
// Make newform 6024.2.a.o in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6024_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_6024_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_6024_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 := [-416, 912, 10776, 8040, -25196, -20277, 16575, 9662, -4890, -1667, 679, 119, -43, -3, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [268101597699285680, 951009769878186960, 655007521450873280, -3059424933048010188, -1688156493700203161, 2047465404860353907, 760936910664972734, -572354612125554522, -127027480494896559, 75149691440341379, 8918302875541603, -4551967250809079, -223956217420031, 102160228984125], [-100571358867112368, 2113188179508749096, 1836550728177771676, -4174940629309736220, -2613787912685535495, 2559020949405016801, 1132282727011900110, -721976110664782158, -191901021333777173, 97599481407614489, 13717313487730393, -6077411015267013, -348803377277369, 139579303918975], [-956081207119446224, 1815396785928819632, 7039789131713671532, -6564333951753128446, -9858656163670110843, 4821180861657057315, 4219524522207086246, -1556108755747599016, -704509837983309381, 229348796620102189, 49579547453945521, -15089905841992425, -1239104231363285, 360141139074321], [-363486457391226928, -1481303134680859336, 663099775296066744, 5785539595387658028, 2697306301042614707, -3943837242891010673, -1604781962689563666, 1121725643694139398, 295109531697037877, -150007569171007185, -21678952567628985, 9239758965660829, 555783816244845, -210653563625063], [-1245424436536462640, -3471198890654064, 9690844697273457388, 405023675285817474, -15320575164739001557, 1944619223607752809, 6807804040762609634, -1334175436317358548, -1150321700462232203, 259114577888169163, 81253766710476831, -19414247019505775, -2031706876941115, 497673575650939], [59117336444021248, 2924304227425531376, 3187077622129062824, -7800292963246667004, -6398240083437233001, 5079989292169782787, 2894637963175190190, -1453335453568403898, -489273620291239679, 196913026046634483, 34559663959115219, -12267181842569951, -865164088681703, 282322126790709], [86686275530816976, -271973509242329460, -1854398370549607904, 1106400353597761585, 3885151382733937299, -1180362333535082848, -1815287127345479202, 495156550711999939, 311384618679919627, -83136857423130809, -22136489252665683, 5856658684055137, 