -1, 1, 0, -2], [1, 0, -2, 1, 5, -2], [4, 2, 0, 6, 1, 1], [10, 3, 3, 1, -1, 0], [2, -4, 2, -6, 3, 3], [-6, -1, 2, 2, 0, 0], [-6, 0, 3, -2, -2, -1], [-3, -6, 1, -4, -4, 1], [-5, 3, -1, 6, 2, 0], [-1, 3, 4, 5, 1, 2], [-2, 0, -1, 7, 5, -1], [-2, -5, -2, -3, -1, 1], [1, 4, -1, -2, 8, -3], [8, -5, -2, 4, 0, 0], [5, 3, -1, 0, -2, 5], [-7, 6, -2, 1, 6, 3], [0, -2, 1, 4, 2, -3], [9, 0, 2, 3, -5, -2], [-2, 0, -3, 1, 0, 0], [4, -5, 1, 5, -3, -4], [0, -1, -3, 7, -3, 1], [-2, 1, 2, -4, -2, 3], [7, -2, -4, -3, -4, -1], [5, 5, 1, -2, -6, 2], [-7, 3, -4, 7, 1, -2], [-5, 4, 1, 2, 0, 5], [-2, 4, -2, -3, 5, 4], [-8, 1, 4, 2, 2, 4], [-20, 5, 0, 3, 3, -1], [2, 4, 3, -3, -6, 4], [15, -6, 0, 1, -8, 1], [-4, -6, 3, 0, 2, -5], [-9, 2, 5, 0, -4, 3], [5, 0, 3, -2, -12, 5], [-4, 4, -2, 3, 9, 0], [4, -3, -4, 0, 2, 2], [-8, 0, 1, -10, 0, 7], [-3, 2, -2, 14, -10, -2], [-11, 1, -3, -2, 5, 2], [8, 1, 2, 4, 0, 4], [-11, 7, -2, 2, 14, -1], [-10, 10, 3, 3, -1, -3], [-9, -8, -3, -14, 9, 0], [-3, 5, -2, 8, 0, 3], [-2, -2, -3, -6, 0, 3], [4, 2, -3, -5, 5, -3], [3, -2, -5, 0, 2, -3], [9, -2, 4, 3, -9, 0], [-1, -2, 0, -3, 13, 0], [-6, 5, -6, 6, 7, 3], [-8, 0, 2, 5, -7, -4], [-17, 2, 3, 8, -1, 4], [9, 2, -1, 10, -8, -1], [-11, 0, -1, 7, 1, -3], [-3, -4, -5, -6, 4, 1], [11, -9, 4, -11, -3, 5], [-16, 3, 1, 1, -3, -1], [-4, 6, -2, 14, 0, 4], [-9, 2, -1, -10, 5, 0], [-16, 8, -6, 4, -3, 3], [-9, 6, -3, 4, -5, 2], [0, -2, 3, -9, 6, 2], [-7, -2, -4, 3, 4, -1], [4, 2, 3, 13, -3, -3], [0, -6, -8, -6, 8, 0], [3, 0, 1, 6, 1, -4], [9, -7, 6, -5, 9, -3], [-2, 2, -5, -7, 11, 1], [-6, -3, -1, 3, 3, 2], [-4, -9, 4, 2, -2, 0], [-2, 6, -5, 11, -11, -7], [5, -4, -1, -8, 10, -1], [7, 0, 4, -1, 7, -4], [-9, 6, 5, -2, 0, -5], [-6, 4, 2, -7, 13, -2], [12, 5, 1, 9, -9, -1], [-8, 6, 0, 4, 12, 2], [10, -1, -1, -9, -6, -2], [6, -4, -4, 3, -1, -2], [-11, 4, 3, 3, -11, -5], [-7, -1, -7, -10, 8, 3], [8, -1, -1, -1, -6, 6], [-15, 1, 1, -5, 5, 6], [-3, 8, 2, 7, -3, -2], [-4, 7, 1, -5, 1, 7], [18, -2, 9, -8, -10, 7], [5, -2, -8, -5, -2, -7], [18, -1, 6, 3, -15, 1], [-9, 7, 3, -6, -8, 2], [9, 6, 2, 10, 0, -2], [3, -4, 8, 3, -12, -1], [13, -15, 0, -9, -6, -1], [-15, 1, -3, -5, -5, 8], [5, -6, 1, -10, -8, 1], [2, 0, 2, -8, -7, 3], [15, -10, -3, -4, 5, -2], [0, 2, -5, -9, 17, 3], [4, 2, 2, 8, -9, 3], [-16, -6, -7, -7, 2, -2], [-4, -2, 3, 1, 3, 5], [-22, 10, -4, 9, 1, -4], [3, -8, -4, -11, -7, 0], [3, -6, -2, -17, 11, 6], [5, -2, 4, -2, 10, -6], [-8, 0, 7, 3, 16, 4], [-4, 1, -7, 0, 10, 0], [-1, 5, 3, 9, -11, -2], [5, 11, 2, 3, -3, 0], [8, 6, 10, 0, -16, 2], [7, 2, 7, 2, 0, 3], [-15, 2, -4, 3, -4, 3], [12, -5, 2, -6, 4, 1], [7, 3, -1, -4, 