
// Make newform 2001.2.a.o in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_2001_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_2001_2_a_o();".
// 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_2001_2_a_o();".
// 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 := [-256, 1408, 2768, -19624, 5201, 60661, -34967, -82362, 52109, 59410, -36791, -24566, 14484, 5985, -3353, -846, 453, 64, -33, -2, 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, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -7, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [67052416, -73689968, -1279285860, 1615059980, 4886184991, -4647412912, -8060495321, 4995760963, 6745265900, -2551075658, -3077890179, 679406561, 796777255, -93997884, -116705443, 5676465, 9004494, -706, -284189, -9977], [42998144, -39969248, -274311304, 447758060, 152363091, -1618911100, 636510631, 2487007763, -993555752, -1915046350, 596421017, 808522329, -181802773, -195494072, 29771565, 26985321, -2493558, -1977318, 83835, 59655], [21780992, 28151104, -326105000, 195615347, 1290653668, -990251463, -2270424875, 1483887288, 1998865072, -1066095561, -951947129, 427557079, 256304866, -101021583, -38936723, 13951816, 3106330, -1039401, -101041, 32190], [65443584, -6205632, -1275029840, 543546028, 4881910035, -765017784, -8047603685, -477260749, 6744972372, 1308880446, -3086463419, -846624863, 800884431, 259419552, -117469803, -41870219, 9067866, 3436418, -286133, -113117], [-8160896, 110604448, -665008808, -167806212, 2337172669, -337309496, -2223325131, 1618257989, 645077396, -1976507934, 87630643, 1090655743, -86908655, -315679888, 18817259, 49733347, -1758962, -4039074, 61925, 132421], [-221220224, 397653248, 3175929024, -4446760952, -10197457825, 11462171224, 14281125551, -13052790841, -10545189400, 7971368478, 4435330241, -2847831847, -1093593473, 614092532, 155862669, -78622707, -11857542, 5495374, 371971, -161261], [-107471168, 476989360, 1641458868, -4484529451, -5750325066, 11341153205, 9238883527, -12364008590, -7739376550, 7028716107, 3571430473, -2296222593, -938038438, 448941315, 139461381, -52040672, -10913794, 3305005, 348943, -88710], [-15271680, 40996096, 205094288, -896358416, -137492405, 3466368864, -467045285, -5549815741, 621554632, 4537659302, -279720755, -2061905747, 55520691, 538837948, -4529143, -80239695, 38394, 6311478, 8703, -203145], [110542464, -316927872, -1635642432, 3454356288, 5854037837, -10620817160, -8841784179, 14266108021, 6853628544, -10021968214, -2978708653, 4013917123, 753143013, -947801932, -109626129, 130255487, 8494062, -9616398, -270767, 294337], [-97520832, 260140592, 1626363316, -3213222030, -5836685909, 9240832926, 9303904093, -11171608865, -7663102560, 7037682580, 3490925219, -2556880073, -910556129, 556857158, 135044723, -71767335, -10572042, 5041136, 338681, -148537], [-178908672, 760925792, 2443697432, -6950567148, -7338969931, 18755286572, 9964491865, -22897375291, -7238359288, 15028081270, 