
// Make newform 99.2.g.b in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_99_g();"
// To make the character of type GrpDrchElt with Codomain the HeckeField, type "MakeCharacter_99_g_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_99_2_g_b();".
// 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_99_2_g_b();".
// 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 := [8649, 0, 13392, 0, 13761, 0, 8010, 0, 3372, 0, 837, 0, 150, 0, 15, 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, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-22396351233, 0, -23155939764, 0, -11995771800, 0, -5823700650, 0, -1489331264, 0, -288594750, 0, -29523650, 0, -2126395, 0], [0, 9265241250, 0, 23155939764, 0, 11995771800, 0, 5823700650, 0, 1489331264, 0, 288594750, 0, 29523650, 0, 2126395], [0, -290195282991, 0, -292920249753, 0, -206255555451, 0, -66244476882, 0, -14824095809, 0, -1890026425, 0, -160857665, 0, -4873266], [0, 551339033751, 0, 607209996627, 0, 477061297716, 0, 195642483900, 0, 49665627558, 0, 8261503794, 0, 812018893, 0, 47500907], [-671327583345, 0, -758542460580, 0, -565719472953, 0, -220344752319, 0, -54770706318, 0, -8872595664, 0, -864786042, 0, -49032332, 0], [-448939285020, 0, -625450988448, 0, -495377443209, 0, -210752440350, 0, -53705137428, 0, -9132887847, 0, -903112393, 0, -54617732, 0], [0, 409545955071, 0, 625450988448, 0, 495377443209, 0, 210752440350, 0, 53705137428, 0, 9132887847, 0, 903112393, 0, 54617732], [208063920222, 0, 33072805413, 0, -2243892963, 0, -66793461054, 0, -23065315299, 0, -6054561519, 0, -683729698, 0, -58397849, 0], [0, -180268196472, 0, 36395013879, 0, 38231208363, 0, 84264563004, 0, 27533309091, 0, 6920345769, 0, 772300648, 0, 64777034], [0, -442049824746, 0, -96696458253, 0, -32110821381, 0, 74672251035, 0, 26467740201, 0, 7180637952, 0, 810626999, 0, 70362434], [-157488193548, 0, -423368055108, 0, -389659389972, 0, -225132595554, 0, -63366471351, 0, -12590096616, 0, -1321129241, 0, -93878026, 0], [303881783580, 0, 574137191214, 0, 479305190679, 0, 262435944954, 0, 72730942857, 0, 14316065313, 0, 1495748591, 0, 105898756, 0], [-446373561123, 0, -813584976426, 0, -654888451842, 0, -341617204785, 0, -92965220511, 0, -17994696072, 0, -1868178342, 0, -131099776, 0], [0, 1277566080147, 0, 1692345725685, 0, 1273655118195, 0, 540350635431, 0, 137437507938, 0, 23664775347, 0, 2350751337, 0, 145719574]];
    Rf_basisdens := [1, 1, 13131109983, 13131109983, 13131109983, 39393329949, 39393329949, 39393329949, 39393329949, 39393329949, 39393329949, 39393329949, 39393329949, 39393329949, 39393329949, 39393329949];
    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_99_g();"
