
// Make newform 5929.2.a.bv in Magma, downloaded from the LMFDB on 11 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_5929_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_5929_2_a_bv();".
// 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_5929_2_a_bv();".
// 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 := [-968, 0, 1884, 0, -1038, 0, 245, 0, -26, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1572, 0, -3108, 0, 1187, 0, -160, 0, 7], [0, 3972, 0, -5912, 0, 2267, 0, -324, 0, 15], [252, 0, -410, 0, 157, 0, -22, 0, 1, 0], [0, 5652, 0, -9472, 0, 3749, 0, -540, 0, 25], [0, -14876, 0, 25672, 0, -10355, 0, 1516, 0, -71], [1024, 0, -1762, 0, 717, 0, -106, 0, 5, 0], [-1080, 0, 1880, 0, -749, 0, 108, 0, -5, 0]];
    Rf_basisdens := [1, 1, 1, 88, 88, 4, 88, 88, 4, 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_5929_a();"
function MakeCharacter_5929_a()
    N := 5929;
    order := 1;
    char_gens := [1816, 2059];
    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_5929_a_Hecke(Kf)
    return MakeCharacter_5929_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, 0, -1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, -1, 0, 0], [0, 0, 0, 0, -1, 0, 1, 1, 0, 0], [0, 0, 0, -2, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, -1], [-1, 0, -1, 0, 0, 1, 0, 0, -1, 1], [0, -1, 0, 2, 0, 0, 0, 0, 0, 0], [4, 0, 1, 0, 0, -1, 0, 0, 1, 0], [0, -2, 0, 0, 1, 0, -1, 1, 0, 0], [1, 0, -1, 0, 0, -1, 0, 0, -1, -1], [0, -2, 0, -2, -1, 0, -2, 1, 0, 0], [2, 0, -2, 0, 0, 0, 0, 0, -2, 0], [0, 2, 0, 0, -1, 0, -3, -2, 0, 0], [0, -2, 0, 0, 1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, -3, 0, 0, 1, -1], [4, 0, 0, 0, 0, -3, 0, 0, 1, -1], [0, 0, 0, 0, -1, 0, -5, -3, 0, 0], [-1, 0, 1, 0, 0, -1, 0, 0, -1, -1], [0, 0, 0, 0, -2, 0, -2, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 2, 0, -2, 0, 0, 0, 1, 0, 0], [0, -2, 0, -4, 1, 0, 1, 3, 0, 0], [0, 0, 0, 0, -1, 0, 0, 1, 0, 0], [4, 0, 0, 0, 0, -2, 0, 0, 2, 2], [-9, 0, 1, 0, 0, -1, 0, 0, 1, 1], [4, 0, -1, 0, 0, -1, 0, 0, -1, 2], [4, 0, 0, 0, 0, -2, 0, 0, -2, 2], [0, 0, 0, 2, 2, 0, -2, -2, 0, 0], [-2, 0, -1, 