3015967983, -5732647449, -741027003, 1306063448, 105738795, -174716497, -8079138, 12633678, 254997, -380439], [-69421504, 272653424, 1148408812, -3330475213, -3672857369, 9802374313, 5243719104, -12375653553, -3991457880, 8203441237, 1727035600, -3127379984, -436217767, 709058137, 63450778, -94271295, -4911368, 6774905, 156362, -202867], [-197504512, 584394208, 3293324216, -8318188780, -10588454955, 24293520488, 16061786213, -29747755059, -13077406708, 19037717322, 5963688187, -7027134489, -1562401159, 1551417160, 232872267, -202063709, -18316426, 14300798, 589261, -423491], [-174423552, 555519872, 2852863952, -8224828108, -8106916351, 25189860044, 9966835125, -32604889607, -6590508888, 22150191358, 2553180667, -8642079917, -597242311, 1999221168, 82762231, -270259309, -6229090, 19683950, 195465, -595707], [286605824, -845754080, -4763008568, 12074218624, 14898925983, -37324091800, -20480764017, 49088306735, 15053725344, -33902595298, -6389315479, 13439770617, 1607414239, -3156059852, -235226483, 432558821, 18413026, -31897570, -593997, 975995]];
    Rf_basisdens := [1, 1, 1, 1, 1, 3404224, 6808448, 3404224, 6808448, 6808448, 6808448, 3404224, 6808448, 6808448, 3404224, 6808448, 3404224, 6808448, 6808448, 6808448];
    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_2001_a();"
function MakeCharacter_2001_a()
    N := 2001;
    order := 1;
    char_gens := [668, 1132, 553];
    v := [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_2001_a_Hecke(Kf)
    return MakeCharacter_2001_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, 1, 0, 0, 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, 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, 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], [1, 0, 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, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 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], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [3, 0, -1, 0, -1, 1, 0, -1, 1, 0, 0, 1, 0, -1, 1, -1, -1, 0, 1, 1], [-1, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, -1], [2, -2, 0, -1, 0, 1, 0, 0, 0, 1, 1, -1, 1, 0, 1, -1, 0, 0, 1, 1], [1, -2, 1, -1, 0, -1, -1, 0, -1, -1, 0, -1, 1, 1, 1, 1, 1, -1, 0, 1], [-1, -3, 1, -1, 1, 0, 1, 0, -1, 1, 1, -1, 1, 1, 0, 1, 1, -1, 0, 0], [1, -1, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, -1, 0], [0, -2, 0, 0, 0, 0, 1, -1, -1, 1, 0, -1, 0, 0, -1, 1, 0, -1, 0, 0], [1, 1, 0, 0, 1, -1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, -1], [2, -1, 1, -1, 0, -1, -2, 1, 0, -1, 1, -1, 1, 1, 1, 0, 2, 0, -1, 1], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, -1, -1], [-1, 0, -2, -1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, -1, 1, 0, 1, 0], [-1, -1, 1, 1, 1, 0, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 0, 0], [2, -3, 1, -1, 0, 0, -2, 0, -1, -1, 1, 0, 2, 1, 1, 0, 2, -1, 0, 1], [-2, 0, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 1, -1, 0], [1, -1, -1, 1, 1, 0, 