function MakeCharacter_99_g()
    N := 99;
    order := 6;
    char_gens := [56, 46];
    v := [5, 3];
    // 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_99_g_Hecke();"
function MakeCharacter_99_g_Hecke(Kf)
    N := 99;
    order := 6;
    char_gens := [56, 46];
    char_values := [[1, 0, 1, 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]];
    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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -2, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0], [0, -1, 0, 1, -1, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, -2], [0, -1, 0, -1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, -1, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, -1, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0], [-2, 0, -2, 0, 0, 0, 0, -2, 0, -1, 0, 0, 1, 1, 0, 0], [-4, 0, 0, 0, 0, 0, 2, -3, 0, -3, 0, 0, -1, -1, -1, 0], [0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, -1, 0, 0, 0, 1], [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1], [-4, 0, -2, 0, 0, 0, -2, 1, 0, -1, 0, 0, -3, 1, 2, 0], [-2, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, -2, -1, 0], [0, 0, 0, 0, 0, 0, -1, -1, 0, 4, 0, 0, 4, 2, 0, 0], [0, -2, 0, -6, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2], [1, 0, 1, 0, 0, 0, 1, -1, 0, 3, 0, 0, -1, 3, -2, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, -1, -1, 0], [0, -3, 0, -1, 2, -1, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0], [0, -1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -3], [0, -2, 0, 0, -3, -3, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0], [4, 0, 8, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, -4, -2, 0], [0, 0, -1, 0, 0, 0, -2, -2, 0, 4, 0, 0, 4, 2, -2, 0], [0, -1, 0, -1, 2, 4, 0, 0, -2, 0, 0, 2, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0, 0, 5, 0, 1, 0, 0, -1, -4, 0, 0], [0, 1, 0, -5, -1, -2, 0, 0, -1, 0, 1, 1, 0, 0, 0, 2], [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0], [1, 0, -1, 0, 0, 0, 5, -6, 0, 2, 0, 0, 2, 1, 0, 0], [0, 6, 0, 4, -1, 0, 0, 0, -1, 0, 2, -2, 0, 0, 0, 0], [0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 3, 0, 0, 0, 1, 4, 0, 5, 0, 0, -3, 4, -1, 0], [0, 2, 0, -2, 1, 3, 0, 0, 2, 0, 2, -1, 0, 0, 0, -1], [0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1], [0, 3, 0, 5, -1, -3, 0, 0, -3, 0, 1, 0, 0, 0, 0, 1], [4, 0, 4, 0, 0, 0, 5, 2, 0, 5, 0, 0, 5, -2, -10, 0], [2, 0, 0, 0, 0, 0, -4, -1, 0, -2, 0, 0, 1, -5, 2, 0], [0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2], [0, 0, 0, 2, -1, 2, 0, 0, 0, 0, 3, -4, 0, 0, 0, -2], [-7, 0, -14, 0, 0, 0, 0, -5, 0, -4, 0, 0, 4, 5, 5, 0], [-1, 0, 0, 0, 