
// Make newform 1950.2.bc.e in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1950_bc();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1950_bc_Hecke();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_1950_2_bc_e();".
// 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_1950_2_bc_e();".
// 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, 0, 0, 0, -1, 0, 0, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rfbasis := [Kf.1^i : i in [0..Degree(Kf)-1]];
    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_1950_bc();"
function MakeCharacter_1950_bc()
    N := 1950;
    order := 6;
    char_gens := [1301, 1327, 301];
    v := [6, 6, 5];
    // 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;

// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_1950_bc_Hecke();"
function MakeCharacter_1950_bc_Hecke(Kf)
    N := 1950;
    order := 6;
    char_gens := [1301, 1327, 301];
    char_values := [[1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0]];
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    values := ConvertToHeckeField(char_values : pass_field := true, Kf := Kf); // the value of chi on the gens as elements in the Hecke field
    F := Universe(values);// the Hecke field
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),values);
    return chi;
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, 1, 0, 0, 0, -1, 0], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 1, 0, 0, 0, 0], [-2, 1, 2, 0, 1, 0, -2, -1], [0, 0, 0, 3, 0, 0, 0, 1], [1, 3, 0, -3, -1, 0, 0, 0], [1, -1, 0, 1, 1, 2, 0, -2], [0, 4, 1, -1, 1, -1, 1, 4], [0, -5, 1, 4, 1, 4, 1, -5], [2, -2, 0, 2, -4, -3, 1, -5], [-4, 5, 4, 3, 2, -3, -4, -5], [0, 4, -5, 1, 0, -1, 5, -4], [-1, -5, 2, 3, 1, 2, -4, 2], [-2, -3, 0, 3, 4, -1, 4, -4], [-1, -1, -4, -1, 0, 2, 2, -1], [-1, -4, -3, 2, -1, 6, 0, -6], [-4, 3, 4, 0, 4, -3, -8, -3], [4, 4, -6, 4, -2, -4, 6, -4], [5, 1, -1, -3, 5, -4, 0, 4], [2, 0, 0, 0, -4, 4, 3, 4], [-1, -3, 0, -3, 0, 6, 0, -3], [2, 1, 0, -1, -4, 3, 1, 4], [4, 6, 1, 1, -2, -1, -1, -6], [1, 2, 0, 8, 1, 6, 0, -6], [0, 1, -1, 0, -11, 0, -1, 1], [3, -3, 0, -3, 0, 4, 0, -1], [0, -6, -1, 0, -7, 0, -1, -6], [-4, 1, 0, -1, 8, -4, -10, -3], [-4, 0, 0, -4, 4, 4, 0, 4], [0, -8, -2, 8, 0, 8, -2, -8], [-5, -2, 10, -2, 0, 4, -5, -2], [3, -4, -9, -1, 3, 3, 0, -3], [-3, 4, -3, -3, 3, -1, 6, -1], [0, -5, 1, -1, 0, 4, 