555371801647469, -145424724115102], [67395399980501772, -42915193060201410, -1445973730133987604, 227523215290734920, 2369546825549565973, -457244144571890015, -1040079786752910940, 231910116232681998, 174210218522018513, -41500706658397755, -12239603188220543, 3006391066330991, 304955783475835, -75770107003455], [360858743825480272, -3267059514933151040, -4912514216771641832, 6852710827847343566, 8472745227809098009, -4721360587001236177, -3754133104704608606, 1486041406241881372, 630455172738299419, -215809398490302811, -44381240552077439, 14065127560125175, 1108710482211023, -333456052243539], [241122880378396768, 4457435940448532192, 6317447348833702460, -12270716022185567878, -14937934247020585373, 9139469180380986209, 7146904819615719730, -2981596068649173852, -1237863978362435707, 440032346472219811, 88533970484338863, -28895623562412591, -2232831647964323, 687568838052891], [2437368238033035472, -4289950497625583680, -21133578636271541724, 15665919370430684002, 37017961598353240159, -14332622337994375115, -16775008908771238990, 5402468584922669604, 2852931504646788297, -860414979803144985, -202301647050933461, 58914509485450421, 5076120118488849, -1437608246229121], [-1192615697745108912, 7117140897075219296, 20690398991875395764, -24732980773534038746, -38405526987464180273, 19906041873294275385, 17374262131005461586, -6692860674237136328, -2944518757895850607, 999279614844233815, 208321575309308339, -65952957071802091, -5220619154611247, 1573378793415459]];
    Rf_basisdens := [1, 1, 113480274736800592, 113480274736800592, 226960549473601184, 113480274736800592, 226960549473601184, 113480274736800592, 56740137368400296, 28370068684200148, 113480274736800592, 113480274736800592, 226960549473601184, 226960549473601184];
    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_6024_a();"
function MakeCharacter_6024_a()
    N := 6024;
    order := 1;
    char_gens := [4519, 3013, 2009, 4273];
    v := [1, 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_6024_a_Hecke(Kf)
    return MakeCharacter_6024_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, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [-2, 0, -1, -1, 0, 0, -1, 0, 1, -1, 0, 1, -1, 0], [-2, 0, 0, -1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0], [1, 0, 0, 0, 0, 1, -1, 0, -1, 1, -1, 0, 0, 1], [0, 0, -1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 1], [-2, 1, -1, -1, 0, 0, -1, 