0, 0, -2, 4, 0, 3, 0, 0, 0, 2, 1, 0], [4, 0, 2, 0, 0, 0, -8, 7, 0, -1, 0, 0, 0, -8, 8, 0], [0, -4, 0, 4, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 2, 3, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2], [-1, 0, 0, 0, 0, 0, -2, 6, 0, 1, 0, 0, -4, 4, 1, 0], [0, -2, 0, 2, -1, 3, 0, 0, 6, 0, 6, -5, 0, 0, 0, -5], [0, 0, 2, 0, 0, 0, -2, 6, 0, -4, 0, 0, -5, -7, -2, 0], [0, 3, 0, -3, 2, -1, 0, 0, -1, 0, -4, 6, 0, 0, 0, 3], [-5, 0, -5, 0, 0, 0, -1, -1, 0, 4, 0, 0, -6, 6, 2, 0], [0, -2, 0, 2, -3, -6, 0, 0, -3, 0, -2, -2, 0, 0, 0, -4], [0, -2, 0, -2, 4, 0, 0, 0, 5, 0, -5, 0, 0, 0, 0, 0], [0, -1, 0, -1, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -1], [-9, 0, -18, 0, 0, 0, 0, -10, 0, 2, 0, 0, 7, 10, 1, 0], [9, 0, -9, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 7, 0, 0], [0, 4, 0, 0, 5, 3, 0, 0, 7, 0, 5, 0, 0, 0, 0, 0], [-1, 0, -2, 0, 0, 0, 0, -1, 0, 6, 0, 0, 2, 1, -7, 0], [0, -6, 0, -2, -5, -2, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0], [0, -1, 0, -5, -5, 1, 0, 0, 1, 0, 5, 0, 0, 0, 0, 3], [0, 7, 0, -1, 3, 3, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1], [0, 4, 0, -4, 5, 6, 0, 0, -3, 0, -3, 4, 0, 0, 0, 4], [0, 0, 0, 0, -8, 0, 0, 0, -5, 0, 5, 0, 0, 0, 0, 0], [0, 6, 0, 0, 3, 3, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0], [-14, 0, 14, 0, 0, 0, -7, 4, 0, -9, 0, 0, -9, -12, 0, 0], [0, 0, 8, 0, 0, 0, 3, -6, 0, 3, 0, 0, 4, 7, 3, 0], [10, 0, 5, 0, 0, 0, 3, 5, 0, 8, 0, 0, -3, 6, -3, 0], [0, 0, 17, 0, 0, 0, -2, 8, 0, -6, 0, 0, -13, -15, -2, 0], [0, 0, 0, 0, -5, -6, 0, 0, -4, 0, -4, -4, 0, 0, 0, -4], [0, -2, 0, -2, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 3], [0, 6, 0, 8, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 4], [-2, 0, -1, 0, 0, 0, 0, -5, 0, -5, 0, 0, 5, -5, 0, 0], [0, -1, 0, -3, -2, 1, 0, 0, 3, 0, 4, -1, 0, 0, 0, -2], [0, 0, -10, 0, 0, 0, -1, 1, 0, 0, 0, 0, -2, -3, -1, 0], [0, 2, 0, -2, -1, -8, 0, 0, -10, 0, -10, 6, 0, 0, 0, 6], [5, 0, 0, 0, 0, 0, -10, 3, 0, -5, 0, 0, -3, -7, 5, 0], [8, 0, -8, 0, 0, 0, -7, -1, 0, 4, 0, 0, 4, -4, 0, 0], [-22, 0, -11, 0, 0, 0, -2, 4, 0, 2, 0, 0, -3, 1, 2, 0], [14, 0, 0, 0, 0, 0, 4, -3, 0, 4, 0, 0, 5, 1, -2, 0], [-3, 0, 3, 0, 0, 0, -10, 8, 0, -8, 0, 0, -8, -10, 0, 0], [0, 0, 0, 0, -2, 1, 0, 0, 7, 0, 7, -5, 0, 0, 0, -5], [1, 0, -1, 0, 0, 0, 11, -6, 0, 8, 0, 0, 8, 13, 0, 0], [0, 0, -13, 0, 0, 0, 6, -8, 0, 2, 0, 0, 1, 7, 6, 0], [0, -2, 0, 8, 5, 6, 0, 0, 1, 0, -6, -2, 0, 0, 0, -4], [-19, 0, 0, 0, 0, 0, 2, 3, 0, -5, 0, 0, -9, 5, -1, 0], [0, -4, 0, -8, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0], [18, 0, 9, 0, 0, 0, -5, 4, 0, -1, 0, 0, -3, -2, 5, 0], [7, 0, 14, 0, 0, 0, 0, 9, 0, 1, 0, 0, -6, -9, -4, 0], [0, -1, 