
// Make newform 8280.2.a.bs in Magma, downloaded from the LMFDB on 24 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_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_8280_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 := [16, 32, -1, -14, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [4, 3, -10, 0, 1], [-28, -39, 14, 4, -1], [-24, -3, 14, 0, -1]];
    Rf_basisdens := [1, 1, 4, 8, 4];
    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], [0, 0, 0, -1, -1], [0, -1, 1, 0, 0], [1, 0, 1, 0, -1], [-1, -1, 1, -1, 0], [1, 2, 0, 0, 1], [1, 0, 0, 0, 0], [-1, 0, 1, -1, 0], [4, -2, 1, -1, -1], [3, 0, 0, -1, 0], [-5, 1, 0, -1, 0], [0, 0, 0, 0, 0], [2, 0, 1, 2, 0], [-1, 2, -2, 1, 2], [1, 0, 0, 1, -2], [0, -1, -1, 0, -2], [1, -2, 0, 1, 2], [-1, 3, 0, -1, 2], [0, 0, -1, -2, 0], [0, 0, -2, 0, 0], [9, 0, 0, -1, 0], [-2, 2, 0, 2, 2], [6, 1, -1, 2, -2], [3, 0, 0, -3, -2], [-2, 1, 1, 2, 0], [9, 2, 0, -1, 0], [-3, -2, 0, -2, 1], [-1, 2, 0, -3, -2], [4, -2, -1, 2, 2], [-2, -2, -1, -2, -4], [-3, -2, 0, 2, 1], [5, 4, 1, -1, -4], [-1, -6, 2, -4, -3], [8, -1, -2, 0, 4], [3, 0, 2, 1, 2], [-3, 0, 1, -2, 3], [4, 0, 0, 0, 4], [2, 1, -3, 0, 0], [2, 4, -5, 2, 4], [-9, 2, 2, 0, -3], [0, 2, 0, 0, 0], [-10, -4, -1, 4, 4], [4, -1, 0, 4, 2], [-8, 2, 0, 2, 2], [5, 0, -4, -1, 0], [2, 0, 0, 2, 4], [10, 4, 0, 0, 2], [-4, 0, 2, 2, 4], [-2, 4, -1, 0, 4], [9, 2, 3, -5, 0], [8, 2, 2, 0, -2], [-3, 2, 2, 0, -3], [2, -4, 3, -4, -4], [-1, -1, 5, -1, -2], [1, -4, 1, -3, 0], [10, 2, 2, -1, 1], [2, 0, -1, 2, 2], [-6, -2, 0, 0, -4], [-3, -4, -2, -1, -4], [5, 6, -4, 3, 2], [-2, -1, -1, 4, 6], [-12, -4, 1, -2, -2], [-2, 4, 2, -1, 3], [-7, 8, 0, -4, 3], [7, -8, 1, -3, -4], [7, 2, 0, -6, -1], [-4, 7, 3, -2, -2], [-15, 6, 1, 1, 0], [6, -2, 3, 4, 0], [10, -6, 0, -4, -2], [15, -6, 2, -1, -2], [8, -4, -4, 0, -2], [6, 3, -1, -2, 4], [1, -6, 2, 1, -6], [-2, 3, 1, 6, 6], [-2, -7, 2, -2, -6], [-12, 4, 0, 4, 2], [8, -2, -3, 1, -5], [2, 0, 0, -6, -4], [13, 6, 0, 2, 5], [6, -8, 0, 4, 2], [2, -4, 0, 5, -3], [17, 4, -3, 0, -3], [-9, -4, 5, -4, -5], [-16, -2, 2, 3, 5], [-9, 2, 0, 1, 6], [4, 0, 1, 2, 0], [20, -2, -2, 2, -2], [11, 0, -6, -1, -6], [-2, -6, -2, 