0, -4], [5, -7, 0, 7, -10, 2, -4, -5], [0, 7, 8, 7, 0, 4, -4, -11], [2, -1, -3, 2, 2, 3, 0, -3], [-6, -13, 5, -7, 3, 7, -5, 13], [2, 4, 2, -10, -2, 6, -4, 6], [0, -7, 2, 10, -3, 10, 2, -7], [0, 10, -4, 10, 0, -3, 2, -7], [3, -1, -3, 3, -3, -2, 6, -2], [0, -4, -3, 0, 0, 0, 3, 4], [2, -5, -11, -8, -1, 8, 11, 5], [5, 1, 2, -6, -5, 5, -4, 5], [0, -7, 0, 5, -1, 5, 0, -7], [-14, 2, -6, 1, 7, -1, 6, -2], [-1, -6, 8, -9, -1, -3, 0, 3], [6, 10, 0, -10, -12, -1, -8, 9], [-4, 8, 12, 8, 0, -6, -6, -2], [1, 1, 0, -1, -2, 6, -15, 7], [5, 6, 3, 2, 5, -4, 0, 4], [-3, -2, -4, -9, 3, 11, 8, 11], [0, 7, -4, -3, 1, -3, -4, 7], [0, -5, -9, 7, -3, 7, -9, -5], [-13, -3, -6, 4, 13, -1, 12, -1], [-2, 3, 5, 10, 1, -10, -5, -3], [4, -3, -8, 2, -4, 1, 16, 1], [8, 3, 0, -3, -16, -2, 11, 1], [0, -2, -1, 7, 4, 7, -1, -2], [7, 1, -2, 2, 7, 1, 0, -1], [-11, -9, 0, 9, 22, -1, 9, -10], [1, -12, 2, -12, 0, 11, -1, 1], [-7, 4, -4, 4, 0, 8, 2, -12], [-8, 2, 0, -2, 16, 11, -3, 13], [6, -3, -13, -2, 6, 1, 0, -1], [3, 16, 10, 16, 0, -14, -5, -2], [0, -4, 9, -3, 0, 7, -18, 7], [-4, -12, -4, -9, 2, 9, 4, 12], [0, 12, -11, 7, 0, -7, 11, -12], [4, -12, 0, 12, -8, 8, 4, -4], [0, 1, -17, -2, -3, -2, -17, 1], [0, -9, 12, 1, 0, 8, -24, 8], [-20, -8, 6, -10, 10, 10, -6, 8], [-3, 9, 7, -4, -3, -13, 0, 13], [-13, -11, 6, -11, 0, 3, -3, 8], [-4, 6, -12, 12, -4, 6, 0, -6], [12, -4, 10, -2, -6, 2, -10, 4], [3, 8, -17, 0, 3, -8, 0, 8], [0, 7, 12, 10, -11, 10, 12, 7], [6, 4, 0, -4, -12, 13, 16, 17], [-6, -13, -11, 3, 3, -3, 11, 13], [-6, 8, 3, -4, 6, -4, -6, -4], [0, 8, 0, 0, -4, 0, 0, 8], [-23, -1, 0, -1, 0, -5, 0, 6], [7, -7, 6, -3, 7, 4, 0, -4], [-14, 8, -16, 4, 7, -4, 16, -8], [4, 1, 11, 1, 4, 0, 0, 0], [5, 3, 0, -3, -10, -14, 2, -11], [1, -3, -16, -3, 0, -7, 8, 10], [0, -14, 2, -8, 0, 8, -2, 14], [-2, 5, 17, -5, -2, -10, 0, 10], [0, -5, -8, 4, -17, 4, -8, -5], [1, 12, 0, -12, -2, -7, 0, 5], [-5, 9, 1, 12, 5, -21, -2, -21], [2, -20, 0, 1, -1, -1, 0, 20], [-14, -4, 0, -4, 0, -6, 0, 10], [0, 0, 0, -6, 20, -6, 0, 0], [4, 17, 0, -17, -8, -6, -6, 11], [12, 3, 18, 3, 0, -20, -9, 17], [8, 14, 16, -4, -4, 4, -16, -14], [-3, 0, -2, 7, 3, -7, 4, -7], [0, 3, -7, -12, 9, -12, -7, 3], [5, 9, -14, 9, 0, -11, 7, 2], [-6, 20, 0, -20, 12, -10, 3, 10], [-22, -3, -24, 8, 11, -8, 24, 3], [0, 17, 0, -17, 0, -20, 1, -3], [-11, -13, 2, -13, 0, 12, -1, 1], [0, -10, -8, 20, 4, 20, -8, -10], [-3, 0, -3, 