1, -1, -1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 2, 0], [1, -1, -2, 0, -1, 1, 0, -2, 0, 1, 0, 0, -1, 0, 2, -1, 0, -1, 3, 1], [-1, 1, -1, 0, 1, 0, -1, 0, -1, 0, 0, 1, 0, -1, -1, 0, 1, 0, 0, 1], [-3, 3, -1, 1, 0, 1, -1, -1, 0, 0, 0, 0, -1, -1, -2, 0, -1, 1, 0, 0], [4, 2, 0, -1, -2, -1, -4, 1, 2, -2, -1, 1, 0, 0, 1, -2, 0, 1, -2, 1], [1, -1, 0, 0, -1, 0, 0, -2, 0, 1, 0, -1, -1, 0, 1, 1, -1, 0, 2, 1], [-1, -1, 1, -1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, -1, 2, -1, -1, 0], [2, 1, -2, -1, -1, 0, 0, 0, 2, 0, 0, 1, 0, 0, -1, -1, 1, 1, 1, 1], [0, 4, 0, 2, -1, 0, 0, 1, 2, -1, -1, 2, -2, 0, 0, -1, -1, 1, -1, 0], [4, 0, 2, 0, 0, -1, -2, 2, 0, -1, 0, -1, 1, 1, 1, -1, 1, 0, -2, 0], [1, 0, 0, 2, 0, 0, 2, 0, 0, 0, -1, 0, -2, 0, -1, 1, -1, 0, -1, -1], [2, -1, 0, 1, 0, 1, 1, -1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 2, 1], [1, -1, 1, -1, -1, 0, 1, 0, 1, 1, 1, -1, 1, 2, 1, -1, 1, 1, 0, 0], [0, -3, -1, -2, -1, 1, 0, -1, 0, 2, 1, -1, 0, 0, 3, -1, 0, -1, 3, 2], [4, -1, 2, 1, 0, 0, -1, 1, 1, -2, -1, 0, 0, -1, -2, 0, -1, 1, -1, 0], [1, 0, -1, 2, 1, 1, 1, -1, -1, 0, 0, 1, 0, -1, -1, -1, 0, 0, 1, -1], [-4, 1, -1, 1, 1, -2, 0, 0, 0, 0, -2, 0, -1, -1, -2, 3, -1, 0, -1, -1], [-4, 3, -3, 2, 1, 0, 0, -1, -2, 0, -1, 0, -2, -1, -2, 2, -1, 0, 1, -1], [-2, -2, 3, -2, 0, -2, -1, 3, -1, 0, 0, -2, 2, 2, 0, 0, 3, -1, -3, 0], [3, -6, 1, 0, 2, 1, 2, 0, -2, 2, 1, -2, 1, 1, 2, 1, 0, -2, 2, -1], [0, 4, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, -1, -1], [2, 1, 1, 0, 0, 0, 0, 2, 0, -1, 0, 0, 1, 0, 2, 0, 0, -1, -1, 0], [2, -3, 3, -1, -1, 1, 1, 0, -1, 1, 0, 0, 1, -1, 2, 0, 0, 0, 2, 1], [6, -3, 4, -2, 0, -1, -3, 2, -1, -1, 0, -1, 2, 0, 1, 0, 0, 1, -3, 0], [1, 2, 0, -1, -2, 0, -1, -1, 1, -1, 0, 1, 1, 1, 1, -2, 0, -1, 0, 0], [4, -2, -1, -3, 0, 0, 2, -1, 0, 1, 1, 1, 1, 0, 3, -1, 2, 0, 0, 1], [0, -1, -1, 0, -2, 1, 2, 0, 2, 0, 0, 1, -2, 1, 1, -1, -1, 1, 1, 0], [-2, 1, 2, -1, 1, 1, 1, 2, -2, 0, 2, -2, 2, 0, 0, -1, 3, 0, -2, -1], [-4, -1, 0, 1, 1, -2, -2, 0, 0, -1, 0, -1, 1, 1, -1, 2, 1, 0, 0, -1], [0, 2, -4, 0, -3, 0, -1, -3, 2, 0, -1, 1, -3, 0, 0, -2, -2, 2, 1, 0], [-1, 0, 4, -1, 0, 1, -1, 0, -1, 0, 1, -2, 0, 1, 0, 1, 0, -1, 1, 0], [-1, -2, 0, 1, -2, 0, 1, 0, 1, 1, 0, -1, -1, 0, 1, 2, -1, 1, 0, 0], [12, -3, 1, -4, -1, 0, -4, 1, 0, 0, 2, 0, 4, 1, 2, -3, 3, 0, 1, 2], [-7, 2, 1, 1, 3, -3, 0, 3, 0, 0, -1, 0, 0, 1, -3, 3, 1, 0, -3, -2], [-1, 0, -2, 2, 1, 0, -1, 1, 0, -1, 0, 0, -1, 0, 2, 0, -1, -1, 2, 1], [-4, 3, 1, 2, 0, -1, -3, 3, 1, -1, 0, 0, 1, 1, 2, 0, 2, 0, 1, 2], [5, -1, 2, 0, -1, 0, 0, -1, 2, -1, 1, 1, -1, -1, 1, -1, 0, 0, -1, 1], [-2, 1, 0, 0, 3, -2, -1, 2, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, -3, -1], [3, 0, -2, -1, 0, 1, 0, -2, 2, 1, 0, 1, -1, 0, 1, -2, -1, 0, 2, 2], [-4, -3, 1, -1, 1, -1, 0, -1, -2, 1, 0, -1, -1, 1, -3, 2, -2, 0, -1, -1], [2, 4, -3, 1, -1, -1, 1, -2, 1, -2, 0, 3, 0, -1, 1, -1, 1, 0, 0, 0], [-5, 2, -3, 1, 0, 0, -4, -1, 0, -1, 0, -1, 0, -1, -3, 0, -1, 2, -1, 0], [-6, -1, 4, 2, 3, -1, 2, 5, -2, 