4, 2], [0, 10, -5, 2, 6], [1, 6, 1, -3, -2], [1, -6, 1, -5, -4], [10, 4, -2, -1, 1], [-10, 2, -5, 6, 6], [2, 0, -2, -4, -8], [-14, -2, 2, -4, 6], [0, -2, 1, -6, 0], [-7, 0, -7, 4, -3], [5, -4, 6, -3, -4], [1, 2, 2, -7, -6], [-22, 0, -4, 8, 4], [14, 1, -3, -2, -4], [12, -4, -1, -4, 2], [6, -1, 0, -6, 0], [-18, 4, 0, 2, 2], [-12, -1, 3, 2, 6], [2, 10, -7, 3, 7], [-12, 0, 4, -4, 0], [10, 8, -2, 0, 0], [-11, -1, -1, -3, -4], [13, -2, 2, -2, 3], [4, 6, -6, 0, -4], [28, 6, -4, 0, -2], [-5, 2, 0, 1, 4], [12, -2, -1, 4, -4], [-5, 4, -5, 0, -3], [14, 4, -8, 2, 0], [-10, -9, -1, 2, -2], [0, -8, 5, -4, -2], [9, -2, 2, 3, -2], [5, 0, 3, -8, 5], [-2, -4, 4, -4, -2], [-9, -6, 0, 4, 5], [0, 1, -1, -4, 2], [-22, -6, 2, -1, -7], [1, 7, 1, -3, 6], [-11, -6, 4, 3, 6], [3, 2, -1, 5, 0], [13, 6, -2, -2, -5], [-6, -6, 2, 2, -4], [5, 8, -4, 5, 0], [-4, 2, 3, -1, 9], [0, 4, 4, 2, 8], [-8, 6, 4, 0, 2], [-3, 4, 4, -3, -6], [15, -2, -2, -9, -8], [9, -9, -1, -9, -6], [-3, -2, 5, 5, 2], [-14, 0, -4, 4, -4], [-14, 14, 1, -2, 4], [1, 4, 0, 9, 10], [3, 2, 2, 5, 10], [20, 0, -4, 2, -2], [11, 4, 0, -6, -9], [10, -4, -1, -2, -2], [5, -2, 5, 1, -2], [-2, -2, -3, 0, -6], [24, -7, -3, 2, -4], [14, -6, 4, 6, -2], [9, -8, 4, 2, -9], [22, -4, -3, 4, -2], [19, -2, 0, -3, 0], [-14, 0, -6, 4, 6], [-8, 4, 0, 16, 8], [-5, 2, -3, 3, 4], [-5, 2, 2, -2, 7], [-4, 5, -1, 4, 2], [27, 0, 1, 4, -1], [-26, -1, -1, 2, 2], [0, 2, -1, 6, 2], [6, -11, 3, 2, -8], [-14, 4, -8, 9, 5], [5, 5, 3, -3, 10], [15, -5, 3, 5, 4], [0, -4, 4, -2, 0], [2, 0, 8, -2, -10], [-14, 11, 2, 10, 6], [4, 8, -2, -4, 0], [3, 8, 3, -5, 12], [24, -4, 0, 2, 2], [-11, 3, 1, 1, 4], [0, 3, -4, 0, 4], [-4, -6, 0, -6, -8], [-22, -2, 7, -2, 0], [-7, -4, 3, 3, 6], [-19, -5, 1, -7, -10], [-21, -2, -4, 6, -1], [6, 6, -1, 4, -2], [-14, 1, -7, 6, 0], [25, 8, -5, 4, 3], [2, 10, 2, -4, -8], [-9, -7, -5, 3, 10], [-15, 2, -8, 2, 5], [5, -8, -4, -2, -3], [15, -2, 0, 7, 14], [-11, -1, -2, 5, -4], [-5, 7, 7, -3, 0], [4, 8, -3, 6, 12], [-14, -8, 0, -6, 0], [2, -8, 6, 2, 4], [-5, -16, 8, -5, -4], [-6, 2, -12, 4, 6], [4, 8, -2, -7, -1], [-14, 2, -2, -12, 4], [6, -8, -2, 8, 4], [2, 0, -6, -8, -12], [-24, 8, -1, -4, 8], [-4, 