15, 3, -15, 6, -15], [-24, 1, -12, 8, 12, -8, 12, -1], [2, -4, 8, 10, 2, 14, 0, -14], [8, -2, 0, 2, -16, 2, -12, 0], [0, -4, -6, -6, 0, -2, 0, 2], [-7, -8, -3, 19, 7, -11, 6, -11], [-8, -2, -4, -4, -8, -2, 0, 2], [0, -7, -1, 3, 9, 3, -1, -7], [0, 15, -5, -17, -12, -17, -5, 15], [-3, -2, -14, -3, 3, 5, 28, 5], [24, 2, -2, -4, -12, 4, 2, -2], [0, 10, 5, -10, -6, -10, 5, 10], [8, 4, 28, 4, 0, 2, -14, -6], [8, -16, -17, -9, 8, 7, 0, -7], [-4, -4, -28, -8, 2, 8, 28, 4], [16, 0, 22, 0, 0, -15, -11, 15], [2, -15, 4, 2, 2, 17, 0, -17], [5, 9, 13, 6, -5, -15, -26, -15], [-3, -17, 30, -17, 0, 15, -15, 2], [6, -12, 0, 12, -12, 9, 16, -3], [-2, 17, -19, 12, 1, -12, 19, -17], [0, -20, 4, -16, 0, 16, -4, 20], [0, 19, 1, -24, 3, -24, 1, 19], [0, -3, -20, 4, -4, 4, -20, -3], [-3, -13, -20, -7, -3, 6, 0, -6], [-26, 26, 21, 20, 13, -20, -21, -26], [-20, 2, 4, 12, -20, 10, 0, -10], [-8, -17, -21, -6, -8, 11, 0, -11], [15, -12, -11, -11, -15, 23, 22, 23], [0, -5, 8, -21, -15, -21, 8, -5], [-2, -18, 0, 18, 4, 4, 6, -14], [-20, 0, -6, -10, 10, 10, 6, 0], [-13, -25, -6, 18, 13, 7, 12, 7], [-12, -5, 0, 5, 24, -5, 1, -10], [0, -10, 16, 4, -8, 4, 16, -10], [13, 5, 23, 1, 13, -4, 0, 4], [-2, -4, 0, 4, 4, 4, -16, 0], [-5, 15, -10, 15, 0, 19, 5, -34], [-6, 35, 6, 35, 0, -28, -3, -7], [3, -12, 0, 12, -6, -7, -5, -19], [12, 1, 10, -11, 12, -12, 0, 12], [0, 1, 2, 11, -11, 11, 2, 1], [-6, -14, -12, -14, 0, -22, 6, 36], [0, -18, -12, 8, -16, 8, -12, -18], [0, -9, -8, -7, 11, -7, -8, -9], [13, -13, -2, -13, 0, 14, 1, -1], [0, 21, -3, -1, 0, -20, 6, -20], [0, 2, -6, 4, 0, 2, 0, -2], [21, -12, 16, -12, 0, 20, -8, -8], [4, 0, 0, 0, -8, -18, 26, -18], [22, -5, 8, 12, -11, -12, -8, 5], [-5, 13, -6, 9, 5, -22, 12, -22], [-2, -12, 0, 12, 4, 8, 24, -4], [5, -16, 5, -6, -5, 22, -10, 22], [0, 8, -44, 4, 0, -4, 44, -8], [-8, 8, 0, -8, 16, 12, 20, 20], [0, 18, -2, -33, -9, -33, -2, 18], [-26, 8, -6, -20, 26, 12, 12, 12], [1, -10, 0, 10, -2, -8, -28, -18], [-1, -13, -4, -13, 0, -4, 2, 17], [4, 2, 0, -2, -8, 2, -14, 4], [4, -1, -12, 22, 4, 23, 0, -23], [-16, 6, -2, -8, 16, 2, 4, 2], [-5, 28, -11, 8, -5, -20, 0, 20], [9, 19, 6, 19, 0, 15, -3, -34], [-20, -3, 1, 4, 20, -1, -2, -1], [-16, -16, 10, -30, 8, 30, -10, 16], [5, -3, 0, 3, -10, -5, 11, -8], [0, -3, -9, -12, 3, -12, -9, -3], [0, -9, 10, 1, -18, 1, 10, -9], [11, 5, 0, -5, -22, -5, 23, 0], [4, 13, 14, 13, 0, 