2, 1, -2, 2, 1, 2, 3, 3, -2, 1, -2], [-5, 1, -2, -1, 0, 2, 1, -3, -1, 1, 0, 0, -3, -1, -4, 0, -1, 0, 1, -1], [2, 4, -3, -2, -3, 1, -6, 0, 2, -1, 1, 2, 1, 1, 2, -5, 2, 1, 2, 2], [4, -2, -2, -1, -2, 1, -1, -3, -1, 0, -1, 2, -2, 0, 1, -2, -2, 1, 1, -1], [2, 2, 0, -1, 0, 1, 1, 0, 0, 0, -1, 2, 1, 0, 0, 0, 0, 1, -1, 1], [-4, 0, -2, 0, 2, 0, -1, 4, -1, 1, 0, -1, 1, 0, 1, 1, 1, 1, -2, -2], [-1, 8, -2, 0, 2, 1, 2, 2, 0, 0, -1, 1, 0, -2, -1, -1, 0, 1, -2, -3], [-4, 0, -2, 0, 1, -2, -4, 1, 0, -1, 1, 0, 1, 0, 0, 1, -1, 1, -3, 0], [0, 7, 4, 0, -2, -2, -1, 0, 1, -3, -2, 2, -1, 0, -2, 2, -1, 2, -2, -2], [7, -1, 0, -1, -1, 2, 0, -5, 0, 3, 1, -1, -1, 0, -1, 0, 0, -2, 2, 1], [-1, -3, 1, -2, 0, -1, -1, 1, 2, 0, -1, -1, 2, -1, -1, 0, 2, 1, -4, 1], [-3, -2, -6, -1, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, 0, 0, -2, 3, -1], [-5, 3, 2, 2, -2, 0, 1, 2, 1, -1, -1, 0, -1, 2, 0, -1, 2, 0, 1, -1], [1, 0, 1, 3, 0, 1, 2, -2, -2, 1, 0, 0, -2, 1, 0, 2, -1, -1, 2, -2], [-3, 3, -2, 1, -2, -2, 1, -2, 3, 0, -2, 2, -2, 0, -2, 0, 0, 1, -1, -2], [4, -2, 1, -4, 2, -2, 1, 2, -2, 1, 0, -2, 4, 3, 3, 1, 2, -2, -2, 0], [2, 0, -1, -5, -1, -1, -3, 2, 1, 0, 0, 1, 4, 0, 3, -2, 3, 0, -3, 1], [-5, 5, 0, -2, 1, -3, 1, 1, 1, -2, 0, -1, 2, 0, -3, 0, 2, 0, -5, -1], [-2, -3, 3, 1, 3, -1, 0, -1, -2, 0, 1, -1, 2, 0, -1, 3, 0, -1, 1, 1], [-10, 3, 1, 1, 0, 1, -3, 2, -1, 0, 1, -2, 0, 1, -4, -1, 2, 1, -1, -1], [-2, 2, -1, -4, -2, -2, -2, -2, 2, 0, 1, 1, 0, 2, 1, -2, 1, -1, 1, 0], [-2, 3, 2, -2, 2, 0, 0, 2, -2, 1, 2, -3, 3, 1, 1, 2, 3, 0, -1, 0], [-4, -4, -2, -1, -1, 1, -1, -1, -1, 1, 0, 2, 0, -2, 0, -1, 0, 0, 0, -1], [2, 0, -1, -2, 0, 1, -1, 4, -1, 2, 2, 0, 1, 1, 2, -2, 4, 0, 1, 0], [5, 2, 5, -2, 0, 0, -2, 2, -4, 0, -1, -1, 0, 1, -3, -1, 1, -1, -3, -1], [-6, -1, 0, 1, 3, -3, -1, 0, -3, 0, 0, -1, 0, 2, -1, 4, 1, -2, 0, 0], [-4, 4, 0, -1, 0, -1, 1, 1, -3, 1, 1, 0, -1, 3, 0, 1, 1, 0, 0, -3], [-5, 0, 4, 2, 2, -2, -2, 3, -2, 0, -1, -2, 2, 0, -1, 3, 0, 0, -1, 1], [4, 2, 1, -2, -1, -1, -3, 1, 1, -1, 1, -1, 3, 0, 1, 1, 2, -1, 1, 2], [-6, -5, 0, 0, 2, 0, 2, -1, 0, 0, 0, -1, -2, 0, -2, 1, -2, -1, 2, 0], [-2, 6, 4, -2, -3, 0, -2, 0, 0, -1, -1, 0, -2, 0, -2, -1, -2, 1, 1, -2], [-6, 1, 1, 3, 2, 0, 2, 2, -4, 2, 1, -2, -2, -1, 0, 4, 0, 0, 0, 0], [-7, 4, -3, 4, 3, 0, 3, 1, -1, -1, 0, 0, 1, -2, -2, 2, -1, 0, -1, -3], [-2, -7, 1, 3, 0, 3, 4, -3, -1, 2, 1, 0, 0, -1, 0, 1, -3, -1, 3, -1], [-1, -2, 5, -1, 3, -1, 2, 2, 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2], [0, 16, -6, 0, -1, -1, -8, 0, 1, -1, -1, 1, -1, -2, -5, -3, -3, 4, -4, -2], [0, -3, -4, 2, 1, 5, 1, -4, 1, 2, -1, -1, -2, -2, 1, -1, -5, -2, 4, 2], [-9, 4, -5, 1, -1, -3, 4, -4, 0, 0, -1, 0, -4, 1, -4, 5, 0, 0, 1, -2], [13, -7, 7, -2, 0, 2, -4, 0, 0, 0, 3, -2, 6, -1, 4, -2, 2, -2, -1, 5], [6, -6, -2, -3, 1, -1, -3, 4, 1, -2, -1, 0, 2, -1, -2, -1, 2, 3, -3, 0], [1, -6, 0, -2, 2, 2, 3, 1, -3, 3, 3, -5, 1, 3, 3, -1, 0, 1, 0, 0], [1, -5, 0, 4, 3, 1, -1, 2, -1, 0, 2, -3, 2, 2, -1, 0, 0, 0, 1, 1], [4, 6, -4, -1, -2, 2, 4, -3, 