0, 0, -3, 0, 0, -1, -2], [0, 2, 0, -2, -2, 0, -4, 0, 0, 0], [-4, 0, -4, 0, 0, 2, 0, 0, 2, -4], [-1, 0, -3, 0, 0, -1, 0, 0, -1, -1], [0, 1, 0, -6, -3, 0, 5, 1, 0, 0], [3, 0, -3, 0, 0, 5, 0, 0, -1, -1], [0, 2, 0, -2, 0, 0, -2, 2, 0, 0], [0, -2, 0, 4, -3, 0, 1, -5, 0, 0], [4, 0, -1, 0, 0, -1, 0, 0, 3, 0], [0, 3, 0, 4, 1, 0, -3, 1, 0, 0], [6, 0, -1, 0, 0, 3, 0, 0, -1, -2], [-10, 0, 2, 0, 0, 0, 0, 0, 0, -2], [-2, 0, 0, 0, 0, 0, 0, 0, 4, -4], [0, 0, 0, 4, 1, 0, -8, -1, 0, 0], [2, 0, -4, 0, 0, -4, 0, 0, 4, -2], [0, -4, 0, -2, -1, 0, -3, -2, 0, 0], [0, 2, 0, 6, 0, 0, 2, -4, 0, 0], [0, -2, 0, -6, 0, 0, 4, 3, 0, 0], [13, 0, 3, 0, 0, -1, 0, 0, 1, 1], [4, 0, 4, 0, 0, 0, 0, 0, 0, 4], [0, -2, 0, 4, -1, 0, -1, 1, 0, 0], [0, 1, 0, 2, -2, 0, 6, -2, 0, 0], [0, -2, 0, -6, -2, 0, 7, 2, 0, 0], [8, 0, 0, 0, 0, -2, 0, 0, 2, -2], [0, 0, 0, -4, 2, 0, 3, 2, 0, 0], [0, 6, 0, 0, 0, 0, -2, -2, 0, 0], [-4, 0, 4, 0, 0, -4, 0, 0, 0, 6], [3, 0, 1, 0, 0, 3, 0, 0, -3, 5], [0, -4, 0, 2, 2, 0, 8, 0, 0, 0], [0, 2, 0, -4, 1, 0, 9, 5, 0, 0], [0, -4, 0, 2, 2, 0, 8, 4, 0, 0], [0, 0, 0, 4, -1, 0, -4, 1, 0, 0], [0, -1, 0, 4, -1, 0, 3, -1, 0, 0], [8, 0, -3, 0, 0, -3, 0, 0, 1, -2], [8, 0, -7, 0, 0, 1, 0, 0, 1, -4], [1, 0, -7, 0, 0, -1, 0, 0, 5, -5], [13, 0, 3, 0, 0, 1, 0, 0, 1, 5], [0, 0, 0, 4, 1, 0, -7, -9, 0, 0], [0, -5, 0, 2, 3, 0, 7, -1, 0, 0], [7, 0, -1, 0, 0, 5, 0, 0, 5, -5], [0, 2, 0, 0, -3, 0, -5, -4, 0, 0], [-8, 0, 2, 0, 0, 4, 0, 0, 8, -4], [-2, 0, 2, 0, 0, -1, 0, 0, 3, 1], [0, 1, 0, 0, 2, 0, 2, -2, 0, 0], [3, 0, -3, 0, 0, -6, 0, 0, 0, -2], [0, -6, 0, 2, 2, 0, 7, 6, 0, 0], [-6, 0, -2, 0, 0, -6, 0, 0, 2, -2], [0, -2, 0, 0, -3, 0, 1, -3, 0, 0], [0, 4, 0, 0, 1, 0, -6, 3, 0, 0], [18, 0, 2, 0, 0, 0, 0, 0, -2, 0], [11, 0, -1, 0, 0, 1, 0, 0, 5, -1], [0, -6, 0, 2, 4, 0, 0, 3, 0, 0], [0, -6, 0, -2, 2, 0, -6, 4, 0, 0], [-6, 0, -3, 0, 0, -3, 0, 0, 5, -6], [1, 0, 3, 0, 0, -4, 0, 0, -4, 0], [6, 0, -6, 0, 0, -6, 0, 0, -2, -4], [0, 6, 0, 4, 1, 0, 1, -3, 0, 0], [-14, 0, -2, 0, 0, 1, 0, 0, -3, 3], [0, 3, 0, 0, 0, 0, -12, -4, 0, 0], [0, -4, 0, 2, 0, 0, -2, 2, 0, 0], [-2, 0, 2, 0, 0, 5, 0, 0, 1, 7], [3, 0, 1, 0, 0, 7, 0, 