
// Make newform 2883.2.a.p in Magma, downloaded from the LMFDB on 14 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_2883_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_2883_2_a_p();".
// 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_2883_2_a_p();".
// 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 := [9, 42, -82, -31, 62, 10, -14, -1, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [-4, 0, 1, 0, 0, 0, 0, 0], [3, -5, -1, 1, 0, 0, 0, 0], [5, -2, -7, 0, 1, 0, 0, 0], [0, -25, -10, 35, 7, -11, -1, 1], [-3, -12, 19, 7, -9, -1, 1, 0], [0, 91, -2, -83, -7, 17, 1, -1]];
    Rf_basisdens := [1, 1, 1, 1, 1, 6, 2, 6];
    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_2883_a();"
function MakeCharacter_2883_a()
    N := 2883;
    order := 1;
    char_gens := [962, 964];
    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_2883_a_Hecke( : Kf := Kf)
    return MakeCharacter_2883_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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [-1, 0, 0, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1], [-1, 0, -1, 0, 0, 0, 0, -1], [-1, 2, -1, 0, 0, -1, 0, -1], [0, 0, 0, 1, 0, 1, -2, 0], [-1, 0, 0, 0, -1, 1, 0, 1], [0, 2, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 1, 0, -2, 1], [-2, 0, -1, 1, -1, 0, 0, 0], [5, 0, 0, -1, 0, 0, 0, 1], [5, 2, 0, 0, -1, 1, -2, 1], [-2, 0, -1, 2, -1, -1, 2, -1], [-5, 2, 0, 0, 1, -4, 0, 2], [0, -2, 1, 0, -1, 0, 0, -1], [5, 0, -1, -1, 0, 1, -2, 0], [1, 0, 0, 0, 1, 2, 0, 2], [-2, 0, 1, 2, -2, -1, 0, 0], [4, -2, -1, -1, -1, 1, 2, 0], [2, 0, 2, 1, 0, 7, -2, 1], [-1, 0, -2, -2, 1, -1, 2, -1], [6, 0, -1, -1, 1, 2, -2, 1], [2, -2, 2, -1, 0, 1, 0, 1], [-1, 0, 1, 0, -1, 0, -2, 1], [0, 0, 0, 0, 0, 5, 2, -1], [2, 4, -3, 0, 0, -2, 0, -1], [3, 2, 1, -1, 2, 1, 0, 1], [5, -2, 0, 1, -1, 4, -2, 3], [0, 2, 2, 1, -2, -4, -2, 2], [3, -2, 4, -2, -1, 6, 2, 0], [3, 0, 1, 2, -3, -1, 2, 0], [6, 2, -2, -3, 2, 2, 2, 2], [6, 0, 0, 0, 1, 1, -2, 2], [7, -4, 0, 1, 1, 1, 2, 0], [-2, 0, -1, -1, 0, 4, -4, -1], [-3, 0, 1, -1, 2, -4, 4, 2], [4, -2, -1, 1, -1, 5, -2, -1], [-7, -2, -2, -1, 1, -4, 0, 2], [-5, 4, -2, 0, -2, 2, 