5, 7, 4, -6], [13, 8, -4, 6, 3], [0, 13, -4, 0, 6], [-16, -6, 6, 0, -2], [16, 0, 4, 8, 8], [22, -12, 1, -6, -6], [6, -6, 8, 0, -10], [-6, -3, -6, 6, 8], [-34, -2, 5, -5, -1], [2, -4, 1, -14, -4], [-18, -2, -5, 2, 2], [-18, 8, -9, 10, 10], [15, 2, -2, 2, 1], [10, -8, 2, 4, 6], [-35, 10, -2, 1, 6], [-16, 2, 0, 6, -4], [22, -10, 1, -4, -2], [-11, 2, -9, 5, 8], [-12, 4, 6, -1, 3], [-18, 0, -1, -2, -10], [3, -12, 1, 7, 0], [4, -2, 4, 2, 6], [-39, -1, 0, 1, 0], [-16, 0, 0, -11, 5], [-10, 12, -3, 0, -2], [13, -12, 1, -11, -8], [-13, 6, 10, 2, -9], [0, 6, -3, 5, 9], [-15, -2, 0, 6, -1], [7, -2, 2, 3, -2], [19, 4, -4, -6, -1], [-8, 5, -7, -4, 4], [-22, 12, -10, 2, 4], [-19, -3, -3, -1, -10], [-9, -10, -2, 9, 8], [-8, 8, 4, -4, -4], [0, -6, -8, 6, 4], [-18, -2, -2, -4, -4], [-17, -14, -1, 3, 2], [15, 1, -4, -9, 2], [-23, -6, -2, -5, 4], [-3, -16, 3, 1, -10], [8, 10, -11, 4, 0], [-4, 8, 1, 2, 4], [0, 10, -10, -2, 0], [-23, 4, -3, -4, -7], [-2, 8, 7, -6, -4], [-25, -2, -4, 4, 11], [-24, -1, 1, 8, 0], [-7, 11, -7, 1, 2], [-4, 4, 2, 4, -2], [20, 12, -4, 12, 2], [0, -8, 6, -1, -1], [0, 2, -4, -8, -10], [10, 8, 4, -4, 4], [-7, 0, 3, -1, -16], [40, 1, -7, 0, -2], [-8, -6, 4, 0, -8], [35, -8, 5, 4, 1], [-38, 0, 3, -6, 6], [-19, 9, -3, -11, 2], [31, 16, -8, 5, -4], [-17, -16, 8, -9, 0], [23, 4, 6, -3, -6], [-28, 0, 4, -2, 4], [34, 1, -1, -2, -8], [-16, 13, -3, 0, 2], [18, -4, 2, -4, 0], [19, 4, -14, 3, -10], [-5, -4, -11, 6, 11], [-5, 8, -5, -1, -8], [13, -2, 4, 9, -2], [-8, -8, -2, 5, -5], [2, 8, 0, 14, 0], [-32, 12, 7, 8, 2], [2, 14, -3, -4, -6], [4, -3, -7, -10, -10], [-33, -8, 0, -7, -14], [12, -4, 8, -6, -4], [9, -14, 6, -2, -9], [-22, 0, 3, -8, -2], [-20, 12, -2, -4, 8], [-18, 7, -11, 2, 0], [0, 12, -8, 2, 16], [7, 8, 8, -4, -17], [-13, 3, 3, 1, 4], [-19, -10, 2, -1, -6], [36, 0, 4, 4, -6], [24, 9, -3, -10, -10], [-4, 9, 1, 10, 0], [18, 20, -4, 0, 4], [-3, 4, 8, 5, 10], [-18, -4, 4, 2, -6], [-9, 6, -16, 10, 1], [-10, -17, 6, 2, 6], [-12, 5, -7, 0, -2], [20, -12, 4, -2, -6], [-16, -7, 0, 4, -2], [-19, -4, 11, 1, -2], [-10, 9, -2, -6, 0], [6, -8, 10, -5, -9], [51, -4, 0, -3, 2], [-8, -2, 6, 8, 8], [-24, -4, -1, 2, 2], [-15, 