0, -5, -1], [-11, 0, -1, 0, 0, 3, 0, 0, 5, 1], [0, 0, 0, 4, -6, 0, 0, -2, 0, 0], [0, 1, 0, 0, 3, 0, 15, 7, 0, 0], [0, -7, 0, 4, -1, 0, -5, -9, 0, 0], [0, -4, 0, 0, 0, 0, -2, 0, 0, 0], [-14, 0, 0, 0, 0, -10, 0, 0, 2, 2], [14, 0, 2, 0, 0, 6, 0, 0, -2, 2], [10, 0, -2, 0, 0, 8, 0, 0, 0, -2], [0, -2, 0, -10, 2, 0, 6, 2, 0, 0], [1, 0, -1, 0, 0, 15, 0, 0, -3, 1], [-6, 0, -4, 0, 0, 2, 0, 0, -6, 4], [0, 6, 0, -2, 0, 0, 0, 7, 0, 0], [0, 8, 0, -4, -3, 0, 14, 3, 0, 0], [0, -4, 0, -4, -1, 0, -1, 5, 0, 0], [9, 0, 3, 0, 0, -9, 0, 0, -3, 1], [0, 4, 0, 0, 3, 0, -13, -1, 0, 0], [0, -6, 0, -2, 0, 0, 6, 2, 0, 0], [-5, 0, -7, 0, 0, -1, 0, 0, 5, -3], [4, 0, 2, 0, 0, 0, 0, 0, -6, 4], [0, 0, 0, -2, 7, 0, 1, 0, 0, 0], [-8, 0, 5, 0, 0, 9, 0, 0, -3, 4], [8, 0, -1, 0, 0, -3, 0, 0, -9, 4], [0, 5, 0, 6, -2, 0, -2, -10, 0, 0], [0, -6, 0, 4, -3, 0, 7, 0, 0, 0], [1, 0, -5, 0, 0, 4, 0, 0, 2, 0], [3, 0, -1, 0, 0, 3, 0, 0, 3, 9], [0, -3, 0, 4, -3, 0, -3, -11, 0, 0], [5, 0, -7, 0, 0, -3, 0, 0, 3, -11], [0, 0, 0, 0, 1, 0, -9, 7, 0, 0], [10, 0, 2, 0, 0, 10, 0, 0, 2, 2], [0, 4, 0, -6, -1, 0, 13, 0, 0, 0], [13, 0, 5, 0, 0, 1, 0, 0, 7, 5], [17, 0, -1, 0, 0, -4, 0, 0, 2, 4], [0, 7, 0, 0, -6, 0, -10, 2, 0, 0], [0, 5, 0, -2, 0, 0, 12, 0, 0, 0], [0, -6, 0, -8, -1, 0, 5, 1, 0, 0], [-12, 0, -4, 0, 0, -2, 0, 0, -2, -2], [-2, 0, 4, 0, 0, 10, 0, 0, 6, -4], [10, 0, 2, 0, 0, 9, 0, 0, -7, 7], [0, 0, 0, 0, 0, 4, 0, 0, 0, 12], [0, 8, 0, 8, 1, 0, -1, -7, 0, 0], [0, -6, 0, 0, 5, 0, 3, 3, 0, 0], [0, -6, 0, -6, 4, 0, 13, 4, 0, 0], [0, -2, 0, 12, 4, 0, -10, -8, 0, 0], [0, 0, 0, 0, 8, 0, 8, 1, 0, 0], [4, 0, 0, 0, 0, -6, 0, 0, -2, 8], [0, -4, 0, 4, 4, 0, -16, -2, 0, 0], [0, 0, -2, 0, 0, 2, 0, 0, 2, 2], [16, 0, 5, 0, 0, -7, 0, 0, 1, 4], [-21, 0, 7, 0, 0, -3, 0, 0, -3, 3], [0, -4, 0, 4, -4, 0, -8, -7, 0, 0], [0, -1, 0, 4, -2, 0, -18, 2, 0, 0], [0, 10, 0, 0, 3, 0, -7, -1, 0, 0], [0, -4, 0, 4, 5, 0, -13, 1, 0, 0], [0, -3, 0, 6, -2, 0, 6, 2, 0, 0], [8, 0, 4, 0, 0, 0, 0, 0, 4, -4], [-27, 0, 9, 0, 0, 3, 0, 0, -3, 3], [0, -5, 0, 12, 1, 0, -11, 1, 0, 0], [2, 0, -2, 0, 0, 14, 0, 0, -6, 2], [0, -8, 0, -6, 4, 0, 4, 8, 0, 0], [-11, 0, -5, 0, 0, -5, 0, 0, -3, 