0, -3], [1, 0, 0, 1, 1, 4, 0, -2], [10, 4, 2, 0, 2, 2, -4, 1], [-2, 4, 2, -2, 2, -6, 2, 0], [3, 4, -2, 1, 0, 0, -4, 1], [-1, -4, 2, 1, -2, 1, 4, 2], [9, -4, 4, 2, -1, 1, 0, 0], [6, -2, 1, -1, 5, 2, 0, 2], [7, 6, -2, 4, -3, 1, 0, 0], [10, -2, 0, 0, 4, -5, -2, 1], [0, 4, 0, -1, 0, 6, -2, 0], [-2, -4, 0, 2, 2, -3, 4, -3], [-3, 0, 2, 1, -5, 4, 4, -2], [-6, 0, 3, 1, -3, -1, -6, -1], [-4, 4, -1, -3, 3, -5, -8, 1], [-5, 4, -4, 1, -1, 7, 0, -5], [3, -2, 0, 0, -2, 3, 2, -2], [3, -4, 4, -1, -3, 1, -2, 1], [14, -2, 1, -1, 1, 8, -2, 2], [5, 0, 2, -5, 4, -6, -8, 1], [-3, -6, 0, -1, -3, 4, 6, -2], [-8, 0, -3, 0, 1, 2, 0, 1], [4, 0, 1, 0, 3, -1, -4, -1], [-8, 4, -3, -2, 2, -11, 0, -4], [11, -4, -3, -5, 2, 5, 0, -1], [4, 2, -2, 3, -2, 5, 2, -1], [-5, 6, -1, 1, -4, 5, -2, -2], [-2, -4, 0, 2, -2, 11, -2, -1], [9, -4, 0, 4, -2, -3, -4, -2], [5, -6, 5, 2, 0, 6, 2, 0], [-3, -4, -3, -3, 0, -1, 0, -1], [3, 6, 0, -6, 1, -7, 0, -1], [6, -4, 4, -2, -4, 12, 4, -1], [-6, 4, -3, 4, -3, -7, 0, -2], [14, 0, 3, -1, -1, 9, 0, 3], [-9, -4, 1, 2, 2, -14, 2, -2], [-1, 0, 3, 0, -4, 6, 0, -1], [10, 2, -2, -5, 0, 0, -6, 0], [1, 0, -4, 3, -3, 0, -2, 0], [9, 0, 0, 6, -3, 7, -2, 1], [8, 6, 1, -3, 2, 9, -2, 4], [-1, 2, 4, -7, 1, -7, -6, -1], [-11, 2, -5, -2, 1, -1, 4, 0], [9, 0, 0, -3, -2, 12, -4, 7], [-3, -2, 6, 4, -3, -8, 4, -2], [6, 6, 7, 0, -1, 7, -4, 1], [-7, 0, 1, 2, 2, -1, 4, 5], [7, -4, 6, 3, 1, 20, -2, 2], [-5, 4, -5, -1, 0, -2, -2, -3], [-2, 2, 3, 2, -5, -4, 0, 2], [-6, 2, 0, -6, 0, 8, 0, 2], [-11, 0, -7, -10, 3, -8, 6, -1], [8, 0, -4, 0, 0, 2, 0, 2], [5, 6, -1, -2, 0, 10, -4, -3], [9, 0, 3, 0, 0, 0, 0, 0], [-20, 4, -5, -5, -3, -7, 2, -1], [5, 2, 2, 0, -3, 16, 0, -2], [-9, 0, -5, 0, 3, -1, 6, 0], [-2, -2, -3, 0, 1, -16, 0, 1], [2, 4, -3, -8, 5, -7, 4, -2], [-3, -2, 5, 0, -2, 3, 0, 3], [-6, 2, 4, 0, 2, -2, 6, -2], [-15, -4, -7, 6, -2, -8, 4, -2], [2, -4, 6, -2, 0, -10, -4, 2], [-6, 2, -6, 6, -5, -6, -4, 1], [-13, -2, -2, 3, 1, -4, 0, -4], [3, -4, 2, 4, -5, 8, 2, 2], [8, -8, 1, 0, 1, 9, 4, -3], [8, 2, -3, 3, 0, 11, 2, 0], [1, 10, 0, -1, 1, -3, -2, 2], [6, 8, -2, -2, 2, 6, 0, 5], [0, 8, -6, -5, 0, -16, 4, -4], [18, 2, 1, -5, 5, 2, -2, 1], [12, 