1, 1, -1, -1, 1, -1, -1], [0, 1, 1, 0, 0, 0, 1, 0, -1, 2, 0, -2, 1, 0], [-3, 1, 0, 1, -1, -1, 1, 2, 1, -2, 1, 1, -1, 0], [-3, 1, 2, 1, 0, 0, 1, 0, -1, 1, 0, 0, 0, 1], [-1, 0, 1, 0, 0, -1, 0, 1, 1, -1, 1, 0, 0, -2], [0, 2, 2, 1, 2, 0, 2, 0, -2, 1, 0, -1, 1, 1], [-2, 0, 0, -1, 1, 0, 0, -1, -1, 1, -1, 2, 1, 0], [0, 0, 0, 0, 0, -1, 0, 0, 3, -1, 0, 0, 0, 0], [1, 3, 1, 0, 1, 0, 2, 1, -2, 1, -1, 0, 0, -1], [-1, 1, 1, 0, 3, -1, 0, -2, -1, 2, -2, -2, 2, 1], [-2, 1, 0, 1, -2, -1, -1, 2, 3, -4, 1, 0, -3, 0], [2, -2, 0, 0, 0, 1, -2, -2, -1, 0, 1, 0, 0, 0], [-2, 1, 1, 1, -1, -1, -1, 0, 0, -2, -1, 0, 0, -2], [-1, 1, -2, 1, -3, 1, -1, 0, 0, -1, 0, 1, -1, 1], [-2, -1, 0, 0, 1, 0, 2, -1, -1, 2, 2, 0, 2, 1], [2, -1, 0, 1, 0, -1, 0, -2, -2, 0, 0, 0, 1, 1], [-2, -1, -1, 0, -1, -1, 0, 1, 2, -2, 2, 1, 0, -3], [1, 0, 0, -2, 1, 1, 1, 2, 0, 1, 0, 0, 2, -2], [-3, -1, 0, -1, 0, 1, -2, 0, 0, 1, -3, 1, -1, -1], [0, 2, 0, 0, 1, 1, 1, 0, -1, 0, -1, -1, 0, 3], [-1, -2, -4, -1, -1, 1, -3, -1, 2, -2, 0, 0, -1, 1], [-2, 0, -2, 1, -1, 0, 1, 1, 0, -1, 2, 0, -1, 1], [-2, 2, 1, -2, 2, 0, 1, 1, 0, 1, 0, 1, -2, 0], [-1, 0, 1, -1, -3, 0, 0, 2, -1, 0, 1, 0, 1, -2], [-6, 0, -1, 0, 0, 0, 0, 1, 1, -1, 1, -1, -1, -1], [-4, -1, 2, 1, -1, -2, 3, 2, 0, -1, 3, 1, 0, -2], [0, -1, -2, 0, 0, 2, 1, -2, 0, 3, -1, -1, 3, 2], [0, -3, -3, 1, -1, 0, 1, -1, -1, 3, 1, -1, 0, 0], [0, 0, -2, 0, 0, 0, -3, 1, 3, -3, 0, -1, -4, 1], [-4, 0, 0, -1, 3, -2, 3, 1, 1, 0, 2, -1, 2, 0], [1, -1, -2, -2, 1, 1, -1, 1, 2, -3, 1, 1, -1, -1], [-2, 0, 1, -1, 1, 2, -2, -1, 1, -1, -2, 0, -2, 1], [-4, -3, 1, -3, 5, 0, -3, -3, -1, 0, -1, 1, 1, -1], [1, -1, -1, 3, -3, -3, -1, -1, 0, -2, 2, 0, -1, -1], [1, 1, 0, 2, -1, -3, 1, 1, 0, -1, 2, 0, 0, -1], [-5, -1, 2, 0, 1, 1, 3, -1, -3, 5, -1, -2, 3, 1], [-3, -1, -2, -2, 0, 0, 1, -1, 0, 1, 1, 1, 1, 0], [2, 0, -2, 0, -1, -2, 3, 0, 1, 0, 1, -3, 2, 0], [-6, 0, -1, -1, -1, 1, -2, 2, 2, -1, 2, -1, -3, 0], [-1, 1, -2, 2, -3, -1, 0, 1, 1, -3, 2, 1, -4, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, -1, -2, 0, 2, 0, 2, 2, 2, 0, 1, 0, -1], [-11, -1, -3, -1, -2, 2, -1, 3, 1, -5, 0, 2, -3, 0], [-2, 1, 3, 0, 0, -1, 1, 0, -1, 3, -2, -2, 1, 1], [-3, -2, -2, 0, -2, 2, -3, 3, 1, -1, 0, 2, -1, 0], [1, 2, -2, -3, 0, -2, 3, 1, 0, 2, -1, -3, 1, -2], [-3, -3, -5, 0, -2, 1, 0, 2, 2, -3, 3, 3, -1, 0], [-5, -3, 3, -2, 1, 0, 2, 2, 0, 1, 2, -1, 2, 0], [1, 1, 0, 3, -1, 1, 0, 0, -2, 1, 1, -3, 2, 2], [-2, -3, 