9], [21, 0, -5, 0, 0, -1, 0, 0, -3, 1], [6, 0, -4, 0, 0, -6, 0, 0, -2, 0], [0, 6, 0, 6, 4, 0, -7, 8, 0, 0], [0, -8, 0, 0, 1, 0, -21, 1, 0, 0], [0, 10, 0, -8, -3, 0, 25, 5, 0, 0], [14, 0, 3, 0, 0, 7, 0, 0, -1, 2], [0, 0, -4, 0, 0, 8, 0, 0, 8, -10], [-3, 0, 9, 0, 0, 5, 0, 0, -3, 7], [0, -8, 0, -6, 5, 0, 3, 8, 0, 0], [-21, 0, 5, 0, 0, 8, 0, 0, 2, 0], [0, 2, 0, 4, 9, 0, -1, 12, 0, 0], [19, 0, -7, 0, 0, 1, 0, 0, 3, -5], [0, -8, 0, 8, -1, 0, 3, 3, 0, 0], [-14, 0, 0, 0, 0, 6, 0, 0, -6, 2], [0, -7, 0, 6, -1, 0, 3, 3, 0, 0], [22, 0, -8, 0, 0, -14, 0, 0, -2, -4], [0, 8, 0, 8, -4, 0, -9, -8, 0, 0], [29, 0, 1, 0, 0, -15, 0, 0, -3, -5], [-11, 0, 9, 0, 0, 5, 0, 0, 3, 9], [0, 1, 0, 8, 10, 0, 6, 6, 0, 0], [0, -11, 0, 2, -5, 0, 3, 3, 0, 0], [-5, 0, -9, 0, 0, 7, 0, 0, -5, -11], [24, 0, -11, 0, 0, -1, 0, 0, 1, -8], [0, -2, 0, -6, -6, 0, 6, 8, 0, 0], [0, -4, 0, -8, -3, 0, 15, 15, 0, 0], [-10, 0, -2, 0, 0, -10, 0, 0, -10, 2], [0, 2, 0, 6, -6, 0, 2, -2, 0, 0], [-5, 0, 1, 0, 0, 2, 0, 0, 4, -6], [0, 10, 0, -8, 1, 0, -3, -5, 0, 0], [26, 0, 1, 0, 0, -7, 0, 0, -3, -2], [0, 4, 0, 0, -6, 0, -3, 2, 0, 0], [-10, 0, -6, 0, 0, 6, 0, 0, 6, -8], [0, 10, 0, 6, -3, 0, -20, -17, 0, 0], [7, 0, -3, 0, 0, 11, 0, 0, 9, -11], [0, 2, 0, -8, 6, 0, 0, 6, 0, 0], [0, 4, 0, -4, -2, 0, 2, 11, 0, 0], [-8, 0, -2, 0, 0, -2, 0, 0, -10, 0], [-20, 0, -8, 0, 0, 13, 0, 0, -3, -5], [0, -4, 0, 0, -4, 0, -5, 4, 0, 0], [-19, 0, -3, 0, 0, 9, 0, 0, 9, -5], [0, 0, 0, 0, 0, 0, 4, -5, 0, 0], [15, 0, -1, 0, 0, 11, 0, 0, 1, -1], [12, 0, 7, 0, 0, -3, 0, 0, 11, -4], [0, -6, 0, 8, 1, 0, -11, -3, 0, 0], [0, 2, 0, 0, -4, 0, 12, 4, 0, 0], [-6, 0, -6, 0, 0, -8, 0, 0, 4, -18], [0, 10, 0, 4, 6, 0, 14, 0, 0, 0], [0, -6, 0, -2, -8, 0, 3, 0, 0, 0], [0, 6, 0, 12, -1, 0, -1, -9, 0, 0], [0, -10, 0, 0, -1, 0, -3, 2, 0, 0], [0, -2, 0, 2, 6, 0, 2, 11, 0, 0], [0, 7, 0, 2, 8, 0, 8, 0, 0, 0], [-4, 0, 6, 0, 0, 2, 0, 0, -2, -8], [-4, 0, -4, 0, 0, 8, 0, 0, 4, 6], [0, 10, 0, -6, 1, 0, 12, 15, 0, 0], [-1, 0, 3, 0, 0, -5, 0, 0, -3, -1], [0, 5, 0, -14, -1, 0, 3, 3, 0, 0], [-18, 0, -3, 0, 0, -15, 0, 0, 1, 6], [0, 6, 0, 6, -1, 0, -32, -15, 0, 0], [0, -2, 0, 8, 0, 0, -26, -6, 