0, 2, -1, 2, -4, 1, 4, -2, 1, 0, 3, -1], [0, 2, -3, 1, 1, -4, 1, -2, 1, -2, -2, 2, -4, -1, 0, 3, -4, 3, -1, -2], [0, 10, 3, 3, -2, 2, 2, 1, 2, -3, -3, 5, -3, -3, -3, -1, -3, 2, -4, -5], [11, -8, 9, -1, 3, -1, 0, 2, -5, 1, 1, -3, 3, 1, 1, 4, 4, -3, -1, 0], [8, 1, 0, 1, -2, 0, -4, -1, 1, 0, 3, -2, -2, 0, -4, 1, 1, 1, 0, 1], [-7, 13, 0, -1, -2, -3, 0, 2, -2, 0, -4, 0, 0, 3, -2, 0, 0, 0, -3, -4], [0, 0, 0, -1, 0, -2, 5, -3, 1, -2, -3, 5, -6, -2, -1, 2, -2, 0, 2, 1], 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0, 2, 0], [-8, -1, -1, -6, -2, -1, -3, -3, 1, 1, 2, 0, 3, -1, -1, -2, 4, 0, 1, 2], [8, 3, -3, -1, 1, -4, 3, 1, 3, -1, -2, -1, -1, -1, -1, 2, -2, 1, 1, 1], [-10, 0, -1, -4, 3, -4, 2, -1, 0, -1, -1, -3, 2, 3, -1, 5, 4, -2, 1, 0], [-9, 3, 0, 3, 0, -2, 6, 0, -2, 0, -4, 1, -2, 1, -5, 2, -1, -1, -2, -2], [-6, 5, 1, 5, 4, 1, -2, 4, -6, 2, 1, -1, -2, 1, -3, 2, 1, 1, 3, -4], [-6, 6, -6, -1, 5, -1, -3, 3, -2, -1, -2, 0, 2, -2, 0, -1, -1, 0, -2, -1], [2, -1, 0, -1, 3, -1, 2, 1, -2, 0, -2, 0, 0, -2, 2, -1, 1, -2, 0, 1], [-3, 1, 0, 0, 0, -1, 0, 3, 2, 1, -1, 0, -1, 0, 4, 1, -1, 1, 1, 1], [0, -5, -2, -1, 0, 0, 3, -2, 1, 2, 1, 0, -1, 0, 4, 1, -3, -1, 0, -1], [5, 10, 1, -4, 2, -3, -2, 2, 0, -1, 1, -2, 3, 3, 2, 0, 6, -1, -3, -1], [-1, 7, -2, -1, -3, 0, -6, -4, 2, -3, -3, 5, -3, -3, -1, -1, 1, 2, -1, 0], [-7, 10, -2, 4, -2, 0, -3, 0, 1, -1, -3, 5, -1, 0, -7, 0, 1, -1, -3, -3], [10, 5, -1, 2, -6, 3, 1, -5, 7, 1, 0, 4, -2, -1, 8, -4, -3, 0, 3, 2], [4, -3, 4, -1, 1, -1, 6, 0, 2, 2, 2, -2, 4, 0, 6, 1, 2, -2, 2, 3], [-5, 2, -1, 1, 1, -6, 5, 4, 0, -1, 1, -2, 4, 5, 4, 2, 6, -2, -4, -2], [-13, 11, -7, 1, 1, 4, 1, -1, -1, -1, -1, 3, -1, -1, -7, -5, 0, 3, -2, -4], [5, 7, -3, 0, -1, -1, 4, -2, 4, -4, 0, 3, -6, -1, -1, -1, -3, -1, -1, -4], [-8, -11, 5, 1, 3, -2, 1, 1, -3, 1, 0, -5, 3, 4, -1, 4, 0, -5, 1, 1], [-2, 2, -4, 4, -2, 3, 0, -4, 4, 0, 0, 1, -2, -2, -3, 0, -1, -1, 1, 0], [-3, -4, -1, 1, 0, 4, 7, -5, -4, 4, 2, 0, -3, -1, 0, 1, 1, -1, 3, -4], [-5, -1, -5, 0, -2, 1, -3, -2, -3, 0, -1, 0, 0, -1, 2, -3, 0, 1, 2, 0], [-8, 5, 2, 0, -1, 3, -3, 0, 0, 3, 3, -2, -1, 0, 0, -2, -1, 1, 0, 0], [-6, -4, 1, -1, -2, -3, 5, 0, -1, -2, -1, 1, 2, 3, 2, 0, 1, -2, 1, 1], [-2, -1, -4, -1, 5, -1, -4, 1, 0, -1, -2, 1, 2, -2, 1, 0, 0, 1, 0, 1], [-4, 15, -1, 1, -3, 1, 6, -1, 2, 0, -2, 5, -4, -3, -3, -1, -4, 3, -4, -5], [-4, 7, 5, -4, -2, -1, -3, 0, 1, -3, 0, -2, -1, 1, -1, -2, 0, 0, -1, 0], [7, -13, -2, -1, -2, 1, -3, -2, -1, -2, 2, 1, -2, -1, -1, 2, 1, 0, 2, 2], [7, 7, 2, 0, 0, -1, 0, 0, 6, -2, -1, 4, 0, -2, 4, -2, 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2], [-16, 3, -3, 2, -1, -4, -1, 3, 1, -3, -3, 5, -3, -1, -5, -1, 0, 3, -5, -3], [-1, -9, 3, 1, 3, 1, 1, 0, -3, -1, 3, -2, 1, 1, -4, 7, -2, 0, -1, -2], [13, 0, 0, 3, -3, 2, -5, -2, 1, 0, -1, 3, -2, 1, 3, -1, -1, -2, 3, -4], [-10, 1, -2, -1, 2, 2, -7, 2, 1, 0, 1, 2, 0, -2, 0, -3, 4, -3, 2, 3], [-7, 7, -6, -4, 2, -3, -2, 5, 2, -2, -3, 0, 0, 0, 2, -2, -1, 2, -6, -3], [9, -17, 4, -9, -4, 0, -3, -3, 1, 2, 