2, -6, -6, -5], [-2, 4, -11, 0, 16], [-30, -7, 13, 0, 6], [-37, 10, -8, 2, 3], [-6, 8, 6, -4, -10], [-10, 7, -9, -8, 0], [-6, -4, 1, -6, -8], [19, -6, 2, 2, 7], [-38, -4, 2, -10, 2], [-16, -3, 6, -8, 8], [8, 0, -2, -5, -5], [-12, 2, -8, 2, 4], [-21, 8, -5, 7, 10], [2, -18, 11, -3, -5], [-31, -2, 8, -5, -6], [-20, 3, 14, 4, 6], [22, -5, -1, 2, 8], [11, -9, -7, -5, 12], [10, 8, -5, -2, 2], [-12, 12, -12, 2, 6], [-17, -21, 11, -9, -8], [10, -2, 12, -2, 6], [-25, -10, -4, 10, 9], [-11, 20, -3, 14, 11], [21, -18, 4, 2, -9], [5, -8, 2, 7, -2], [11, 6, -7, -11, -2], [8, -23, 12, -4, -10], [21, 2, -5, -5, 4], [11, 4, 3, 10, 5], [0, 20, -2, 8, 0], [37, -8, 15, -12, -7], [6, 3, 3, -2, 10], [26, -4, -2, -4, 0], [24, 15, 4, -12, -2], [-1, -11, 1, 3, 2], [-30, 12, 5, 2, 2], [22, -3, 3, 10, 2], [-8, -2, -2, 4, 18], [6, -8, 10, 8, 6], [-15, -14, 6, 3, 6], [-37, -14, -2, 7, -2], [-17, -10, -9, 11, 0], [-3, -8, -4, -8, 1], [16, 14, -4, -6, -6], [33, -8, 0, -9, -6], [-29, -6, -3, 3, -10], [-12, -4, 3, 0, 6], [-3, 2, 6, 9, 20], [1, 13, -5, -3, -2], [20, -8, -6, 2, -4], [26, -10, -2, 0, 4], [26, 10, 2, -6, -12], [3, -6, -8, 0, -5], [-30, 12, 5, 14, 6], [-4, -2, 2, -2, -22], [-9, 10, -10, 3, 0], [9, -18, 3, 1, -16], [2, -10, -3, 0, 6], [-10, 17, -1, 6, 12], [-6, -9, 8, 2, -4], [-38, 12, -1, 10, 6], [10, 15, -6, -2, 10], [-47, 2, 0, 5, 6], [64, -6, 2, 2, 0], [-27, -8, -1, -11, -14], [31, 0, -4, -5, -10], [24, -10, 3, 8, -4], [4, -13, 9, 0, -10], [-52, -4, -12, 20, 8], [35, 8, 9, -12, -11], [-17, -10, -3, -1, -2], [-2, 6, -4, -6, 8], [29, 27, -9, 9, 4], [-8, 2, 0, -6, 4], [-4, -10, -1, 14, 4], [-10, 23, -1, -10, -2], [-22, -15, 1, -6, -2], [12, -6, 6, -16, -4], [2, 4, -5, 14, 14], [-20, -8, 8, 0, -4], [-6, 4, -1, 12, -6], [16, 2, -1, 15, -5], [23, 4, -8, 8, 9], [-1, 0, -2, 1, 8], [20, 8, -4, 9, 21], [6, -4, 2, 0, -20], [25, -4, -8, -6, -7], [-9, 18, -17, 1, 8], [-24, 16, -8, 0, 12], [-20, 10, -10, 6, 2], [-18, 4, 4, 1, 13], [-32, 2, 14, 10, 10], [22, -26, 0, 2, -14], [-23, 2, -2, -10, 7], [-15, -10, 2, -9, -10], [-9, -10, -1, 13, 2], [28, 4, -11, 6, 8], [-21, 18, 2, -1, 10], [-18, -4, -2, 17, 9], [5, 20, -1, -1, -2], [-15, -9, -2, 9, 14], [39, 