10, -5], [0, -3, -8, 9, 11, -1], [0, -6, -2, 9, -1, -4], [19, -3, -1, 2, -20, -3], [-10, 10, -2, 2, 4, 6], [-3, 14, 2, 8, 0, 0], [-9, 9, -1, 18, 2, 6], [-1, -2, 1, 2, 14, 3], [-26, -5, -1, -9, -4, 4], [-3, 1, 1, -10, 0, -7], [6, 0, 3, -17, -5, -1], [9, -1, 8, 9, -7, -8], [18, 1, -6, 2, -2, 1], [17, -17, 4, -16, 2, 5], [-21, 6, -1, 11, -7, -1], [16, 4, 10, 8, -17, 3], [-5, 9, 0, -12, 6, 5], [7, 10, 5, -4, -18, 3], [-1, -6, 3, 12, -13, -2], [-2, -9, 4, 4, -12, -3], [-25, 0, 0, 15, -9, -4], [2, 9, 2, 10, 13, 1], [-7, 0, -2, -2, -12, 2], [6, -6, -9, 3, -5, -5], [-13, 7, -5, -1, 17, 0], [-9, -10, 2, 7, -2, -3], [-19, -8, -1, -5, -9, 3], [21, 9, 5, 0, -12, 7], [10, 0, -6, -1, -5, -8], [0, 14, 3, 9, -2, 8], [-1, -2, 2, -1, -17, 0], [26, -8, 1, 3, -22, -6], [18, 6, 0, 9, -23, 2], [-3, -2, -6, 5, 3, -4], [-20, 0, -5, 12, 12, -3], [4, -5, -6, -16, 13, 5], [-8, -2, 3, 13, 0, -4], [-8, -2, 5, 13, 5, 1], [-8, 6, -2, 17, 1, -4], [0, -6, -13, 3, 5, -7], [11, -4, 1, -5, 9, -1], [0, -9, 0, 11, 5, -7], [12, 1, 6, 14, 5, -1], [18, 2, 1, -2, 0, 3], [14, -20, 1, -19, -3, -3], [-7, -4, -13, -7, 7, 1], [8, -10, -2, -16, 5, -1], [-14, -16, 0, -14, 12, -4], [-13, 7, 2, 7, -5, -1], [0, -3, -1, 1, -9, -9], [-20, 9, -4, 19, -15, -7], [-21, 15, -3, -3, 1, 8], [-18, 7, -1, 0, 4, -10], [4, -4, 6, -12, -8, 8], [4, -5, -8, 14, 1, 5], [34, -11, 4, -11, -13, 3], [-14, 2, -5, -5, -8, 2], [15, -8, -7, -2, -10, -1], [5, 11, -2, 11, 3, -9], [-7, 8, 3, 14, -7, 4], [4, -2, 0, -5, -1, 2], [-16, -6, 6, -4, -8, 2], [7, -1, 7, 6, -16, -5], [-13, -7, 0, -18, -6, -7], [27, -7, 4, 5, 0, -5], [12, -4, -10, 4, 4, -6], [-5, 7, 4, -17, 9, 7], [2, -9, 10, -8, 17, 5], [-9, -5, 0, -9, -14, -9], [22, -14, 0, 2, -11, -1], [1, -4, 7, -17, 19, -1], [-8, -14, 8, -6, -8, -4], [11, 6, -1, -14, 8, -1], [-16, -2, 0, 8, 6, -8], [-9, -9, 1, 3, 9, -12], [-15, -11, 6, -2, -6, -1], [8, 2, 6, 22, -17, 3], [8, -6, -4, -13, 7, -2], [-12, 11, 2, 8, 24, 0], [-19, 10, -7, 18, 10, 1], [-4, 12, -3, 10, -12, -3], [9, -14, -3, 0, -2, -1], [-20, 9, 0, 0, 1, -3], [-5, -6, -10, 5, -12, -1], [-5, 4, -2, -9, 10, 3], [-8, 6, 2, -9, -3, -8], [18, 4, -1, 1, -11, -1], [1, -8, 2, -15, -15, 2], [-26, -7, -9, 4, 4, -4], [29, 2, 6, 7, -7, -2], [9, -20, -2, 5, 2, 3], [-15, 9, -14, 8, -4, 3], [8, 7, 6, 0, -8, 9], [2, 4, -5, 1, 13, 9], [15, 11, 11, 6, -3, 6], [-28, 14, 4, 6, -5, -1], [7, -14, 1, 10, 17, 0], [29, -6, -1, 10, -1, -4], [6, 10, -2, 4, -4, 8], [-6, -20, 6, -9, -3, 6], [9, -15, 3, -6, 9, -2], [-18, -11, 3, 5, -6, 2], [-19, 8, 4, -5, 2, -11], [12, 6, 17, -5, -11, 5], [-26, -3, 9, -1, 5, -1], [-1, 5, -4, 18, -4, -3], [11, -14, -5, 11, -3, -11], [-26, 