0, 0], [0, -7, 0, -8, 1, 0, -23, 5, 0, 0], [-13, 0, -1, 0, 0, 5, 0, 0, -7, -9], [0, 0, 0, 4, 9, 0, 25, 11, 0, 0], [3, 0, -3, 0, 0, 9, 0, 0, -13, 3], [-15, 0, -1, 0, 0, 4, 0, 0, 2, 4], [-27, 0, 5, 0, 0, -3, 0, 0, 11, -7], [0, 0, 0, 2, 12, 0, 8, 0, 0, 0], [-25, 0, 13, 0, 0, 4, 0, 0, 0, 4], [20, 0, -7, 0, 0, -7, 0, 0, 9, -4], [0, 20, 0, -8, 0, 0, 6, 0, 0, 0], [-21, 0, -3, 0, 0, 9, 0, 0, -1, -1], [0, 2, 0, -2, -8, 0, -7, -12, 0, 0], [18, 0, 6, 0, 0, 10, 0, 0, -2, 18], [0, 4, 0, -2, 0, 0, 14, 10, 0, 0], [-17, 0, 15, 0, 0, -3, 0, 0, 5, 3], [-6, 0, -5, 0, 0, -19, 0, 0, 3, 2], [0, 12, 0, -8, 0, 0, 28, 2, 0, 0], [-6, 0, -2, 0, 0, 6, 0, 0, 2, -6], [26, 0, 4, 0, 0, 6, 0, 0, -2, 10], [0, -11, 0, 14, -2, 0, -6, -2, 0, 0], [0, 10, 0, 6, -2, 0, -22, -12, 0, 0], [0, 3, 0, 0, -3, 0, -19, 9, 0, 0], [-4, 0, -2, 0, 0, -6, 0, 0, 6, -2], [16, 0, -12, 0, 0, -5, 0, 0, -5, 5], [0, 12, 0, -18, -3, 0, 7, -2, 0, 0], [-4, 0, 8, 0, 0, -7, 0, 0, 9, -1], [0, 8, 0, 2, 4, 0, -6, 0, 0, 0], [0, -2, 0, -2, -7, 0, -2, 11, 0, 0], [37, 0, -1, 0, 0, -6, 0, 0, 2, -10], [0, -10, 0, -4, -3, 0, -5, -7, 0, 0], [0, -2, 0, 10, 0, 0, -6, 10, 0, 0], [0, -2, 0, -10, 9, 0, -10, 7, 0, 0], [0, 8, 0, 8, 7, 0, 10, -11, 0, 0], [-12, 0, -2, 0, 0, 2, 0, 0, 10, -4], [-18, 0, -4, 0, 0, 0, 0, 0, -4, 2], [-6, 0, -12, 0, 0, 2, 0, 0, -6, -10], [0, 14, 0, -4, -3, 0, -25, -5, 0, 0], [-2, 0, -10, 0, 0, -9, 0, 0, -9, -7], [0, 6, 0, -2, -2, 0, 1, 10, 0, 0], [0, -16, 0, -4, 7, 0, 5, 3, 0, 0], [18, 0, -8, 0, 0, 4, 0, 0, -8, -2], [16, 0, 2, 0, 0, 12, 0, 0, 10, 0], [0, 14, 0, -8, 4, 0, -6, 12, 0, 0], [0, -9, 0, 0, 11, 0, 15, 15, 0, 0], [0, 6, 0, 8, 11, 0, 19, -3, 0, 0], [-1, 0, 5, 0, 0, 17, 0, 0, 9, -3], [16, 0, -4, 0, 0, 0, 0, 0, 4, 4], [0, 10, 0, 12, 7, 0, 19, -5, 0, 0], [0, -4, 0, -4, 3, 0, -13, -5, 0, 0], [0, 6, 0, -2, 6, 0, 5, 10, 0, 0], [0, -4, 0, 0, 5, 0, 26, -5, 0, 0], [9, 0, -5, 0, 0, 6, 0, 0, -6, -2], [0, -5, 0, 6, 5, 0, 13, 9, 0, 0], [-5, 0, 9, 0, 0, -1, 0, 0, -13, 7], [-15, 0, -3, 0, 0, 9, 0, 0, -1, -7], [0, 16, 0, 4, -4, 0, 4, -1, 0, 0], [-8, 0, 16, 0, 0, 5, 0, 0, -3, 15], [0, -4, 0, -8, 2, 0, 17, 14, 0, 0], [22, 0, 2, 0, 0, 2, 0, 