4, 3, 0, -1, -1, 0, -2, 0, 0, -1, 1, -2], [0, -4, 1, -1, 0, 1, 0, -2, -4, 3, -1, 0, 3, -3], [1, 0, -2, -1, 2, -1, 2, 1, 0, 0, 0, 0, -1, -1], [-7, -2, 0, 0, -3, 2, -1, 0, -1, 1, 1, 2, 2, -2], [-4, 1, 6, 1, 0, 1, 1, 1, -2, 1, -1, 0, 0, -3], [0, -3, 4, -4, 3, 1, -3, -1, -3, 3, 0, 2, 1, -3], [-9, 1, -4, 3, -5, 3, -3, 0, 3, -3, 1, 0, -5, 3], [-5, -2, 2, 2, -5, 1, 2, 0, -1, -1, 1, 2, 0, 1], [-4, 1, 3, 2, 1, -2, -2, 0, 1, -4, 0, 3, -3, -1], [-11, 2, -1, -1, 1, -2, -1, -1, 3, -3, -1, 0, -1, 1], [0, -1, -2, 0, 0, -3, 1, 3, 3, -1, 4, -3, 1, -3], [-5, 4, -1, 3, -4, 2, 2, 4, 0, -4, 3, 2, -3, 1], [0, -1, -1, -1, -1, 3, -1, -1, -1, 3, -4, 0, 0, 2], [-3, -1, -1, -1, 4, 3, -6, -1, -1, -1, -5, 1, -1, 1], [-4, 4, 3, 1, 3, -1, 0, -4, -1, 2, -3, 1, 2, 3], [-2, -1, -1, -2, 4, 1, 1, 2, 0, 0, 2, -1, 1, 2], [0, 4, 1, 1, -1, 2, 2, 0, -1, 3, 1, -1, 1, 0], [-3, 1, -4, -1, -2, -1, 2, 6, 5, -3, 3, 0, -1, 1], [-7, 0, -1, -2, -3, -2, 0, 3, 4, -2, 0, -1, -2, -5], [-2, 4, 2, 2, 2, 1, 6, 0, 1, 6, 0, -3, 2, 2], [-8, 2, -1, 3, -3, -1, 0, -1, -1, 3, 0, 0, -2, 1], [1, 1, 2, 1, 2, 1, 2, 0, 1, 3, 1, -2, 5, -1], [-1, 1, 3, 1, 4, 0, -2, -3, -4, 1, -1, 2, 0, 1], [-15, 2, -1, -1, -4, -2, 1, 7, 5, -5, 1, 1, -3, -4], [4, 0, 0, 1, -1, -1, 3, -1, 1, 1, 2, 3, -1, 1], [4, -1, -4, 0, -4, 1, -1, 1, 0, -2, -1, -1, -1, 0], [-7, -1, -1, 2, -4, 1, -5, 4, 2, -10, 2, 3, -4, -3], [-5, 2, 6, -3, 6, 0, 2, 3, -5, 4, -3, 0, 3, 1], [-3, 3, 4, 1, 6, -5, 4, 0, -2, 0, -2, 0, 0, 0], [-13, 0, 1, -3, -2, 0, 3, 2, 5, -3, 2, 0, 0, -5], [1, -1, -2, 0, -3, 2, -6, 3, 1, -6, -2, -1, -3, 1], [-6, 0, 1, 2, -2, -1, 1, -5, -2, 5, 2, -3, 3, 2], [-6, -3, -3, -5, 0, 2, -2, 1, 0, -4, 1, -1, 0, -1], [-6, 0, -2, 3, -1, -3, 3, -1, 2, -3, 1, 1, -1, 1], [2, 8, 4, 2, 6, -1, 7, -2, -5, 9, 0, -3, 3, 6], [2, -2, -4, 0, -3, -2, 1, 0, 1, 1, 1, -3, 2, -2], [-3, -2, 2, 1, -1, 0, -4, 2, 0, -4, -2, 3, -5, 0], [-1, 1, 3, -3, 4, -1, 3, 3, -2, 4, -4, -1, 4, -3], [8, -5, -1, 0, 1, -1, -1, -5, -1, 0, -4, 1, 3, 1], [4, -2, -2, -4, 1, -2, -2, -2, 1, -3, 0, 4, -1, -2], [-18, -1, -1, -2, -2, 3, -2, 4, 1, -2, 1, 0, -2, 2], [11, -1, -2, 3, -3, -1, -5, -7, -1, -3, -2, -1, 0, -2], [-4, -3, -3, -2, 3, 0, -1, -1, 0, 0, -1, 1, -3, 1], [0, 0, -4, 2, -3, 2, -1, 0, -2, 2, 1, 4, -2, 0], [-7, -2, 1, 3, -6, -2, -2, -2, 4, -6, 1, 2, -7, 1], [8, -1, 1, -2, 1, 2, -3, -1, 0, 5, -3, -3, -3, -1], [-7, 2, 1, 1, -2, 1, 2, 2, 2, -2, 4, -1, -1, -1], [-10, -3, 4, -2, 0, 