0, -2, -1, -2, 2, 0, -1, -1, 1, 6], [0, 0, -4, -1, 2, -1, -2, 1, 2, -1, -1, -5, 0, 0, 3, 3, -3, 0, 3, 1], [-7, 8, 0, -2, -4, 2, 1, -2, -2, -1, -1, -1, -2, 0, 2, -2, -1, -3, 3, 3], [7, -9, 0, -3, -2, 2, -2, 0, 5, 0, -2, 0, 4, -2, 6, -4, -6, 1, -3, 2], [3, -1, -1, -10, -6, 3, -3, -4, 1, 1, 1, 2, -1, 3, 7, -9, 3, -2, 4, 3], [-5, 4, -6, 3, -2, 3, -1, -8, 3, 1, 0, 5, -4, -2, 1, -2, -5, 0, 8, -2], [-4, 4, 4, -1, 3, -2, 6, 1, 0, -1, 0, -2, -3, 0, 0, 2, -1, 1, -1, 0], [16, 7, -1, -8, -3, -3, -9, 0, 3, -4, 2, 4, 2, 0, 8, -7, 2, 3, -5, -2], [1, -10, 3, -5, -2, 4, 1, -8, 2, 2, 2, -2, 1, -1, -1, -1, 2, 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-2, -6, 7, -8, -2, 5, -5, -3, -1, 6, 0], [-15, -8, -1, 0, 0, 3, 10, -6, -4, 5, 5, -2, 1, 0, -2, 0, -2, -1, 3, -1], [-13, -18, 9, 1, 6, 4, 2, 2, -12, 6, 4, -10, 5, 5, 0, 5, 0, -3, 1, 0], [-16, -7, -1, -4, 3, -5, -7, 4, -3, 0, 3, -2, 3, 5, 6, 1, 10, -3, 0, 4], [7, -21, 5, -6, 2, 2, -5, 2, -7, -1, 7, -5, 5, 5, 5, -1, 9, -7, 5, 3], [-7, -13, -1, -6, -4, 1, 6, -2, 6, -1, -5, -1, -5, 0, 1, -1, -5, 2, 1, 1], [11, 3, 3, 4, -5, 3, 7, -5, -1, -3, -4, 4, -7, -2, 4, 1, -9, 4, 0, -1], [16, -2, 1, -6, -13, 5, -4, -9, 10, -5, -1, 8, -5, -3, 8, -7, -3, 3, 8, 6], [-13, 2, -5, -4, -5, 0, -8, 2, 10, -3, 0, 3, -1, -3, 1, -8, -4, 8, -2, 3], [13, -2, 7, -1, -2, -5, 1, 1, 3, -1, -4, -1, 3, 3, 5, 3, 4, -3, -4, 3], [5, -9, 2, -3, 4, -4, -1, 3, -11, 2, 4, -8, 6, 4, -10, 6, 5, 1, -9, -6], [2, -4, 0, 0, -7, 4, -2, -5, 7, -3, -3, 6, -2, -6, -2, -7, -3, 3, 3, 2], [1, 9, -9, 10, -1, 1, 3, -2, 9, -1, -2, 4, -7, -3, 8, 2, -4, 0, 9, 2], [-1, -5, 7, -7, -7, -1, 3, 1, 4, 0, 1, -1, 2, 5, 5, -2, 0, 3, -3, 2], [12, 0, 2, 3, -2, 3, 4, -7, -2, 0, -5, 1, -6, -4, -5, 1, -6, -5, 5, 4], [2, -4, -11, 1, -2, 1, 0, -9, 1, 0, -5, 5, -10, -7, -7, 2, -12, 2, 3, 3], [10, 11, -8, 1, -4, 6, -5, 1, 7, -1, -1, 6, -1, -8, 6, -6, -7, 4, 3, 7], [-5, 1, 1, 3, 6, -3, 4, -4, -3, 0, 2, 0, 0, -1, -6, 8, -4, 1, 0, 0], [-2, -8, 16, -2, 4, -1, 7, 0, -1, 1, 2, -2, 7, 2, -3, 5, 4, -2, -7, -2], [3, 6, 4, 0, -1, -5, -2, 6, 2, -5, -2, 1, 3, 0, 3, 2, 1, 0, -9, 1], [-4, -6, 1, -3, 4, -1, 13, 1, -1, -1, -3, 1, 1, -1, 3, 2, 6, -1, 1, 0], [-16, -5, 0, 4, 2, -4, -1, 2, -3, 0, -4, -2, -2, 0, -10, 7, -2, -3, -9, -2], [8, -3, -5, 2, 2, 4, -3, -6, -3, 4, 6, 0, 1, 3, 4, -3, 6, -4, 10, 0], [11, -2, 4, -7, 0, -3, -12, 1, 6, -3, 4, -1, 11, 4, 3, -2, 11, -2, -2, 2], [8, 14, -7, 1, -9, 3, -6, -3, 10, -7, -2, 10, -3, -4, 2, -13, -3, 5, -1, -1], [-20, 15, -3, 8, 2, 1, 5, -3, 1, 1, -7, 4, -11, -3, -8, 3, -5, 0, 5, -7], [-12, -2, -10, 3, -2, 1, 5, -3, 1, -1, -3, 2, -11, -2, -2, -1, -7, 2, 6, -1], [13, -8, 5, -1, 3, -2, 5, 3, 2, -4, 1, -1, 8, -1, 7, 1, 6, -3, -4, 2], [7, -6, -3, -4, 1, 6, -1, -5, -6, 6, 4, -6, 5, 1, 7, -1, 5, -5, 4, 3], [-5, 15, -7, 2, -2, -1, -6, 1, 4, -2, -4, 1, 0, -2, -3, -4, -2, 5, -5, 1], [13, 13, 6, 3, 2, -5, -1, 5, 0, -5, -4, 4, -1, -2, 0, -1, -2, 3, -8, -10], [-4, 9, -6, 4, 1, 3, 7, -4, 1, -2, -3, 5, -6, -10, -9, 1, -5, 2, 2, -2], [-8, 5, -6, 1, 0, -8, -3, 