4, -1, 0, 1, 9, -8, -4], [-3, -2, 2, 0, -5, 11, -4, -1], [-9, 6, -2, 1, -1, 2, -2, 1], [-1, 0, 9, -3, 2, 4, 0, 4], [3, 4, 2, 1, -5, -7, 8, -1], [-5, 4, -7, -1, -4, 2, 2, 2], [-3, 6, 1, -4, 3, -7, -4, 6], [1, -8, 4, 4, -2, -5, 8, -4], [-13, -6, 2, 0, -3, 0, 0, 6], [-17, 6, -5, -1, 0, -8, 0, -2], [-12, 4, 0, 1, 0, -13, -2, -2], [2, 8, 2, -4, 6, -17, -2, 1], [6, 0, 7, 5, -3, 4, -2, -2], [-13, 2, -6, 0, -1, 12, 0, 0], [6, 2, 3, 2, -5, 15, -4, 3], [-9, 10, -5, 1, -6, -14, -2, -2], [5, 8, -1, -7, 0, -9, -6, 2], [-3, 12, -9, -3, 0, -5, -4, -5], [6, -2, -4, -1, -4, 4, 2, -2], [-12, -4, -4, 2, -2, -8, 0, -3], [-3, 10, 1, -2, 2, -6, -10, 6], [-11, 0, -4, 6, 0, 2, 4, 3], [-6, -2, -2, 0, -4, -12, 12, 0], [-2, -2, -2, -5, -2, -4, 2, -10], [16, 2, 4, -2, 6, 8, 0, -4], [-18, -2, 2, 7, -2, -18, -2, 0], [-3, -2, 5, 5, -4, -4, -2, -4], [-13, -6, 1, 6, -2, 0, 4, 6], [-16, -2, -2, 3, -1, -13, 4, 6], [3, -2, 2, 6, 1, 1, -6, 1], [6, 12, -2, 6, 2, -6, 0, -1], [-7, 10, -5, -1, 10, -14, -6, -2], [7, -12, 0, 3, -1, 2, 2, 2], [7, 4, 0, 1, -5, 14, 0, 8], [-13, 8, -3, -2, -3, 3, -6, 4], [12, -12, 0, 3, 0, 10, 10, -2], [29, 0, 2, -5, 7, 12, -6, 0], [-6, 0, 1, 2, 5, 9, -8, 3], [-2, 14, -8, -1, 1, -8, -4, -1], [21, 10, 2, -3, 1, 18, -12, 6], [-1, 0, -2, 4, -5, 17, 4, 4], [-5, 0, -3, 6, -2, 1, -8, 1], [-1, 6, 9, 2, -4, 10, -4, 3], [-1, -10, -1, -1, 6, 4, -2, -2], [3, 2, 0, 3, 4, -10, 2, -3], [-28, -6, -1, -7, 3, -22, 2, 2], [-25, -6, -10, 3, -3, -3, 10, -9], [6, 8, 4, -3, 2, 11, -16, 5], [4, 12, 0, 2, 5, 12, -2, 1], [1, 6, 8, -7, 5, -4, -8, 2], [2, 0, -2, 3, -2, -1, 6, -1], [-14, -12, -2, 4, 0, -6, -2, 0], [21, -6, 3, 0, 0, 22, 0, 3], [7, 0, -1, 3, 3, -8, 2, -1], [13, -2, 0, 2, -1, -2, 8, -8], [-13, 0, -2, -2, 7, 1, 2, 1], [-13, -10, -6, 5, 5, -23, 6, -5], [7, 4, -1, 7, 3, 2, -6, -3], [2, 10, 11, 2, -3, 6, -2, 0], [-13, 2, 2, 0, -3, -15, 8, -4], [5, -8, 9, -3, 8, 14, 2, 1], [-23, -6, 2, 1, -1, -14, 10, -8], [5, 4, 11, 6, -5, 14, -6, 3], [1, -4, 10, 4, -3, -10, 10, -4], [-9, 0, 8, 5, -1, -9, 2, 3], [19, 0, 5, -2, 0, 13, 8, -5], [-21, 0, 2, 1, 2, -5, -4, 8], [-16, -12, 4, -1, -2, -1, 14, -1], [7, 0, -1, -4, -4, -16, 4, -5], [2, 