
// Make newform 8280.2.a.br in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_8280_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_8280_2_a_br();".
// 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_8280_2_a_br();".
// 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 := [-4, 84, 5, -21, -1, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0], [-8, -1, 1, 0, 0], [-20, -36, 13, 4, -1], [60, -16, -21, 0, 1], [60, 0, -21, 0, 1]];
    Rf_basisdens := [1, 2, 8, 8, 8];
    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_8280_a();"
function MakeCharacter_8280_a()
    N := 8280;
    order := 1;
    char_gens := [2071, 4141, 4601, 1657, 3961];
    v := [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_8280_a_Hecke(Kf)
    return MakeCharacter_8280_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+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, 0, 0, 0], [-1, 1, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 0, 0, -1], [-2, -1, 0, -1, 0], [-1, 0, 0, -1, 0], [1, 0, 0, 0, 0], [-2, 1, -1, 0, 0], [1, 1, -1, 0, 1], [1, 1, 0, 0, 0], [-2, -1, 1, 1, -1], [0, 0, 0, 1, -1], [-1, 0, 0, -1, 0], [0, 1, 1, 1, -1], [-2, 3, -1, -1, 1], [3, 0, 1, -1, -1], [-1, 1, -1, -1, 0], [-2, 1, 1, 0, 0], [3, -2, 0, -1, 0], [4, 0, 1, 2, -1], [4, 1, 0, 1, 0], [-4, 0, -1, -1, 2], [0, 0, 2, -1, 1], [-2, -1, -1, -2, 0], [0, 2, -1, 0, 1], [-4, -1, 2, 1, 0], [7, -2, 1, -1, 1], [0, -3, 2, 1, 0], [1, 0, 2, 0, -1], [0, 0, 0, 0, 0], [2, -2, -1, 0, 1], [3, 1, -1, -2, 1], [-5, 2, -2, 1, 0], [2, -2, 0, -2, 2], [3, 1, 0, 2, 0], [-2, -2, -2, -2, 0], [-11, 4, 0, -1, 2], [8, -2, 0, 0, 0], [-2, -2, 2, -2, 0], [6, -2, 1, -2, 1], [-1, 0, 0, 1, -2], [6, 2, 0, -2, 0], [-4, 0, 4, 2, 0], [12, 2, -1, 0, 1], [5, -1, 1, 2, -1], [-8, 0, 2, -1, -1], [-4, -4, 1, -2, -1], [10, -2, -3, 0, -1], [4, -2, 0, -2, 2], [-10, -1, 3, 2, -2], [9, -2, 2, -1, 0], [4, -4, -1, -1, 0], [-3, 6, 0, 1, 0], [12, 1, 1, 1, -3], [0, -1, -1, -2, 2], [5, 1, 1, 0, -1], [0, 2, 0, 3, -3], [11, -2, 1, 2, -2], [-3, -3, 1, 3, 0], [0, 1, -3, -3, -1], [3, 0, 0, 1, -2], [2, 2, 0, 1, 3], [5, 1, -1, 1, 2], [1, 6, 0, 1, 0], [-1, -3, 3, -2, -3], [8, 2, 2, 3, -1], [-6, 4, -2, -2, 2], [-1, -5, 3, 0, -1], [5, -2, 2, -1, -4], [-3, 4, 0, -1, 2], [1, 1, -2, -2, 