0, 2, 14], [0, -2, 0, -8, -5, 0, -9, 3, 0, 0], [0, 0, 0, -6, -3, 0, 35, -2, 0, 0], [-12, 0, -3, 0, 0, 5, 0, 0, 9, -8], [-12, 0, -8, 0, 0, -2, 0, 0, -6, 8], [2, 0, -8, 0, 0, -20, 0, 0, 0, -12], [0, -6, 0, -4, -8, 0, 4, -2, 0, 0], [0, -4, 0, 8, 0, 0, -20, 4, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, -9, -3], [0, 4, 0, -8, 6, 0, -6, 0, 0, 0], [0, 20, 0, 12, -3, 0, -13, -9, 0, 0], [0, 2, 0, 4, 0, 0, 26, -4, 0, 0], [46, 0, 6, 0, 0, -9, 0, 0, -1, -7], [-8, 0, 4, 0, 0, 14, 0, 0, 4, -6], [32, 0, -4, 0, 0, 2, 0, 0, -6, 4], [0, 5, 0, -8, -2, 0, -6, 10, 0, 0], [0, 0, 0, 8, 11, 0, 19, 7, 0, 0], [-15, 0, -1, 0, 0, -22, 0, 0, 2, 2], [0, 0, 0, 0, 3, 0, -22, 9, 0, 0], [9, 0, 1, 0, 0, 9, 0, 0, 7, -3], [0, 0, 0, 2, 0, 0, 24, 2, 0, 0], [-14, 0, -2, 0, 0, 8, 0, 0, -4, 6], [0, 2, 0, 8, 7, 0, -11, -15, 0, 0], [0, 2, 0, -8, -5, 0, 1, -8, 0, 0], [0, 6, 0, 6, -8, 0, 20, -5, 0, 0], [0, 14, 0, -4, 4, 0, 10, 16, 0, 0], [0, -4, 0, -12, -6, 0, 6, 14, 0, 0], [0, 4, 0, 4, 1, 0, 11, 13, 0, 0], [-13, 0, 7, 0, 0, -5, 0, 0, 5, 7], [-13, 0, -5, 0, 0, 19, 0, 0, -5, 9], [-7, 0, 3, 0, 0, 19, 0, 0, 5, -3], [-22, 0, -2, 0, 0, -7, 0, 0, 1, 7], [-16, 0, 1, 0, 0, -5, 0, 0, -7, -4], [6, 0, 9, 0, 0, -7, 0, 0, 9, 6], [0, -14, 0, 2, 2, 0, 10, 5, 0, 0], [18, 0, 2, 0, 0, 2, 0, 0, -2, 6], [-2, 0, 6, 0, 0, -14, 0, 0, -2, 4], [0, -2, 0, -6, 0, 0, 30, 6, 0, 0], [-8, 0, -8, 0, 0, 0, 0, 0, 4, -16], [11, 0, 11, 0, 0, 9, 0, 0, -1, 5], [-12, 0, -3, 0, 0, 5, 0, 0, 1, -8], [21, 0, -9, 0, 0, -15, 0, 0, 5, 1], [0, -10, 0, -8, 7, 0, 15, 15, 0, 0], [0, -8, 0, 2, -13, 0, -7, -20, 0, 0], [36, 0, 6, 0, 0, -14, 0, 0, -2, -4], [0, -4, 0, -12, 6, 0, -5, 6, 0, 0], [25, 0, -1, 0, 0, -5, 0, 0, -3, -7], [0, -12, 0, 2, 2, 0, 0, 0, 0, 0], [-37, 0, 1, 0, 0, -12, 0, 0, 6, 0], [0, -2, 0, 4, -5, 0, -5, -13, 0, 0], [-4, 0, 1, 0, 0, 5, 0, 0, -3, -8], [6, 0, 10, 0, 0, -12, 0, 0, 8, 10], [0, 20, 0, -12, 4, 0, 12, 9, 0, 0], [6, 0, -2, 0, 0, -9, 0, 0, 7, 5], [0, 8, 0, -2, 3, 0, 21, 4, 0, 0], [9, 0, -13, 0, 0, -3, 0, 0, -3, -11], [-5, 0, -13, 0, 0, 3, 0, 0, -3, -13], [-54, 0, 4, 0, 0, 6, 0, 0, -10, -2], [-12, 0, 6, 0, 0, 0, 0, 0, 2, -16], [0, 4, 