4, -3, -3, -1, 28, 2, 4], [-6, -12, 6, -1, 0, 5, -2, 5], [10, 8, -1, 7, -1, 4, -8, -2], [33, -2, -4, -3, 2, 9, -2, -2], [-12, 14, -1, -4, 2, -16, -6, 3], [4, 4, -2, -2, 6, 15, -4, -4], [1, 12, -3, 2, -2, -16, -4, 2], [-14, 12, -5, 1, -5, -9, 6, -3], [10, -10, 4, 7, 0, 12, 2, 6], [8, 8, 2, -4, -5, 2, -10, 3], [-1, 8, -11, 3, -2, -22, 6, -4], [23, 4, -3, -5, 2, 14, -6, 2], [-13, 2, -5, 5, -8, 10, -2, -2], [-20, 2, -2, 6, -11, -14, 0, -7], [14, -6, 5, 8, -3, 8, 0, 1], [11, -10, 5, 3, -6, 6, 6, -6], [3, -14, 3, 5, 0, 2, -4, -4], [15, -14, 5, 5, -2, 0, -6, 0], [15, 8, 6, -3, 10, -16, -8, 3], [13, -6, 9, -2, -1, -10, 8, 9], [-1, -2, -7, 2, 1, 6, 4, 1], [-3, 2, -2, 7, -7, -7, 12, -7], [20, -2, 0, 7, -4, -5, 0, -5], [-10, -10, 0, 0, 8, -3, 0, -4], [-2, 6, -6, 4, -8, -3, -6, 3], [-14, 12, -1, -3, 5, -16, 2, 2], [-5, -4, -7, -6, 3, -9, -2, -2], [-6, 8, -1, 9, 7, -13, 2, 4], [-21, 16, -1, -1, 4, -18, -4, 6], [5, 6, -2, 5, -5, 3, -10, 2], [2, 2, -3, -3, 5, -9, -6, 3], [-12, -8, 4, 0, 2, -3, -8, 3], [-23, 0, 5, -4, 0, -12, 12, -6], [20, 6, 3, -13, 5, -14, -6, 3], [11, -8, 9, -4, 8, 0, 2, 6], [11, -2, -9, 2, -4, 3, 12, 3], [23, 8, -4, -8, 9, -3, 2, 3], [16, -6, 1, -6, 1, 17, -4, 5], [-12, 6, -17, -6, 6, -15, 2, -2], [-14, 4, -3, 0, 1, 10, -10, -2], [-11, -4, 0, -1, 5, -3, 6, -3], [1, 8, 1, -4, 6, -7, -4, -1], [-11, -4, -5, 11, -5, 3, -6, -2], [-6, -14, 4, 3, -4, 3, 4, 9], [35, 0, -3, -3, 2, -2, -8, -2], [12, -2, 6, 10, 0, -1, -4, 4], [6, 0, 10, 7, -4, 16, -10, 4], [-11, 2, -3, -5, 4, 1, 6, -6], [-19, 4, 0, -2, -7, -6, 0, -7], [2, 12, -7, -4, 3, 14, -4, -5], [-13, -2, -1, -3, 0, 20, 6, -4], [13, -20, 6, -4, -5, 6, 12, 5], [-16, -14, 3, -3, -1, 4, 2, -2], [4, -8, -7, 8, 0, 3, 4, 4], [-3, 8, 0, 7, -3, 4, -4, 4], [6, -2, 1, 11, -1, 8, 0, 2], [6, -4, -8, -3, 8, 11, 12, -1], [25, 2, 5, 2, 2, 1, 0, 7], [-8, 8, -2, 5, -6, -15, 2, 8], [-4, -8, -1, 14, -3, 7, 0, 0], [-14, 10, -3, 0, -1, 7, -12, -5], [5, 8, -5, 1, -8, -8, 4, 4], [10, 2, -2, 2, -6, 5, -4, -1], [3, -2, -5, 10, -4, 25, -4, -6], [-21, 2, 13, -2, 2, 0, 10, 0], [-12, -6, 3, 2, -14, 14, 2, -3], [5, -2, 0, -9, 5, -6, 4, 0], [-2, 2, -2, -2, -5, -1, 12, 0], [38, -4, 3, 4, -1, 