3, 7, -2, 0, 2, 4, 3, 4, -1, 1, 3, -9, -7], [-15, 6, 1, 5, 13, -1, 10, 9, -4, 4, 2, -4, 2, 1, -4, 6, 3, -2, -5, -7], [-2, 4, -4, -2, 0, 0, -4, 3, 8, 0, 2, 2, 2, -2, 4, -8, -3, 2, 2, 6], [9, -7, -1, -4, -2, 7, 1, 3, -1, 1, 3, 2, 1, 1, 4, -3, 1, 2, 4, 1], [12, 0, 14, 4, 4, -1, 2, 10, 0, -2, 4, -3, 8, 6, 11, 2, 5, -3, -3, 2], [0, -4, -6, -6, -1, -1, 9, -6, 1, 2, -1, 2, -2, 2, -2, 4, 4, -1, 4, 6], [0, -9, 8, -2, 4, -1, 5, 5, -3, 3, 5, -5, 11, 9, 15, 2, 10, -7, 6, 0], [18, 2, 10, 1, 0, -2, 4, 2, 2, 1, 1, 0, 5, 2, 4, -1, 0, 3, -4, -3], [8, 5, 9, -2, -4, -3, -4, 2, 2, -2, -4, 1, 0, 1, 7, 3, 1, 3, 1, -2], [15, -5, -4, -5, -3, 1, 1, -1, 6, -2, 3, 0, 6, 0, 0, -2, 3, 0, -3, 2], [-8, -7, 3, -10, 0, -4, 3, 2, 1, 5, 4, -1, 9, 3, 8, 0, 12, -1, 0, 0], [9, 6, 0, -6, -2, 1, -4, -5, 0, -3, 3, 3, 5, 2, 3, -5, 4, 0, -2, 6], [-14, -7, -9, 4, 6, 2, 12, 0, -6, 1, 0, -2, -3, 0, -2, 8, -2, 1, 1, -2], [10, -1, 0, 4, 0, 2, 8, -1, -4, 5, 4, -3, -1, -1, 1, -4, 0, -4, 5, -4], [-11, 6, 1, 0, 5, 3, -2, 2, 2, 3, 2, -2, 1, -1, 2, 0, 1, 1, -1, -1], [8, -7, 11, 1, 0, -1, 10, 0, 2, -1, -3, -1, -4, 1, 3, 2, -1, -4, 7, 3], [17, 4, 8, 5, -2, 0, 2, 1, 0, -2, 1, 0, -2, 0, -8, 3, -1, 4, -7, -4], [14, 11, 6, -4, -4, -2, -3, 3, -1, -1, -4, 0, -1, 4, 6, 0, -1, 2, -4, -2], [-5, -15, 1, -7, 2, 3, 1, 1, -9, 3, 6, -5, 6, 1, -7, -1, 6, 2, -6, -4], [-23, -6, -2, 4, 6, -1, 6, 0, -8, 0, -3, -3, -3, 2, -13, 5, 4, -1, 0, -3], [-20, 12, -6, 4, -4, -1, 0, 1, 5, -3, -8, 2, -5, 0, -2, -1, -3, 4, 1, -2], [18, -14, -1, -2, 2, 0, 2, -1, -6, 3, 2, -5, 3, 6, 3, 5, 8, -6, 1, 2], [-13, 5, -4, 0, 0, -3, 4, 0, 6, -4, -3, 2, -2, 0, 4, 4, -3, 2, 2, -1], [-17, 10, 0, -5, -3, -8, -1, 7, -3, -1, 1, -3, 2, 8, 11, 2, 10, -3, 0, 0], [4, 0, -2, 1, 0, 0, -1, 2, 1, 0, -4, -1, -4, -5, -3, 2, -7, 0, -3, -3], [2, 8, 1, -1, -1, -2, -3, 6, 3, -6, 0, 6, 0, 1, 4, -6, 4, 1, -6, 1], [-7, -11, -5, -10, 0, -2, -2, 1, -8, 4, -1, -2, 0, 3, -1, -4, 3, 0, -1, -1], [-4, -5, 7, 2, 7, 0, 4, 2, -6, 0, -2, -4, 2, 1, -8, 7, 2, -4, 1, 0], [7, 11, -1, 1, -3, -4, 2, -1, 6, -4, -5, 4, 0, 1, 2, -4, -1, 2, -4, -2], [15, -4, 5, 0, 5, 0, -3, 2, -1, 0, 4, -6, 2, 1, -2, 3, 0, -3, 0, -1], [-9, -2, 3, 2, 3, 2, -4, 0, -2, 5, -2, -3, 1, 1, 5, 2, -2, -4, 8, 3], [21, -3, -1, 0, -2, 9, 7, -7, 1, 1, 3, 6, -2, -5, -4, -3, -8, 0, 10, 9], [-1, 4, 5, 2, -1, 3, 0, 3, -3, 2, 4, -1, -2, -1, -3, -3, 3, 4, 3, -1], [-13, -18, 0, 0, 1, 4, 6, -1, -2, 5, 0, 0, -1, 4, -2, 0, 3, -1, 0, -1], [0, 13, -2, 0, 5, -4, -3, 8, -1, -1, 1, -4, 1, -2, 2, 1, 2, -2, -5, 1], [-9, -1, -5, 8, 2, -1, 9, 1, 3, -2, -1, 2, -2, -7, -12, 0, -7, 7, -3, -9], [26, -7, 3, 0, -5, 4, 1, -1, 2, 1, 1, -2, 1, 3, 10, -6, -4, -1, 15, 8], [-8, -6, -5, 2, 0, 0, -9, 1, -5, -1, 0, 0, -3, 1, 8, 3, 1, 4, 2, -2], [21, -3, 3, -2, 2, 6, 7, -3, -3, 7, 5, -1, 3, 3, 8, 1, 0, -3, 5, 3], [4, -19, 8, -9, 4, 0, 0, 5, -2, 5, 5, -5, 9, 0, 5, -2, 7, 0, -4, 1], [32, -1, 5, -5, -2, 2, 1, 1, 2, 1, -1, 0, 3, 1, -2, 0, 3, 1, -2, 1], [8, 6, -2, 5, -7, -2, 3, -4, 1, 0, -6, 3, -6, 0, 7, 3, -7, 2, 5, 2], [8, 17, 