1, -7, -14], [-12, -27, 16, -27, 0, 7, -8, 20], [-9, -19, 0, 19, 18, 5, 33, -14], [0, 0, 34, 0, 0, 0, -34, 0], [19, -1, 4, 0, -19, 1, -8, 1], [-16, -22, 24, -22, 0, 5, -12, 17], [0, 33, 0, -33, 0, -8, -5, 25], [18, 4, -26, 14, -9, -14, 26, -4], [-9, 1, -35, 6, -9, 5, 0, -5], [9, 14, 17, -6, -9, -8, -34, -8], [-14, -12, 21, -13, -14, -1, 0, 1], [12, -1, 30, -1, 0, -12, -15, 13], [10, 20, 2, 19, -5, -19, -2, -20], [13, 16, -4, 19, -13, -35, 8, -35], [0, 23, -9, 0, 17, 0, -9, 23], [-5, 12, 0, -12, 10, 0, 25, 12], [-12, 7, -16, -20, 12, 13, 32, 13], [13, -4, 0, 4, -26, 19, 2, 15], [-3, 16, 6, 16, 0, 19, -3, -35], [8, 3, 9, -17, 8, -20, 0, 20], [10, -2, 26, -6, -10, 8, -52, 8], [-4, 8, 2, -14, 2, 14, -2, -8], [19, -14, -14, -14, 0, 22, 7, -8], [0, 18, 2, -4, 0, 4, -2, -18], [0, -4, -24, -3, 3, -3, -24, -4], [-18, -10, 0, 10, 36, 10, -12, 0], [2, -8, -17, -17, -2, 25, 34, 25], [-4, 0, 25, -9, 2, 9, -25, 0], [16, 9, 3, 4, -16, -13, -6, -13], [0, 28, -3, -16, 0, -16, -3, 28], [10, 36, -18, 36, 0, -27, 9, -9], [0, -4, -12, -11, 17, -11, -12, -4], [-1, -8, 8, 11, -1, 19, 0, -19], [18, 8, 16, 0, 18, -8, 0, 8], [11, -28, 0, 28, -22, 22, -12, -6], [7, -7, -28, -7, 0, 12, 14, -5], [-4, 12, 0, 6, 4, -18, 0, -18], [10, 8, -27, 1, -5, -1, 27, -8], [-10, -4, 0, 4, 20, 7, -3, 3], [0, 31, -12, -19, -8, -19, -12, 31], [20, -2, 0, 2, -40, -9, -7, -11], [-15, 26, 0, -26, 30, -5, 18, 21], [4, -15, -29, -23, 4, -8, 0, 8], [0, 19, 2, -30, -7, -30, 2, 19], [-24, -11, -8, -11, 0, 12, 4, -1], [0, 11, -23, -6, -23, -6, -23, 11], [0, -4, -10, 14, 0, -10, 20, -10], [-3, 10, -11, -31, 3, 21, 22, 21], [-1, 0, 0, 0, 2, 24, 13, 24], [0, -27, 2, 17, 0, 17, 2, -27], [0, -3, -4, 21, 31, 21, -4, -3], [-12, 2, -40, 8, 6, -8, 40, -2], [15, 9, 10, 9, 0, 7, -5, -16], [2, -8, 52, -8, 0, 14, -26, -6], [-17, 5, 0, -5, 34, -12, 11, -7], [-11, 10, 35, 12, -11, 2, 0, -2], [66, 5, 1, 4, -33, -4, -1, -5], [24, -12, -9, -17, -24, 29, 18, 29], [0, 5, -5, 19, 15, 19, -5, 5], [-22, 3, 8, 0, 11, 0, -8, -3], [0, -16, 18, -4, -12, -4, 18, -16], [8, 2, 14, 10, -8, -12, -28, -12], [-12, -19, 30, -17, 6, 17, -30, 19], [-24, 17, -1, 10, -24, -7, 0, 7], [-19, -8, -6, -8, 0, -13, 3, 21], [8, 3, -27, -13, 8, -16, 0, 16], [-46, 0, 15, 2, 23, -2, -15, 0], [12, -15, -9, -28, 12, -13, 0, 13], [0, -16, -12, 10, 14, 10, -12, -16], [-24, -17, 2, -15, 12, 15, -2, 17], [-12, -14, 5, -9, 6, 9, -5, 14], [-17, -1, 