7, 10, -11], [21, 8, 6, 1, -9, 39, -2, 3], [19, -10, -5, -11, 0, -5, -2, 0], [-9, -4, -5, -1, 8, -35, 0, 1], [21, -8, -4, -4, 7, -8, -4, -2], [12, 6, 9, 1, 10, 3, -10, -2], [19, -2, 0, 0, -1, 12, -8, -6], [5, 4, -11, -11, 4, -2, 2, 4], [6, 6, -7, -3, 8, -10, -6, 3], [0, -8, 4, -8, 3, -9, 2, 4], [-16, -2, 1, -1, -5, 0, 14, 0], [-18, 0, -2, -1, -3, 5, 10, 0], [16, -8, -4, -11, -3, -4, -2, -3], [0, 16, 2, -7, -8, 12, -4, 0], [12, -6, -2, 3, -3, -15, -4, -2], [12, -2, 3, 0, -3, 37, -6, 7], [4, 6, 0, 1, 4, -12, -10, 0], [-1, -4, -3, 6, -3, 4, 6, -1], [13, -2, 6, 9, -11, 16, -8, -8], [-14, -6, 5, -1, 0, 6, 2, -5], [0, 2, -15, -7, 3, 18, -2, -1], [11, -10, 4, 15, -4, 15, -6, 4], [26, 4, -1, -7, 1, 9, 6, 3], [-16, 12, -4, 2, 10, -26, -8, -2], [-10, -4, -5, 4, 7, -3, -4, 2], [-29, -10, 3, 0, -2, 1, 6, 1], [10, -4, -6, -8, 4, 13, 4, 0], [-28, -6, 5, 0, 3, -24, 0, -1], [-29, -6, -3, -1, 4, -43, 2, -7], [-30, 6, 3, 5, -9, -12, 2, 0], [-21, 6, -11, 6, -4, -2, 4, -15], [-22, 8, -3, -6, 5, -21, 6, 3], [16, 6, 0, 1, -8, -6, 10, -1], [25, -4, 5, 7, 2, 5, 6, -8], [36, -4, 0, -8, 0, 10, 4, 4], [20, -10, 5, 5, -2, 17, 6, 0], [36, 8, 0, -13, 6, 6, -12, 0], [16, -8, 5, -3, 6, 35, -4, 6], [4, 6, -3, 0, -5, 1, -16, 7], [29, 4, 15, -10, 2, 4, -14, 4], [7, 8, 2, -1, 5, 24, 0, -6], [48, 4, -1, -15, 7, 23, -4, 5], [23, -12, 5, 6, 0, 12, 0, 12], [-19, -12, 1, 12, 2, -19, 4, -1], [-1, 22, 1, 0, 4, -9, 0, 3], [10, 4, 9, -1, 2, -3, -8, -2], [8, 12, -6, -2, 8, -10, -6, 2], [47, -10, 8, -1, 9, 15, -6, -3], [11, 2, 3, -5, 9, 24, 0, 1], [13, -6, -2, 2, -3, 30, 12, -1], [20, -4, 3, 3, -7, 15, 4, -3], [-9, -8, -18, 6, -3, -8, 16, -9], [20, -10, 2, -9, 6, 4, -8, 10], [-7, -6, 2, -1, 15, -1, 10, -8], [7, 4, -7, -7, 3, 14, 18, 3], [18, -10, 13, -6, 5, 10, 4, 4], [-8, 0, 10, -8, 6, -21, -16, -4], [-15, 4, 7, 12, -10, 3, 10, 3], [-9, -4, -9, -4, -2, 7, -4, 1], [-31, 0, -4, -6, -3, 9, 6, 3], [46, -4, 10, 1, 0, 6, 2, 0], [-7, -2, 3, -11, -4, 31, 8, 1], [-3, -2, -3, -10, -6, 16, -8, -3], [4, 8, 3, 0, 1, 4, 0, -8], [2, 12, 5, -3, -3, 5, -6, 4], [-5, 4, 4, 1, 9, 4, 4, 10], [3, -2, 14, -5, 1, -8, -4, -2], [4, -2, 7, 8, -3, -4, -12, 1], [-18, 4, -9, -11, 