2], [0, 2, -1, -2, 1], [0, 4, 0, 0, 4], [-2, -1, 3, 1, -1], [4, 0, -4, 0, -2], [2, -4, -4, -1, 1], [6, 6, -3, -3, 2], [5, 1, 1, -4, 1], [11, 4, 1, 2, -2], [-5, 6, -1, 1, 1], [2, 0, 2, 2, 2], [7, 1, 3, 1, 0], [12, -2, 2, 0, -4], [5, 4, 0, 3, 2], [24, 3, 1, -1, -1], [5, 5, -3, 3, 2], [18, -6, 0, 1, -3], [-9, 2, -2, 2, 1], [0, 3, -4, 3, 0], [-1, -4, -4, -3, 2], [-7, 0, 4, 2, -1], [6, -1, 1, 1, -3], [1, -1, -3, -2, 3], [10, -1, -1, 1, -1], [0, 0, 4, 1, -3], [9, -2, 3, 0, 0], [-2, -2, 2, 3, -5], [-26, 2, 0, 0, 2], [-8, 0, -4, 0, 0], [8, 5, 3, -1, -1], [16, -3, 4, -3, 0], [10, -6, -3, 1, -2], [-13, -6, 0, -1, -2], [-16, 2, 2, -2, 4], [-10, 2, 4, 0, 0], [7, -2, 0, -1, 4], [-4, 2, 0, -3, 1], [-1, -3, -1, -2, 3], [7, -4, 2, 0, 1], [6, 0, 3, 0, -1], [16, -3, 2, -1, 2], [-12, 0, 4, -2, 2], [3, -6, 1, 1, 1], [17, 6, -3, 0, 2], [-19, -3, -1, -1, 2], [-9, -2, 2, -3, 2], [-13, 0, 0, 1, 4], [1, 4, -1, -4, 0], [0, 0, 1, -4, -1], [9, 0, 0, -1, 0], [0, -5, 5, 1, -3], [15, 4, -2, 1, 4], [-18, 2, -2, 4, -2], [21, 2, 4, 1, 0], [7, 8, -3, 1, 5], [-26, 5, -3, 2, -2], [-13, -1, 2, 0, -4], [7, 1, -2, -2, 6], [3, 5, 3, 2, -3], [-12, -4, -2, -4, 2], [15, -4, 5, -5, 1], [-3, -3, -4, -2, -2], [6, 5, 1, 1, -3], [-1, -4, 6, 1, -2], [16, 0, 2, 4, -4], [-15, -7, -1, -1, 2], [-16, -1, -3, -3, -3], [14, -3, 5, -3, -3], [5, 7, -3, 2, 3], [-8, 0, -2, -5, 5], [-14, 2, 2, -3, 5], [-2, 1, -6, -3, 0], [-5, 3, 3, 0, 3], [-6, 6, 0, -2, 2], [18, -6, 2, -3, -1], [-6, 0, 2, 0, 2], [17, -5, -3, 2, -5], [8, 6, -2, 0, 4], [-10, 2, 0, 5, 1], [-7, 4, 7, 2, 0], [3, -6, -2, -3, 2], [-32, -2, -2, -4, 0], [-9, -3, -3, 3, -2], [-20, 0, 2, 2, -4], [24, -4, -3, 2, -5], [10, -1, 1, 1, -5], [8, -4, -6, -1, -3], [-7, -6, -2, -1, 0], [-18, -4, 6, 6, -2], [6, 4, -1, 6, -3], [-15, -8, -4, -6, -1], [8, 6, 3, 1, 0], [-2, -3, -4, 1, 0], [-16, 1, 1, -3, 5], [13, -1, -3, 0, 1], [16, -12, 2, 1, -5], [8, 2, -2, 0, -2], [-15, 6, -2, -1, 0], [-10, 6, 1, -1, 6], [-1, 5, -3, -4, -1], [-10, 6, 4, 0, 0], [25, -7, 3, -1, -4], [8, 4, -6, -2, 0], [13, -4, 5, -4, 0], [-16, 6, -6, -2, -2], [12, 1, -1, 0, 6], [-21, 1, 4, 2, -2], [13, -6, -3, 1, -3], [17, 2, -2, 0, 5], [3, 2, -3, -2, -4], [-18, -2, 4, 1, -3], [13, -12, 0, -1, 0], [12, 1, 1, 5, -7], [-19, 8, 0, 3, 0], [-11, -8, 4, 