18, -8, 14, 7, 9], [31, -13, -4, -9, 15, 7], [10, 22, -1, 14, -2, -3], [36, 1, 1, 1, 3, -3], [22, 21, -3, 5, -21, 6], [-10, -2, 0, -24, -1, 1], [-23, 12, -3, -3, 1, 3], [-4, -1, 1, 2, -16, 10], [-6, -18, -5, -25, 2, -2], [-17, 6, -5, 0, 11, -2], [1, 5, -5, 10, 10, -4], [36, 4, 0, 16, -26, 4], [-36, -10, -6, -12, 6, 0], [18, 16, -4, 6, -5, 7], [6, -12, -11, -6, 2, -7], [21, -7, 3, -1, -13, -4], [4, -8, -2, 2, -21, 5], [8, 2, -5, 11, -17, -1], [-20, 11, 5, 11, -23, -6], [39, 0, -5, 8, 3, -6], [17, -10, 3, -17, -13, -1], [26, -5, 11, -21, 6, 8], [-19, -8, -11, -19, 7, 9], [-13, 7, -3, 4, 15, 2], [-16, -6, -4, 6, 1, -9], [-8, 4, -10, -8, 14, 10], [-13, 16, -7, 12, -10, -13], [-3, 3, 1, -2, 26, -1], [3, -13, 6, -11, -26, 7], [-9, 4, -4, -1, 6, 9], [29, 10, 5, 24, 4, -11], [16, -1, 9, 2, 8, 2], [35, -2, 12, -1, -31, 6], [1, -2, 11, 6, -25, 0], [-16, 4, 0, -3, 9, 6], [-40, -2, 0, -8, 14, 0], [4, -16, 6, -14, 3, -9], [14, 12, -6, 9, 7, 14], [35, -4, -2, 21, -3, -20], [23, 9, -4, -5, -3, 2], [32, -13, 3, -3, -5, 2], [39, -1, 3, 2, -2, -5], [-1, -8, -6, -11, 3, 0], [-8, 4, 1, -19, 1, 1], [-22, 19, -5, -1, 16, 12], [-12, -2, -5, -7, 19, -1], [13, 2, -8, 7, -14, 5], [-6, -6, -8, 12, -21, 5], [32, 8, -8, 1, -5, -2], [8, -12, 2, -26, 8, 8], [-15, -2, -10, 5, 10, -9], [26, -6, 9, -1, 10, 8], [-4, -2, -7, -11, 23, 3], [36, -14, 9, -13, -15, 1], [-41, 8, -8, 17, 4, -1], [-11, 9, 7, 10, -8, 0], [25, -5, 4, -19, 13, -6], [-19, 22, 2, -8, -2, 10], [-8, 6, 7, 9, -12, -12], [29, -6, 1, 7, 5, -9], [3, -8, 0, -19, -7, 0], [0, -9, -8, 18, 11, -7], [21, -12, -5, -4, 8, 7], [17, 2, 6, -3, 11, -6], [42, -8, 17, -25, 5, 1], [11, 6, -1, -4, 7, -8], [11, 10, -5, -4, -8, -1], [-23, 26, 4, 17, -7, 0], [-16, 6, 0, 2, 11, 3], [-12, 16, 0, 8, 6, -4], [-14, -10, 14, 16, -14, -4], [44, 6, 2, -6, 6, 0], [-5, 13, 3, -7, -5, 0], [-3, 0, 9, -1, -11, 5], [-8, -8, 0, -4, 16, -8], [-4, -4, -10, 6, 7, -11], [-21, -7, 5, -6, -2, -1], [-11, -4, 7, 4, -8, 15], [7, 6, 4, 28, 2, 4], [11, -12, 3, -18, -14, -1], [-5, -14, -5, 0, 9, -2], [-14, -6, -12, -12, 3, 11], [-27, -2, 0, -9, 18, 9], [-29, -5, -2, -23, -3, 4], [13, -7, -4, 4, -22, -1], [11, -5, -11, -5, 3, 4], [28, -5, 10, -6, 0, 9], [3, -15, -1, -6, -21, 0], [36, -19, -1, 3, -25, -4], [-26, -10, -10, -6, 12, -14], [30, 0, 1, -6, -8, -9], [13, -10, 3, -8, 7, 12], [-44, -7, -1, -17, 27, -2], [-24, 15, -6, 26, 5, -7], [-2, -2, -4, 27, -9, -12], [26, -8, 9, -15, 5, -11], [19, -8, 10, -23, 7, 14], [4, -18, 16, -7, 23, -6], [-5, -11, 2, -23, -2, 13], [31, -15, 6, 20, -8, -17], [-11, 12, -8, 0, 24, -10], [-2, 0, -7, 15, -14, -2], [10, -26, 3, 5, -1, -11], [13, 