3, -24, 6, 0], [3, -16, 0, 13, 4, 6, -4, 1], [1, -12, 10, 1, 9, 7, 10, 6], [19, 0, -2, -17, 3, 10, -4, 10], [0, -16, 9, -3, 4, 7, -8, -4], [17, -24, 5, 5, 6, 18, 14, 0], [10, 6, 7, -4, 1, 13, 0, 1], [-37, -6, -2, -4, -4, -27, 14, -8], [-35, -2, -8, -2, 7, -1, 0, -7], [-33, 2, -1, -8, -2, -3, 12, -9], [-20, -14, -1, 5, 5, 2, 8, 2], [25, 0, 9, -2, -8, 16, -8, -9], [-3, -14, -4, -9, -5, 6, 0, 6], [10, -16, -3, -4, -5, 8, 4, -5], [-5, 12, -1, -5, 2, 2, -10, -4], [37, 6, -9, -7, 5, 24, 4, 7], [-32, 2, -7, 0, -7, -27, 8, -9], [24, -14, 10, 4, 3, -3, -4, -8], [20, -8, 13, 6, 7, -14, 4, -2], [-9, -10, -6, -2, 1, 23, 0, -7], [37, -12, -13, 0, -3, 10, 2, 5], [-36, -4, -3, 12, -8, -16, 12, 3], [6, 0, 12, -6, 0, -10, -8, 2], [-24, -12, -2, 5, 2, 9, 12, -3], [-23, -12, 2, 8, -7, -11, 16, -6], [34, -16, 1, 0, 9, 2, -6, 8], [24, 6, 0, -13, 0, -1, -8, -1], [6, -6, -4, -12, -1, 4, 0, 5], [-7, -6, -4, 2, -5, -27, 0, -9], [30, 4, 0, -3, 6, 43, -10, 1], [1, 0, 8, 6, -7, -13, 4, -1], [-4, -2, 9, 7, 5, -19, 2, 4], [-8, 14, -12, 1, -8, -26, -6, -3], [-24, 14, -7, -8, 1, 2, 4, -4], [-17, -4, -3, 9, -14, -14, 10, -9], [14, -8, 8, -1, 1, -15, 6, 10], [1, 4, -5, 1, 0, 10, -10, -2], [-37, 6, -15, 7, -10, -2, 4, -8], [-25, 4, -3, 3, -10, 15, -2, -9], [10, -2, 0, 4, -2, 1, 8, 13], [-11, 18, -5, -5, -6, 1, 4, -5], [6, 20, -6, -14, 0, -17, 0, -6], [-15, -20, -14, -1, -1, -3, 24, -15], [-36, -18, -1, 9, -11, -9, 16, -3], [-5, 2, -13, -2, 8, 4, -2, -2], [-39, -4, 4, 10, -7, -4, 4, 13], [3, -14, 9, 2, -5, 26, -4, 3], [12, -16, -7, 7, 1, 10, 10, -8], [5, -16, 0, 0, 11, 3, -4, 2], [-3, -22, -5, 1, 2, 1, 6, 0], [-37, 12, -11, 3, 10, -2, -14, -2], [-7, -4, 12, 21, -12, 5, -12, 0], [8, -14, -2, 7, 10, -6, 12, 0], [9, -8, 0, 6, -15, 22, 0, -8], [-9, 22, -5, -4, 2, 8, -4, 1], [6, -8, 0, 11, -5, 7, -6, -10], [-16, -6, -3, -6, 5, 4, -2, -2], [-40, 8, -2, 3, -14, -5, 2, -11], [-3, 16, 3, 1, 1, -10, -6, -3], [-53, -2, -9, 21, -2, -43, 2, -13], [13, 16, -2, 5, 9, -11, -6, -6], [7, -8, 15, 3, -2, -23, 4, 1], [13, 12, -2, -3, -3, -11, 4, 1], [-20, -2, 8, 4, -4, 10, -8, 9], [49, -4, 1, 8, -6, 24, -2, -6], [-10, -8, 5, -8, 3, -12, 0, 5], [-12, 12, -7, -1, 