1, 0, 1, 2, 1, 2, 0, 4, 0], [8, 3, 2, 0, 1, -1, 2, 4, 1, 0, -1, -1, 2, 1], [-4, 0, -1, -4, -1, 2, -1, 5, 2, -7, -1, 7, -5, -3], [-1, -4, 1, -3, 1, -2, 1, 0, 4, -4, 4, -2, -1, 1], [-3, -1, 3, -6, 4, 0, 2, -1, 0, 0, 0, 2, -2, -2], [8, -1, -2, 1, -1, 3, -1, -2, -3, 5, -1, 0, 3, 4], [-7, 0, 1, 2, -2, -1, -3, -1, 0, -6, 4, 4, 0, -1], [3, -2, -5, -1, 0, -3, -5, -4, 1, -4, -4, 2, 2, 0], [3, -6, -8, -1, 0, -2, -3, -5, 1, -3, 0, -1, 2, 1], [-3, 3, 0, 0, -2, 3, 0, -1, 1, 4, 0, 5, -3, 0], [-11, 3, -2, -4, 2, 2, -5, 1, -1, 2, -3, 3, 1, 2], [6, -1, -4, -2, 2, 2, 0, -1, 0, 6, 0, -2, 1, -1], [1, -2, -1, 0, 1, -3, -4, -3, -1, -5, 1, -1, 2, -1], [-4, 8, -2, 3, -3, 0, 1, 2, 2, -3, 5, 1, -4, 4], [-3, -3, 3, -2, 1, 1, 1, 1, -4, 5, -2, -1, 4, -4], [2, -6, 1, 1, 2, 2, -6, -8, -4, 1, -1, 3, 4, 0], [3, -1, -1, 2, -5, 0, 0, -2, 2, -1, 2, -3, 0, 0], [0, -4, -1, 2, -4, 7, -6, 1, 0, -2, 3, 4, -2, 2], [5, -1, -1, -3, 1, 1, 1, 0, -5, 4, 2, 0, 3, -5], [13, -1, 5, 1, 0, -4, -2, -2, 4, 1, -1, -2, 0, -4], [5, -2, -1, -2, -3, 1, -3, 5, 2, -3, 1, 2, 0, -2], [5, -1, 0, 0, 4, 4, 3, -3, 0, 3, 0, 1, -2, 5], [9, 4, 5, 0, 7, -4, 5, -8, -5, 4, 1, -1, 6, 0], [6, -6, 4, 2, 1, -3, -6, 0, 1, -3, 0, 1, -3, -4], [8, 1, 1, -2, 0, 1, -4, 5, 0, 1, -5, -2, -1, -3], [1, 5, 5, -2, 5, 1, 7, -2, -5, 12, -2, -4, 5, 8], [13, -9, -3, -1, -1, 4, -5, -7, 0, 3, -2, 0, 4, 2], [7, 0, -6, -2, 1, 4, 0, -3, -4, 9, -3, -3, 3, 2], [3, 2, 4, 3, -1, -1, 4, -3, 3, -1, 2, -2, -2, -1], [2, 7, 4, 0, 4, -7, 3, -1, -1, 3, 0, -5, 4, -5], [7, -3, 4, -4, 4, 3, -1, -1, -6, 6, 0, -1, 2, -2], [2, 3, 1, -5, 4, -3, 6, 3, 2, 6, -5, -1, 0, 0], [2, 7, 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4, -4, 4, -2, -2, -3], [-9, 2, -2, 3, 0, -8, 3, 3, 1, -5, 6, -1, 0, -5], [-16, 7, 5, 4, -3, -2, 1, 8, 2, -9, 4, 0, -12, -2], [-14, 4, 1, 11, -10, -1, 6, 9, -1, -13, 9, 4, -4, -2], [9, 13, 2, 3, 0, 0, 7, -4, -1, 3, -2, -5, 1, 8], [11, -10, 2, -5, 0, 2, 0, 5, -3, 6, 7, 0, 3, -3], [-5, 0, -7, 2, 0, 3, -9, -11, 0, -3, -4, 2, -8, 7], [-5, -9, -4, 3, -2, 2, 3, -1, 0, -4, 2, -4, 5, 4], [2, 2, 1, -3, -3, 6, 9, 3, -6, 13, -1, 0, 0, 0], [1, 4, 0, -1, -4, 1, 4, -1, -2, 0, 6, 0, -1, -1], [-15, 1, 6, 4, -2, -2, 4, -7, -5, -4, 6, -2, 5, -2], [-1, -6, -4, 4, -4, 1, -3, 2, 4, -5, 4, 5, 2, -1], [18, -8, -1, -3, 10, 3, -11, -14, -3, 0, -7, 8, 7, -2], [-6, -10, -1, -9, -5, 7, -4, 4, -5, -2, -4, 6, 2, -7], [-15, -8, -4, -5, -3, 6, -10, -7, 5, 3, -2, 