0, -1], [-19, -1, 1, 3, 2], [11, 3, -1, 0, 3], [6, -7, -3, -2, -2], [15, -6, 0, 1, -2], [6, 6, 4, 8, -4], [-3, 8, 6, 3, 0], [-2, 9, -5, 0, 4], [-6, -6, 3, -4, -1], [0, -9, 2, -1, -4], [-15, 2, -2, -3, 2], [18, -2, -3, -4, -1], [-18, -4, 5, 2, -1], [-14, -2, -6, -2, -4], [7, -2, 2, -1, -2], [6, 2, 0, 2, -2], [-1, 4, -6, -4, 7], [-21, -6, 0, -3, -2], [21, -6, -3, 0, -4], [20, 8, -6, -2, 2], [17, -6, 1, -5, 5], [-9, 2, -6, -9, 0], [10, 3, 1, 3, 5], [18, 2, -2, 4, 2], [12, 0, -2, -4, 4], [2, -6, -2, 1, -5], [0, 6, 1, 0, -1], [-22, -6, 1, -8, 1], [-10, 1, 1, 4, 4], [11, 0, -6, -7, 2], [-6, 0, 2, 7, -7], [14, 7, -1, -5, 3], [0, -11, 7, 1, -5], [-15, 12, 2, 3, -2], [-5, 7, 1, 6, -1], [4, -6, 3, -4, 1], [-6, 7, -5, -5, 3], [31, -3, -4, -2, 2], [3, 10, 2, 3, 0], [3, -9, -3, -2, -5], [-12, 4, 3, 4, -7], [2, -5, -1, 8, -4], [-20, -8, 3, -6, -3], [-18, 3, -5, 3, 1], [-27, -4, -2, -2, -1], [-11, 0, 4, -5, -2], [4, -2, 3, -4, -3], [-4, -5, 3, 3, -7], [-11, 1, 1, -1, 0], [-18, 10, 0, 4, -4], [-15, 8, 0, 3, -4], [-18, 0, -4, 2, -2], [20, 3, 1, -3, 3], [-14, 7, 3, 4, 0], [14, 5, 8, 7, 0], [13, 1, -5, -8, 5], [2, -8, 4, -1, -5], [22, 2, -2, 0, 0], [0, 2, 0, -10, 2], [-12, 2, -8, 5, 1], [-3, -8, -2, 0, -1], [-33, 8, 1, 2, -2], [0, 6, 2, 4, 4], [10, -7, 7, -5, -1], [-6, 6, 3, 2, 7], [32, -2, 3, 1, -2], [14, -9, 3, 1, -1], [-16, 0, -6, 4, 4], [1, 0, -2, 3, -2], [-6, 3, 7, -7, 3], [-9, 0, -1, 1, 7], [-14, 10, 6, -1, 3], [-11, 0, 0, 3, 4], [-22, -4, -2, 4, -2], [1, -11, -4, -6, 8], [10, 1, 0, 1, -2], [5, 5, 1, -2, -1], [5, -3, -2, 2, 4], [-10, -10, 4, 6, 0], [23, 2, -2, -5, 4], [-7, 2, 2, -3, 6], [32, -2, -5, 1, -2], [-39, -3, 1, -3, 2], [-24, -2, 2, -10, 4], [-11, -5, -5, 4, 1], [13, -11, 7, -5, -2], [19, 11, -7, -5, 2], [6, 2, 3, -2, 1], [-5, 4, 0, 9, -4], [9, -6, 2, 2, -1], [-23, -4, 0, 3, -2], [-3, 3, 5, 6, 1], [5, 0, 8, 3, 0], [-5, -2, 1, -2, -4], [-38, -2, -2, 0, -2], [-3, 2, -3, 7, 1], [-30, 0, -4, -2, 0], [0, 6, -5, -8, 3], [-31, 8, 4, 1, 0], [0, -9, 3, -8, 2], [25, 5, -3, -3, 4], [-6, 12, 0, 2, -6], [8, 6, 2, 0, 0], [16, 8, -2, 0, 0], [-4, 4, -4, 10, 0], [-32, 7, 2, 1, 4], [2, -10, -2, 2, 2], [-5, -6, -1, -2, -2], [-7, 6, -8, -4, 1], [-12, -6, 2, 0, -2], [-15, -4, -1, -3, -5], [-33, 8, 0, 3, -2], [16, -7, 1, -1, 3], [-2, 