7, 7, -8, -11], [4, -4, 21, -3, 8, 6, 0, 1], [-11, 10, 1, -7, -8, -21, 6, -9], [3, -2, 13, -6, -4, 44, -8, 1], [17, -2, 3, -1, 2, -37, -8, -1], [-28, 0, -5, -7, 11, -14, -6, 4], [-31, -16, 2, 19, -3, -1, 8, -1], [-29, -10, 9, 7, -2, -5, -6, 1], [22, 4, 11, 3, -6, 28, -12, 5], [-13, 10, -1, 6, 0, -26, 14, 10], [22, -6, 5, 2, 11, -7, 0, -14], [37, 12, -6, -12, 7, 0, 0, -7], [-28, -18, -4, 4, 12, -8, 10, -8], [19, -20, -1, -5, 2, 31, -2, -6], [-2, 0, 19, -2, 3, 19, -2, 7], [17, 6, 13, -11, -2, -10, 10, 1], [26, -12, 15, -6, 11, 24, -10, 6], [-25, -10, -10, 10, -2, -13, 2, 12], [-3, -24, 13, 1, -4, -23, 4, 7], [-28, 2, -15, 14, -7, -23, 12, -17], [-1, -10, 0, 2, -9, 6, 8, 0], [-3, 0, -8, -2, 6, 24, -8, -5], [12, 6, -13, 5, -5, -8, 2, 4], [-13, 0, 3, -9, 2, 7, 2, 6], [-26, 4, -1, -6, -1, -1, -4, -1], [21, -16, 8, 0, -4, 16, 8, -7], [27, 10, 4, -7, 5, 23, -2, -1], [6, 2, -7, -2, 1, -20, -2, -8], [-21, -6, -5, -5, 0, -26, 2, 10], [-18, 6, -12, 2, -11, 3, 8, 4], [-7, -2, 3, 1, 2, 3, -4, 3], [5, 16, -6, 8, -1, 6, -4, 0], [-6, 6, 9, -6, 7, 6, -16, 18], [-9, 8, -4, -5, 7, 19, 14, -5], [-21, -22, 14, 12, -11, -2, -10, 4], [-26, 2, 8, 8, -10, -17, -6, 7], [-24, 6, -6, 4, -11, -18, 12, 1], [50, -6, 0, -13, 8, 25, -8, 1], [15, -8, 3, -7, 12, 0, -2, 0], [-48, -24, -3, 4, 4, -34, 20, -3], [-20, 6, -3, -11, 1, 6, -2, -6], [-16, -8, 1, 14, -5, -1, 8, -7], [-7, -8, -1, 6, 12, -11, 12, 7], [36, -12, -15, -14, 9, 4, 0, -3], [5, -14, 16, -1, -5, 16, 4, 4]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2883_a_Hecke( : Kf := Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2883_2_a_p();".
// 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_2883_2_a_p(:prec:=8)
    chi := MakeCharacter_2883_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_2883_2_a_p();".
// 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_2883_2_a_p( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2883_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![9, 42, -82, -31, 62, 10, -14, -1, 1]>,<11,R![144, -384, -328, 512, 217, -108, -28, 5, 1]>,<13,R![-99, -795, 365, 1129, 272, -145, -41, 4, 1]>],Snew);
    return Vf;
end function;