0, -7, -4, -7, -7, 3, 3, -6, -4, 3, -2, -3, 5, -5, 0, 6, -6, -1], [11, 0, 6, -3, 1, 0, 1, -1, 1, 3, 0, -5, 1, 1, 3, 4, 2, 1, -5, -2], [1, 0, -4, 11, 2, 2, 4, 1, -4, -1, -4, 0, -7, 0, 8, 6, -6, -1, 9, 2], [-16, -7, -2, 0, 0, 0, -2, -2, 6, 0, 2, -1, 5, 2, -3, -1, 5, -3, 0, 4], [-1, -2, 8, -3, 0, 4, 0, 6, -2, 5, 4, -6, 5, 4, 0, -4, 0, -1, -5, 2], [-2, 5, -11, 0, -6, -1, -5, -8, 3, -4, 0, 8, -6, -2, 8, -9, -10, 1, 8, 2], [9, 5, -1, -2, 0, 0, -1, -5, 5, -1, -1, 1, -1, -1, -9, -3, 2, 1, -7, -1], [-5, 7, -2, 1, -2, -5, -7, 6, -1, -7, 0, 1, 1, 6, 3, 1, 7, -1, -1, 6], [-17, 8, 4, 0, -3, 0, -4, 0, 2, 1, 0, -2, -7, 2, -4, 0, 1, 1, -4, -7], [41, -16, 3, -4, -3, -2, -6, 0, 0, -1, 5, -5, 9, 7, 7, -1, 1, 0, -4, 2], [33, -5, 13, -10, -6, 6, -2, -6, 4, -1, 5, -2, 5, 0, 6, -8, 2, 1, 3, 8], [9, -2, -3, -1, -2, 6, -6, -6, 2, -1, 4, 1, 5, -3, -1, -4, -1, 0, 3, 6], [-16, -11, 2, 4, 5, 1, 3, -6, -3, 2, 1, -3, -4, -2, -5, 7, -5, -8, 8, 0], [-3, 0, -13, -5, 3, -1, 0, -3, 2, 2, 1, 4, 2, 1, -1, -1, 1, 0, 3, 0], [4, 28, -4, -1, -5, -3, 0, -1, 10, -2, -4, 9, -5, -2, 1, -6, -3, 3, -2, -5], [25, -2, 1, -5, 4, -2, -2, 3, 2, 4, 4, -3, 4, -1, 3, 0, 0, 5, -5, 1], [28, -15, 1, 1, -3, 8, 5, -6, 1, 4, 8, -5, -2, -3, -3, -2, -5, -2, 7, 6], [1, -10, 5, 1, 0, 3, -1, -5, -7, 5, 2, -3, -3, 4, 1, 4, 0, -1, 5, 4], [-3, -8, -4, 0, 7, -1, -8, 2, 0, -1, 2, -3, 3, 2, 9, 2, 4, -6, 5, 3], [-3, -16, 2, -3, 4, 3, 5, 0, 0, 2, 4, -4, 6, 2, -4, 3, 4, 1, -2, 6], [1, -12, -9, -2, -2, 2, 8, -8, 3, 5, -3, -2, -3, -1, -4, -2, -2, 0, 5, 1], [15, -7, -2, 0, 5, 4, 11, -1, 1, 2, 4, 0, 2, 0, -3, -2, 4, -1, 0, -3], [-4, 14, -2, -5, -2, -2, -4, 6, 0, -1, -1, 0, -3, -2, 0, -1, 2, 1, -4, -3], [8, -3, 8, -8, 1, 0, 6, -1, -2, 4, 7, -3, 4, 6, 1, 2, 6, -1, -1, -1], [5, 3, 0, -3, 0, -6, 1, 2, -1, -6, -4, 2, -2, 5, 0, 4, 10, -1, -1, 0], [-19, 2, 2, 3, 4, 1, -2, 3, -2, -1, 0, -3, 1, 2, -17, 0, 6, -2, -4, 0], [-1, 1, -9, -4, -3, 0, 1, -7, -1, 2, 0, 3, -2, 5, 11, -2, 0, -4, 4, -3], [3, -8, -14, -2, -5, 5, 1, -5, 7, 2, -2, 8, -2, -8, -6, -11, -3, 5, -1, -5], [-3, 16, -4, 1, 2, 2, -3, 5, 3, 2, 4, 1, 6, -4, 3, -3, 2, 0, -5, -6], [-3, 11, -4, -1, -3, -1, 2, -4, 0, -1, -7, 4, -3, -2, 0, 0, -2, 1, 5, 1]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_2001_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_2001_2_a_o();".
// 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_2001_2_a_o(:prec:=20)
    chi := MakeCharacter_2001_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_2001_2_a_o();".
// 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_2001_2_a_o( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_2001_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-256, 1408, 2768, -19624, 5201, 60661, -34967, -82362, 52109, 59410, -36791, -24566, 14484, 5985, -3353, -846, 453, 64, -33, -2, 1]>,<5,R![34304, -347648, -2574080, -805952, 9824768, 1611680, -12185864, -659076, 6895808, 4762, -2075476, 50979, 359215, -12062, -36939, 1202, 2230, -56, -73, 1, 1]>],Snew);
    return Vf;
end function;