0, -5, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3], [0, 7, 0, 1, -3, 0, 0, 0, -4, 0, -1, -2, 0, 0, 0, -1], [7, 0, 7, 0, 0, 0, 4, 5, 0, 2, 0, 0, 6, -7, -8, 0], [3, 0, 6, 0, 0, 0, 0, 4, 0, -7, 0, 0, 10, -4, -7, 0], [0, 0, 0, -2, 6, 8, 0, 0, 0, 0, 2, 4, 0, 0, 0, 2], [-13, 0, 0, 0, 0, 0, 12, -1, 0, 3, 0, 0, -2, 11, -6, 0], [0, -4, 0, -4, 3, 1, 0, 0, 1, 0, -1, 1, 0, 0, 0, -1], [4, 0, 4, 0, 0, 0, 6, -18, 0, -3, 0, 0, 15, 9, -12, 0], [0, -1, 0, 7, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -2], [-4, 0, 4, 0, 0, 0, 0, -6, 0, 10, 0, 0, 10, 4, 0, 0], [2, 0, 4, 0, 0, 0, 0, -10, 0, -3, 0, 0, -1, 10, 14, 0], [0, 12, 0, 4, 2, -3, 0, 0, 5, 0, -7, 4, 0, 0, 0, 0], [0, -13, 0, -7, 3, 2, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0], [0, -1, 0, 3, 1, 4, 0, 0, 4, 0, -1, 0, 0, 0, 0, -5], [0, 3, 0, -3, 2, -9, 0, 0, -11, 0, -10, 3, 0, 0, 0, 6], [0, -8, 0, -8, -1, 0, 0, 0, -5, 0, 5, 0, 0, 0, 0, 0], [0, -8, 0, 0, -4, -6, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0], [0, 2, 0, -2, -1, -1, 0, 0, 7, 0, 7, -1, 0, 0, 0, -1], [-1, 0, 0, 0, 0, 0, -16, 7, 0, -1, 0, 0, 0, -9, 8, 0], [-24, 0, -12, 0, 0, 0, 7, -13, 0, -6, 0, 0, 10, -3, -7, 0], [0, -1, 0, 7, -6, -6, 0, 0, 0, 0, 5, -1, 0, 0, 0, -2], [4, 0, -4, 0, 0, 0, 6, -3, 0, -5, 0, 0, -5, -2, 0, 0], [0, -6, 0, -12, 3, -1, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0], [0, 8, 0, -8, 1, -3, 0, 0, -1, 0, -1, 5, 0, 0, 0, 5], [0, 4, 0, 0, 8, 3, 0, 0, 5, 0, -1, 4, 0, 0, 0, 0], [-3, 0, 3, 0, 0, 0, -10, 0, 0, 8, 0, 0, 8, -2, 0, 0], [0, 0, 17, 0, 0, 0, 2, 6, 0, -8, 0, 0, -9, -7, 2, 0], [20, 0, 0, 0, 0, 0, 20, -6, 0, 21, 0, 0, 17, 14, -10, 0], [26, 0, 13, 0, 0, 0, 6, 3, 0, 9, 0, 0, 10, -4, -6, 0], [-5, 0, -5, 0, 0, 0, 5, -18, 0, -3, 0, 0, 13, 10, -10, 0], [-2, 0, -4, 0, 0, 0, 0, -3, 0, 6, 0, 0, 14, 3, -17, 0], [-2, 0, 2, 0, 0, 0, 8, -2, 0, -15, 0, 0, -15, -9, 0, 0], [0, -14, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0], [-2, 0, -2, 0, 0, 0, -10, 6, 0, -11, 0, 0, -9, -7, 20, 0], [0, 5, 0, 15, 3, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0, -5], [0, -12, 0, 4, -7, -10, 0, 0, 4, 0, 1, -8, 0, 0, 0, -4], [-11, 0, -22, 0, 0, 0, 0, -8, 0, 8, 0, 0, -2, 8, 2, 0], [0, 0, -4, 0, 0, 0, 5, 1, 0, -6, 0, 0, -2, 3, 5, 0], [0, 1, 0, -15, 3, -1, 0, 0, -4, 0, -6, 1, 0, 0, 0, 2], [0, 0, 5, 0, 0, 0, 2, -12, 0, 10, 0, 0, 6, 8, 2, 0], [6, 0, 12, 0, 0, 0, 0, 11, 0, -9, 0, 0, -1, -11, -1, 0], [0, 0, -1, 0, 0, 0, 6, 6, 0, -12, 0, 0, -12, -6, 6, 0], [0, -2, 0, 2, 1, 2, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0], [0, -4, 0, -6, -9, -2, 0, 0, -7, 0, -10, 8, 0, 0, 0, 0], [0, 4, 0, 4, -2, 4, 0, 0, 2, 0, -2, 4, 0, 0, 0, -4], [4, 0, 4, 0, 0, 0, -1, 5, 0, 8, 