2, -1, 4], [-1, -1, -2, 5, -5, 0, -4, -1, -4, -6, 6, -4, -3, 0], [8, -2, 3, -2, 6, 2, -3, -11, -5, 3, -1, -5, 5, 4], [-4, 0, 6, 3, 1, -2, -3, 3, 0, -9, 0, 0, -9, 1], [0, -6, 1, -6, 0, 3, -1, 2, 4, 2, 3, -4, 3, 0], [-2, -11, -1, 2, 1, -4, -3, -4, 3, -13, 5, 7, -2, -4], [0, 3, -2, 5, -10, -7, 1, -2, 0, -7, 6, -4, -3, -1], [-9, -3, 1, 6, 3, 6, -4, -11, -5, 8, -4, 2, 3, 8], [-4, -8, 3, 1, -1, 4, 4, -2, -7, 11, 5, -5, 8, 4], [21, 5, 0, -5, 0, 0, 9, -4, -6, 16, -1, 3, 8, 1], [-6, -1, 0, -6, -2, -1, -3, 4, 8, -8, 4, 6, -10, -7], [-17, -1, -4, -2, -1, 3, 0, 5, 3, 1, -1, 12, -4, -2], [15, 2, 2, 3, 2, -1, 5, -9, -9, 12, -6, -7, 9, 6], [-9, 5, 4, -1, 0, 7, 4, 5, -9, 13, -2, -7, 4, 4], [4, 5, -3, 1, -6, 6, 6, -5, -4, 10, -6, -4, 0, 10], [-7, 9, 16, 7, 10, 3, 3, -2, -11, 11, -6, -3, 6, 1], [6, 2, 6, 2, 4, 3, 2, 2, -2, 2, 3, -5, 6, -4], [21, 3, 0, -1, -1, 2, 1, -12, -5, 7, -6, -1, 9, 5], [-9, -4, 1, -3, -8, 2, -5, 4, 10, -17, 4, -1, -8, -3], [6, 7, 1, 3, -7, -1, 7, -1, 7, 1, -2, -4, -6, -2], [-14, -3, -5, -2, -4, 0, -8, 0, 9, -9, 1, 7, -3, 2], [16, 13, 1, 2, 6, -11, 8, -11, 1, 6, -4, -4, 2, 4], [5, -5, 0, -2, -1, -1, 1, 3, -2, 9, -5, 1, 1, -3], [-2, -2, -15, 1, -8, 2, -3, -3, 1, -10, 3, 0, 1, 4], [-37, -11, -2, -2, -3, 10, -4, 3, 8, -6, -1, 9, -10, -3], [-8, -1, -8, -3, -3, 5, 2, 10, 6, 2, 3, 1, 1, 2], [-10, -2, -5, -4, -5, 3, -3, 8, 13, -5, 2, -2, -8, -2], [-1, -1, 6, 7, -11, -2, 3, -3, -1, 3, 5, 1, 3, -9], [2, 0, 4, -2, 0, 1, 7, 1, -5, 5, 3, -2, 2, 1], [4, 16, 4, 3, 7, -8, 6, 0, -1, 11, -6, -11, 2, 3], [4, 2, 4, 6, -2, -2, 1, 4, -6, 9, -3, -3, -1, 0], [-18, 14, 3, 4, 5, -3, 14, 7, 0, 0, -1, -6, -1, 1], [6, 5, 2, -1, 0, 0, 7, 8, 1, 6, -1, -1, -5, 0], [2, 6, 1, 2, 3, -4, 10, -3, -2, 11, -3, -5, 3, 7], [-8, 15, 5, 0, 4, -3, 3, 4, -6, 9, -2, 2, 3, 0], [19, 0, 2, -1, 9, 6, -5, -15, -7, 14, -7, -4, 3, 9], [-7, 7, 5, 3, 3, 3, 1, -4, -8, 4, -3, 1, 0, 12], [14, -2, 11, -9, 7, 1, 0, 4, -4, 3, -6, -1, 5, -4], [6, 3, 0, 4, -2, -8, 5, 0, 0, -7, 1, -5, -5, 0], [-10, -12, 4, 4, 5, -1, -1, -4, -8, -2, 0, 5, 10, -4], [-18, 10, 2, 2, -9, -3, 2, -4, 2, -3, 3, -2, -3, -2], [5, 11, -4, 7, -4, -9, 5, 0, -1, -2, -1, -2, 1, 1], [-19, -10, 11, 6, -3, 5, -10, -3, -3, -12, 1, 5, -2, 1], [-3, 1, 10, -3, -2, -6, 3, -3, -6, 4, -2, 2, 7, -12], [-36, 3, -1, -3, -6, 2, 1, 5, 3, -7, 9, 6, -13, -2], [-5, 10, -1, 0, 2, -1, 0, 17, -1, -3, -5, 0, 0, -8], [3, 7, 2, -6, 0, 1, 2, 11, 6, 1, -7, 