0, -12, -16, 0, 10, -6, 0, 0], [0, 10, 0, 6, -2, 0, -20, 8, 0, 0], [-17, 0, 3, 0, 0, -17, 0, 0, -13, 5], [0, 5, 0, 10, -6, 0, 2, -18, 0, 0], [18, 0, -1, 0, 0, 13, 0, 0, -13, 14], [0, 6, 0, -12, -5, 0, 1, 3, 0, 0], [0, -8, 0, 8, 4, 0, -12, -13, 0, 0], [0, 4, 0, 8, 2, 0, -28, -22, 0, 0], [4, 0, -5, 0, 0, 23, 0, 0, -5, -6], [-12, 0, 7, 0, 0, 17, 0, 0, 3, 12], [0, -6, 0, -12, -3, 0, 21, 3, 0, 0], [-12, 0, 9, 0, 0, -3, 0, 0, 1, 16], [-33, 0, 1, 0, 0, 0, 0, 0, -2, 0], [-28, 0, 6, 0, 0, 0, 0, 0, 0, 6], [0, -4, 0, -4, 6, 0, -6, -7, 0, 0], [-20, 0, -4, 0, 0, -3, 0, 0, -11, 15], [0, -28, 0, -8, 4, 0, 12, 0, 0, 0], [0, 7, 0, 14, 5, 0, -3, 1, 0, 0], [0, -6, 0, 6, -2, 0, -14, 2, 0, 0], [-29, 0, -7, 0, 0, -12, 0, 0, 8, -8], [38, 0, 4, 0, 0, -20, 0, 0, 4, -8], [0, -6, 0, 0, -4, 0, 12, 16, 0, 0], [-18, 0, -16, 0, 0, 14, 0, 0, -10, 2], [0, 0, 0, -12, -5, 0, 23, -5, 0, 0], [0, 13, 0, 0, -10, 0, -14, -6, 0, 0], [0, -2, 0, 24, 6, 0, -18, 6, 0, 0], [6, 0, 12, 0, 0, 6, 0, 0, 6, 14], [8, 0, -1, 0, 0, -21, 0, 0, -1, -12], [4, 0, 0, 0, 0, -10, 0, 0, 2, 0], [0, 10, 0, 4, 1, 0, -9, 5, 0, 0], [20, 0, 1, 0, 0, 29, 0, 0, -11, 8], [27, 0, -9, 0, 0, -19, 0, 0, 5, -5], [0, -10, 0, -4, 9, 0, -13, -2, 0, 0], [-6, 0, -1, 0, 0, -15, 0, 0, 3, -18], [0, 10, 0, 8, 5, 0, -23, 3, 0, 0], [4, 0, 10, 0, 0, -16, 0, 0, 4, 14], [-24, 0, -2, 0, 0, 12, 0, 0, -4, 0], [-16, 0, -4, 0, 0, -5, 0, 0, -9, -3], [0, -6, 0, -2, -9, 0, -12, 13, 0, 0], [-6, 0, -6, 0, 0, -14, 0, 0, -10, -14], [12, 0, 12, 0, 0, -12, 0, 0, 4, 2], [0, -4, 0, 4, -4, 0, 8, -16, 0, 0], [13, 0, -5, 0, 0, 6, 0, 0, 6, -2], [0, -24, 0, 4, 5, 0, 26, 11, 0, 0], [3, 0, -9, 0, 0, -17, 0, 0, -1, -19], [0, -10, 0, -24, 3, 0, -3, 11, 0, 0], [0, -14, 0, 0, 5, 0, 9, 11, 0, 0], [0, 6, 0, -4, -9, 0, -41, -11, 0, 0], [0, 8, 0, 0, 0, 0, -27, 4, 0, 0], [13, 0, -13, 0, 0, -4, 0, 0, 8, 4], [9, 0, -9, 0, 0, -23, 0, 0, -3, 5], [-30, 0, 8, 0, 0, -4, 0, 0, 16, -8], [0, 10, 0, 2, 2, 0, -10, -22, 0, 0], [0, 8, 0, 2, -5, 0, -31, 2, 0, 0], [4, 0, 0, 0, 0, -8, 0, 0, -4, -12], [0, 0, 0, -4, 0, 0, 20, 15, 0, 0], [32, 0, 0, 0, 0, -14, 0, 0, -2, 2], [0, 12, 0, -18, 1, 0, 23, 10, 0, 0], [14, 0, -7, 