0, 0, -10, 4, 2, 0], [-7, 0, 0, 0, 0, 0, -16, 9, 0, -21, 0, 0, -22, -7, 8, 0], [0, 4, 0, 4, 4, -5, 0, 0, -1, 0, 1, -5, 0, 0, 0, 5], [0, -6, 0, 6, 6, 14, 0, 0, 8, 0, 8, -2, 0, 0, 0, -2], [-5, 0, -10, 0, 0, 0, 0, -4, 0, -16, 0, 0, 1, 4, 19, 0], [0, 8, 0, -8, 10, 14, 0, 0, 9, 0, 9, 6, 0, 0, 0, 6], [1, 0, -1, 0, 0, 0, -4, -4, 0, -2, 0, 0, -2, -10, 0, 0], [0, -1, 0, -9, 2, -5, 0, 0, -7, 0, -10, -1, 0, 0, 0, -2], [0, -4, 0, -2, -9, -3, 0, 0, -6, 0, -3, 0, 0, 0, 0, 0], [0, -1, 0, 3, 1, -2, 0, 0, 10, 0, 7, -6, 0, 0, 0, -3], [-11, 0, -11, 0, 0, 0, -5, -3, 0, -14, 0, 0, 4, -6, 10, 0], [0, 3, 0, -9, 0, 3, 0, 0, 3, 0, 6, 3, 0, 0, 0, 6], [11, 0, 0, 0, 0, 0, 10, -9, 0, -2, 0, 0, 2, 1, -5, 0], [18, 0, 9, 0, 0, 0, 0, 17, 0, 17, 0, 0, -12, 12, 0, 0], [0, -3, 0, -5, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -1], [0, 2, 0, -2, -5, -5, 0, 0, -9, 0, -9, 4, 0, 0, 0, 2], [-20, 0, -20, 0, 0, 0, 4, -18, 0, -1, 0, 0, 9, 13, -8, 0], [4, 0, 8, 0, 0, 0, 0, 13, 0, 4, 0, 0, -24, -13, 7, 0], [0, -12, 0, 12, -9, -5, 0, 0, 3, 0, 3, -13, 0, 0, 0, -13], [8, 0, 16, 0, 0, 0, 0, 9, 0, 10, 0, 0, -9, -9, -10, 0], [17, 0, 0, 0, 0, 0, 16, -5, 0, 15, 0, 0, 12, 11, -8, 0], [0, 14, 0, 14, 9, 2, 0, 0, 1, 0, -1, 2, 0, 0, 0, -2], [0, 0, 2, 0, 0, 0, -10, -2, 0, 12, 0, 0, 14, 4, -10, 0], [20, 0, 10, 0, 0, 0, -5, -1, 0, -6, 0, 0, -8, 3, 5, 0], [0, -17, 0, -5, -14, -6, 0, 0, -8, 0, 1, -7, 0, 0, 0, 0], [-30, 0, -15, 0, 0, 0, -11, -18, 0, -29, 0, 0, -16, 5, 11, 0], [0, 1, 0, -1, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, -8, 0, -8, 1, 2, 0, 0, 5, 0, -5, 2, 0, 0, 0, -2], [-12, 0, -6, 0, 0, 0, 1, -1, 0, 0, 0, 0, -2, 3, -1, 0], [0, -2, 0, -8, -1, 7, 0, 0, 8, 0, 7, -2, 0, 0, 0, -4], [0, -10, 0, 10, 1, 5, 0, 0, 3, 0, 3, -3, 0, 0, 0, -3], [10, 0, 20, 0, 0, 0, 0, 19, 0, -2, 0, 0, -6, -19, -11, 0], [-20, 0, 20, 0, 0, 0, -3, 5, 0, -3, 0, 0, -3, -1, 0, 0], [24, 0, 12, 0, 0, 0, -5, 3, 0, -2, 0, 0, 2, -7, 5, 0], [17, 0, 0, 0, 0, 0, -4, 12, 0, 7, 0, 0, -3, 8, 2, 0], [0, -3, 0, 1, 1, 10, 0, 0, 10, 0, -1, 0, 0, 0, 0, -7]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_99_g_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_99_2_g_b();".
// 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_99_2_g_b(:prec:=16)
    chi := MakeCharacter_99_g();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(997) - 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_99_2_g_b();".
// 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_99_2_g_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_99_g();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![8649, 0, 13392, 0, 13761, 0, 8010, 0, 3372, 0, 837, 0, 150, 0, 15, 0, 1]>],Snew);
    return Vf;
end function;