8, -8, 9, 14], [-27, 8, 13, -4, -1], [-14, -4, -4, 16, -6], [4, 0, -8, 0, 8], [-2, -16, 1, 8, -8], [-8, -13, -6, 8, 10], [-28, -8, 2, 0, 4], [-10, 17, -9, 2, 8], [16, -8, 0, 11, -15], [-18, 8, -3, -6, 2], [9, -4, -8, 10, 3], [10, 20, 0, -12, -10], [23, -9, 9, -9, -16], [-19, -14, -6, 2, 7], [14, -9, 1, 2, -6], [6, 6, -12, 4, 8], [-16, 0, 0, 10, -6], [-18, -4, 4, -4, -18], [20, -6, 1, 4, 10], [32, 20, -5, 0, -6], [20, 8, 2, -8, 12], [10, 2, -2, -9, 11], [8, -6, -3, -10, -10], [-9, 13, -2, 7, 2], [2, 8, -2, 10, 2], [-48, 5, 3, -4, -4], [10, -4, -4, 12, -14], [25, 1, 11, -15, -6], [-4, 0, -12, 14, -4], [6, -20, -2, -2, 6], [-21, -21, -2, -1, -4], [50, -2, -1, 2, 2], [-2, 17, -6, -2, 4], [-2, -6, -8, 6, 20], [18, -4, 3, 8, 10], [0, 18, -4, 4, 14], [-27, 20, 9, 1, -4], [20, 4, -2, 12, -8], [5, 9, -8, -19, -20], [-18, 14, 9, 0, -4], [26, 8, 11, -8, 2], [8, -2, -7, 10, -18], [-41, 1, 12, 7, 8], [-26, -1, 9, 2, 14], [5, 8, 1, 4, 1], [-20, -4, -2, -10, -6], [18, 1, -2, -6, -4], [-9, -12, 7, 0, -11], [43, -6, -14, -10, -9], [13, -2, -17, 3, -6], [3, -6, 6, 13, 2], [-12, -18, 9, -10, 2], [35, 2, 2, -9, 0], [-19, -9, 7, -11, -20], [27, 14, -11, 7, 10], [-42, -4, 4, 2, 8], [43, 6, -8, 6, 1], [-11, 0, 1, -3, 8], [20, -21, -1, -2, -2], [-16, 18, -14, -2, 12], [22, -20, -6, 4, -14], [3, -6, 6, 5, -16], [-6, 10, -4, -8, 20], [0, -5, -3, -16, 16], [-12, 0, 12, 0, 12], [22, -12, -5, 4, 10], [-29, 16, 0, 6, 9], [17, -24, 8, -22, -15], [-25, 8, -7, -3, 4], [35, 6, 0, 9, 18], [-41, -6, 2, -1, -20], [14, -12, 8, -4, 2], [34, 20, -13, 10, 8], [12, -13, 12, 8, -2], [-6, 2, -2, -10, 6], [-20, 8, -6, 2, 0], [29, -3, 3, 5, 0]];
    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_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_8280_2_a_bs(: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_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_8280_2_a_bs( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8280_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![256, 128, -57, -28, 2, 1]>,<11,R![-64, 172, 28, -35, -1, 1]>,<13,R![500, 600, 75, -46, -4, 1]>,<17,R![-32, -138, -157, -46, 4, 1]>],Snew);
    return Vf;
end function;