0, 0, -13, 0, 0, -7, -10], [0, -7, 0, 24, 7, 0, -33, -9, 0, 0], [36, 0, 0, 0, 0, 1, 0, 0, -19, 15], [0, 4, 0, 10, 13, 0, 27, 0, 0, 0], [-8, 0, 5, 0, 0, 9, 0, 0, -7, 4], [3, 0, 1, 0, 0, -7, 0, 0, -13, 19], [0, 2, 0, -8, -4, 0, 18, 10, 0, 0], [0, -2, 0, 10, -2, 0, -17, -6, 0, 0], [-11, 0, 11, 0, 0, 15, 0, 0, -11, -7], [-19, 0, -3, 0, 0, -7, 0, 0, -5, 13], [0, -8, 0, 4, 11, 0, -17, 1, 0, 0], [-16, 0, 7, 0, 0, 7, 0, 0, -5, 6], [36, 0, 6, 0, 0, 0, 0, 0, -4, -10], [0, 18, 0, 2, -6, 0, -21, -22, 0, 0], [0, 8, 0, 16, -3, 0, 13, -11, 0, 0], [0, -20, 0, -14, 2, 0, 12, 2, 0, 0], [18, 0, 12, 0, 0, 0, 0, 0, -12, 4], [12, 0, 2, 0, 0, 8, 0, 0, -12, 0], [0, -8, 0, -12, 1, 0, 6, 23, 0, 0], [0, -15, 0, 0, 12, 0, -16, 0, 0, 0], [0, -4, 0, -8, 3, 0, 25, -9, 0, 0], [-17, 0, -11, 0, 0, -21, 0, 0, -7, -15], [58, 0, -10, 0, 0, 6, 0, 0, 2, -6], [1, 0, -5, 0, 0, 3, 0, 0, 11, 3], [9, 0, -7, 0, 0, 23, 0, 0, -7, -9], [0, 4, 0, -12, -12, 0, 4, 9, 0, 0], [-36, 0, -2, 0, 0, 16, 0, 0, -12, -2], [0, 9, 0, -8, -2, 0, 26, 10, 0, 0], [0, -2, 0, -22, 2, 0, 9, 22, 0, 0], [0, -6, 0, 8, -10, 0, 4, 2, 0, 0], [-3, 0, -5, 0, 0, 16, 0, 0, 18, -8], [0, 10, 0, -4, -1, 0, -3, 13, 0, 0], [9, 0, -9, 0, 0, -1, 0, 0, -7, 5], [0, 16, 0, -4, -4, 0, 0, 2, 0, 0], [0, 6, 0, -10, -6, 0, 25, 6, 0, 0], [0, 13, 0, -12, -5, 0, -17, -13, 0, 0], [22, 0, 2, 0, 0, -15, 0, 0, 1, -17], [-17, 0, -9, 0, 0, -1, 0, 0, -7, -13], [0, -11, 0, 14, -10, 0, -10, -22, 0, 0], [0, -16, 0, -8, 6, 0, 42, 32, 0, 0]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_5929_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_5929_2_a_bv();".
// 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_5929_2_a_bv(:prec:=10)
    chi := MakeCharacter_5929_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_5929_2_a_bv();".
// 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_5929_2_a_bv( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_5929_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![8, 12, -9, -9, 1, 1]>,<3,R![-968, 0, 1884, 0, -1038, 0, 245, 0, -26, 0, 1]>,<5,R![-8, 0, 204, 0, -1214, 0, 365, 0, -34, 0, 1]>],Snew);
    return Vf;
end function;