0, 1, 34, -2, 9, -3], [0, -14, 1, 22, 8, 22, 1, -14], [-10, -4, 20, -4, 0, 12, -10, -8], [4, -4, 17, 17, 4, 21, 0, -21], [-16, 13, 28, 2, 16, -15, -56, -15], [-6, -17, 3, -4, 3, 4, -3, 17], [35, -13, -18, -13, 0, 9, 9, 4], [16, -14, 39, 14, 16, 28, 0, -28], [27, 19, -8, 19, 0, -2, 4, -17], [0, 29, -9, -6, -6, -6, -9, 29], [-6, 26, 0, -26, 12, 12, 16, 38], [0, -15, 20, 21, -10, 21, 20, -15], [0, 27, -23, 8, 0, -19, 0, 19], [-20, -12, 4, -16, 20, 28, -8, 28], [8, -8, 24, -12, 8, -4, 0, 4], [-9, -13, 0, 13, 18, -13, -11, -26], [-13, 1, -30, 3, -13, 2, 0, -2], [18, -42, -6, 4, -18, 38, 12, 38], [-26, -14, -20, -14, 0, -20, 10, 34], [-4, 19, 0, -19, 8, 18, 5, 37], [-10, 26, -21, 4, 5, -4, 21, -26], [-2, 7, -3, -7, 2, 0, 6, 0], [13, 10, -7, -24, -13, 14, 14, 14], [12, -24, -26, -10, -6, 10, 26, 24], [-17, 10, 25, 14, -17, 4, 0, -4], [-8, -20, 0, 20, 16, 34, -22, 14], [-7, -22, 12, -34, -7, -12, 0, 12], [42, -24, -11, 1, -42, 23, 22, 23], [0, 22, -2, 16, -16, 16, -2, 22], [-18, 14, -44, 5, 9, -5, 44, -14], [-11, -24, 18, -24, 0, -3, -9, 27], [16, 9, -32, 17, -8, -17, 32, -9], [-2, 1, 0, -1, 4, 12, 7, 13], [19, -11, 14, -11, 0, -8, -7, 19], [24, 14, 24, 14, 0, -26, -12, 12], [-19, -21, 0, 21, 38, 24, 10, 3], [3, -3, -10, 6, 3, 9, 0, -9], [50, 15, 9, -18, -50, 3, -18, 3], [0, 9, -11, -18, -41, -18, -11, 9], [14, 16, 7, 3, -14, -19, -14, -19], [32, 6, 17, -3, -16, 3, -17, -6], [-5, -6, -25, 30, -5, 36, 0, -36], [6, -25, 8, -11, -6, 36, -16, 36], [-39, 7, 0, 7, 0, -18, 0, 11], [40, -12, -10, -12, 0, 5, 5, 7], [0, 0, -12, 3, 27, 3, -12, 0], [0, 29, 1, -22, -18, -22, 1, 29], [-2, -9, 38, 13, 1, -13, -38, 9], [-22, -4, 14, 12, 22, -8, -28, -8], [11, -23, 0, 23, -22, 20, -26, -3], [0, 9, 15, -1, -44, -1, 15, 9]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_1950_bc_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_1950_2_bc_e();".
// 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_1950_2_bc_e(:prec:=8)
    chi := MakeCharacter_1950_bc();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(1999) - 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_1950_2_bc_e();".
// 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_1950_2_bc_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1950_bc();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![4, -24, 60, -72, 38, 0, -6, 0, 1]>],Snew);
    return Vf;
end function;