7, -14, -8, 20, -3], [-12, -4, -7, -9, -5, -3], [-23, -19, 1, -14, 5, 2], [8, -20, 1, -10, 0, -11], [-10, 0, -6, 4, -11, 1], [3, 4, -10, -18, 20, 6], [-3, -22, -1, 1, 5, 1], [-61, 13, -7, 12, 5, -2], [-3, 16, 13, 2, -3, -4], [-32, 10, 3, 1, 2, -6], [17, -22, 1, -30, 4, -9], [40, 13, -2, 0, 2, -3], [-25, -11, 9, 16, -9, -4], [-20, -6, -6, 3, 7, -14], [-16, 4, -6, 10, 28, 0], [-5, -15, 0, -25, -15, -10], [12, 5, -9, -7, -30, -4], [17, -22, 5, -9, -29, 9], [-6, -21, -2, -2, 3, -9], [-6, 6, 2, -19, -1, 2], [-30, 0, 5, 3, 8, -2], [7, -16, 1, 6, 12, 3], [11, 8, 9, 18, -2, 3], [11, -5, 1, 11, 17, 6], [-21, 16, -8, -13, 19, 10], [-43, 8, -6, -6, 18, 10], [1, 19, -1, -15, 13, 0], [15, 14, 2, 15, -26, -5], [37, -9, -7, 17, -17, -14], [-35, -13, -3, -12, 15, -10], [-31, 9, -4, 7, -7, -10], [-34, -13, -13, -9, 9, 1], [29, -2, 1, -10, 8, 13], [9, -16, -9, -16, 4, -1], [-27, 7, -14, 13, -16, 1], [-16, -10, 15, 2, -20, -7], [20, 6, -5, -8, -4, -3], [11, 0, 7, 16, 1, 2], [6, -2, 3, 5, 6, 2], [-2, -2, 2, -26, 2, 4], [-19, 5, -13, -7, 7, 12], [11, 4, -9, -10, -1, -10], [-39, 16, 4, -5, -3, 6], [23, 10, -1, 14, -4, -1], [-9, -11, -17, -30, 16, 4], [7, -28, -9, 7, 9, -9], [13, 6, 8, 18, -20, 4], [-1, 2, 17, -6, -26, -1], [-26, -14, -8, -25, 5, 0], [11, 11, 12, -5, 3, 5], [54, -29, 11, -21, -5, -5], [-4, -1, -9, -5, 15, -20], [19, 6, 7, 19, 3, 3], [-17, 6, 2, 3, 12, 1], [-13, -2, -19, -2, 24, -5], [-7, 5, -18, 3, 15, -9], [2, 22, 19, -4, 0, -1], [-2, -3, 3, -7, -26, 10], [-12, -18, 1, 23, -14, 0], [-31, 7, -15, 23, -3, -10], [-24, 20, -10, 11, 15, -4], [23, -15, 1, -16, -7, -2], [-16, -20, 3, -15, -10, 6], [-36, 5, -4, 13, 3, -7], [-13, -7, 2, 1, 8, -11], [24, 19, -1, 21, -25, 4], [8, 8, 9, 32, -46, -7], [6, 14, -3, 9, 27, -7], [-32, 6, -4, -10, 1, 19], [5, -8, 1, 4, -2, 15], [9, -34, -5, 5, 13, -5], [-10, 22, 13, -27, 3, 3], [6, -29, -2, -19, 11, -1], [16, -14, 6, 26, -8, -14], [-11, -9, -11, -8, -10, -5]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_9025_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_9025_2_a_bs();".
// 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_9025_2_a_bs(:prec:=6)
    chi := MakeCharacter_9025_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_9025_2_a_bs();".
// 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_9025_2_a_bs( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_9025_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-1, -3, 1, 1]>,<3,R![-5, 25, 18, -21, -8, 3, 1]>,<7,R![-67, 38, 123, 20, -21, -2, 1]>,<11,R![247, -871, 522, 9, -46, 1, 1]>,<29,R![-12781, -2693, 3140, -97, -108, 3, 1]>],Snew);
    return Vf;
end function;