10, 6, 0, 2], [7, 3, 5, -7, 4], [22, -5, 1, 7, -7], [-10, 8, -9, 8, 1], [15, -16, 4, 1, -2], [28, -4, 0, -2, 2], [-39, -8, 6, 7, -2], [-9, 6, -2, 7, -8], [-6, -4, -1, 6, 1], [25, 0, -2, -3, 2], [5, -14, 2, 0, -1], [-12, 4, 4, -2, 6], [-3, 4, -6, -7, 8], [1, -4, -3, -10, 2], [-4, 4, -4, 4, -4], [40, -9, 3, -1, 3], [-21, -4, 2, 7, 0], [12, 3, 3, 3, -1], [-38, -1, 3, 0, -4], [-1, 1, 7, 5, 0], [10, -6, 10, 2, -2], [13, 2, -12, -1, 4], [17, -7, 3, 5, -10], [-4, 10, -2, 1, 5], [0, 0, -2, -3, -3], [20, 1, -2, -1, -2], [-23, -12, -4, -3, 2], [-3, -2, 8, -1, -4], [11, 0, 0, 9, -2], [4, -4, -4, -4, 8], [16, -3, -1, 3, -1], [15, 11, -5, -2, 1], [-25, -4, 12, 5, -4], [-13, -5, -3, -2, 5], [19, -14, 8, 3, -2], [36, -8, -4, 6, -6], [-28, 4, -2, -8, 10], [-48, 0, -1, 2, -1], [32, 8, -5, 2, 3], [-14, -6, -4, -8, -2], [-9, -9, 2, 0, 0], [-10, 14, -2, -1, 9], [10, 0, 11, 4, 3], [-38, -6, 2, 1, -1], [3, -10, 5, 1, 1], [-18, -1, -1, -1, 3], [36, -5, 3, 1, 1], [-13, -9, 1, -6, 3], [-21, -4, 4, 3, -4], [62, -2, -4, 2, -2], [-2, 1, -7, -3, 1], [19, -1, 5, 8, -5], [33, -8, 0, -3, 2], [52, 3, -9, -4, 4], [11, -7, -2, 2, 0], [19, 8, 1, -1, -1], [-34, 8, 0, 0, 4], [11, -14, 0, -3, -8], [12, 0, 3, 1, 6], [-3, -8, 8, 7, -4], [8, 6, -6, -6, -2], [-13, -3, 2, 4, 4], [-2, -17, 3, -3, -3], [-20, 6, 2, -2, -2], [8, -2, 11, 9, 0], [36, 2, -2, -6, 6], [40, -4, 6, -4, 4], [-9, 6, -8, 3, 4], [-41, 3, -4, -6, 4], [-16, 10, -8, -10, 2], [20, -11, -1, -7, 7], [7, 1, 7, -2, -3], [-14, 2, 2, 4, 10], [22, 2, 4, -8, 2], [-8, -4, -1, 2, 5], [-33, 8, -4, 4, 5], [4, 11, -7, 3, 5], [32, -2, -4, -8, 2], [-33, -3, 5, -1, 0], [4, 4, 1, 7, 0], [4, -4, -6, 4, -4], [-4, -12, 0, -8, -2], [-8, 4, -11, 4, -1], [-46, 6, 8, 3, 1], [5, 8, -2, 9, 0], [-6, -4, -4, -2, -4], [-2, 2, -2, 14, -8], [-9, 3, -1, 10, -1], [43, -10, 4, -4, 7], [3, 3, -11, -7, 2], [26, -15, 9, 3, 1], [-31, -6, 8, 9, 0], [-24, -4, 4, 0, -6], [36, 15, 3, 7, -1], [-13, 14, -2, -1, 4], [47, -10, 0, 7, -10], [-29, -3, 5, -1, 4], [-36, -2, -1, -4, 1], [44, 4, 5, 1, 2], [32, -4, 2, 4, 2], [4, -15, 3, 6, -4], [-63, 3, 1, 4, -5], [30, 4, 0, 10, -2], [9, 11, 0, 2, 2], [-6, 17, -6, 7, 0], [-24, -1, 1, -4, -2], [-61, -1, -1, -2, 3], [-15, 7, -10, 0, -4], [8, 0, 10, 2, 2], [24, -8, 2, -5, -1], [20, 8, 8, -2, -2], [-7, 0, 0, 13, -6], [-43, -8, -6, 1, 0], [4, 8, 1, 0, 9], [-10, 12, 6, 0, 0], [-7, 3, -3, 7, 8], [-24, 6, -6, -7, 9], [20, -2, 8, -9, 3], [11, -8, 8, 6, -7], [-44, 3, 10, 3, 0], [2, -16, 0, -2, 4], [17, -4, 4, 3, -12], [10, 2, 3, 0, -3], [-11, 14, -6, 5, 0], [-20, -12, 6, -2, -8], [53, 8, 0, -3, -2], [-12, -2, 2, 8, -2], [30, 4, -3, -4, -1], [-36, 21, -1, -5, 7], [-20, -2, 2, 2, -2], [16, 19, -9, 2, 8], [32, 22, 2, 6, 0], [8, 8, -1, 7, -8], [16, -2, 2, -2, -2], [0, -3, 1, 1, 5], [-19, 2, 2, -6, -3], [5, -4, -1, 2, -4], [27, 1, -9, 4, -3], [30, 0, 0, 2, -2], [-34, 10, -2, 2, 0], [36, -14, 9, -4, -1], [10, -2, 0, 0, 4], [-11, -14, -5, -10, 2], [-59, 9, -1, 2, -3], [-4, -4, 8, -2, -6], [19, -5, 7, 2, -7], [-13, 6, -8, -7, 6], [-18, -6, -6, 2, 4], [-17, -8, 0, -5, -4], [-17, -5, 5, -4, 1], [22, 4, -1, -6, 1], [31, -6, 2, -1, 8], [13, 10, 0, 5, 2], [-17, -6, -4, -5, 6], [-4, 8, 4, -4, -2], [-52, -12, 0, -11, 1], [-30, -7, -5, 6, 2], [27, -5, 7, 0, -1], [10, 8, 0, 2, 0], [45, 3, -10, 0, 4], [24, 11, 6, -1, -4], [11, -3, 7, 10, -7], [-31, 20, 5, 1, 5], [50, 2, 3, -1, 0], [-11, 3, 5, 4, -5], [10, 4, -4, -8, -2], [25, 4, 6, 9, 0], [7, -2, 5, -3, 1], [2, 13, -8, 11, 0], [15, 14, -3, -6, -2], [-6, -2, 6, 10, 4], [-36, -10, 6, 3, -7], [-23, -2, 10, 5, 0], [-36, -12, 14, 13, -7], [44, 2, 6, 6, 4], [-10, -15, -1, -7, -3], [65, 9, 0, 6, 2], [-4, -7, 5, 2, -6], [-8, -24, -3, -6, -1], [9, 16, 0, -3, -4], [-40, -16, 8, -8, -6], [5, -12, 0, 3, -4], [-10, 12, 5, 5, -8], [27, 9, -11, -5, 4]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_8280_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_8280_2_a_br();".
// 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_8280_2_a_br(:prec:=5)
    chi := MakeCharacter_8280_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(3457) - 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_8280_2_a_br();".
// 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_8280_2_a_br( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8280_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![128, 104, -54, -19, 4, 1]>,<11,R![-1312, 408, 160, -46, -4, 1]>,<13,R![-3584, 968, 248, -66, -4, 1]>,<17,R![-2416, -2148, -584, -25, 10, 1]>],Snew);
    return Vf;
end function;