2, -5, -8], [-8, -8, 0, -3, 9, -3, 1, -7, -6, -3, -6, 5, -2, 4], [-22, -2, 1, -1, -2, -4, 11, 5, 2, 1, 3, 1, -2, 1], [20, 12, -1, 2, 9, -9, 9, -5, 0, 4, 0, -4, 2, 4], [-2, -9, -9, 5, 1, 0, -1, -7, 4, -3, 5, -2, 4, 4], [-19, -3, 6, 5, -2, 5, -4, 2, -4, -2, 6, 4, -9, 4], [15, -6, 8, -5, 7, 6, 9, 3, -6, 16, -2, -3, 11, 3], [4, 8, 4, 0, -6, 2, 4, 5, 1, 3, 3, 8, -2, -4], [10, -4, -8, 1, -5, 4, -8, -6, -4, -9, -4, 2, 0, 1], [-14, -1, 1, -13, 7, 9, 2, 5, -3, 12, -6, -4, 1, 4], [-33, 2, -3, -1, -12, 2, -2, 18, 13, -14, 5, 7, -13, -5], [-7, -7, 8, -3, 4, -3, -4, -5, -1, 2, -4, -5, 3, -1], [8, 1, -5, 2, 0, -8, -2, -6, 10, -18, -2, 5, -2, 1], [16, 2, 2, 3, -3, 3, -6, -4, -2, 1, -3, -1, -8, 9], [0, 7, 10, -3, 11, -6, 9, -1, -6, 10, -7, -9, 8, -2], [-8, -3, 8, 0, 8, -3, -1, -4, -8, -4, -6, -2, 10, -3], [5, -11, 0, -5, 3, 5, -7, -3, -3, 9, 4, 3, 8, -2], [11, 4, 7, 9, 3, -4, 1, -2, -10, 4, -8, -2, 5, 7], [24, 2, -2, 2, -5, -4, 0, 0, -2, -1, -1, -2, 9, -3], [1, -6, -4, -2, 3, 2, -6, 6, -2, -12, 1, 3, -1, -4], [-12, -6, -2, -1, -11, 4, -1, 0, 2, 4, 7, 5, -1, -7], [1, 15, 3, 1, 6, -7, 3, 5, -2, -1, -1, -4, -2, 2], [16, -4, 7, 2, 4, 5, -6, -1, -6, 14, -8, 1, 0, 4], [-14, -2, 1, -3, -2, -7, -2, -2, 8, -9, -2, 2, -7, -9], [-10, 5, 7, -5, 2, 2, 9, 7, -8, 16, 0, -4, 11, -1], [0, 8, 4, 11, -5, -3, 0, -7, 4, -5, -4, -2, -1, 2], [-8, -12, -11, 3, -14, 6, -13, 2, 14, -18, 2, 16, -15, 0], [-7, -2, -1, 0, 7, -1, -3, 2, 3, 6, -3, 5, 6, 0], [-10, -12, -2, -6, 0, 11, -11, -2, -1, 4, -5, 3, 3, 0], [7, -11, -13, -5, -6, 11, -3, 3, 3, 0, 0, 10, -6, 5], [21, -1, -9, 0, -1, -3, -1, -8, 2, -9, 4, 7, 2, 3], [-31, -1, -6, -3, -4, 6, -8, 8, 10, 1, -2, 2, -3, 5], [-5, 0, 0, -3, 8, -2, -2, -15, -4, 6, -7, 7, 5, -3], [-7, -3, 6, 2, -10, -3, -4, -1, 4, -6, 5, -4, -1, -6], [10, -10, 7, -2, -4, 9, -13, 1, -3, -1, -2, 0, -1, -2], [-5, 2, -1, -10, 3, -5, 11, 9, 3, 4, 6, -4, -3, -7], [14, -1, 7, 2, 4, 2, 4, 1, 4, -2, 3, -4, -6, 4], [11, -6, 2, 0, 1, -1, 12, -6, -5, 15, 0, 3, 10, -5], [-3, 0, 6, -1, -4, 6, 7, 10, -8, 11, 3, 3, 7, -8], [-2, -10, -6, -10, -1, 2, -14, -9, 5, -2, -8, -7, -1, -4], [-7, -5, -1, -2, 9, 4, 8, -1, 2, 9, 4, -3, 3, 10], [8, -16, 1, -5, 2, -3, 3, 0, -2, 1, -4, 0, 5, -5], [-6, 11, 5, 1, 5, -7, 2, 5, 1, 2, -3, -5, -1, -4], [-6, 7, 6, -1, 5, -5, 6, -8, -8, 3, -6, -2, 10, 1], [1, -2, 17, 9, 8, -7, 2, 3, -4, 2, 1, -4, 4, -8], [14, -2, -10, -6, -2, -2, -7, 2, 7, -2, -5, -2, 4, -7], [-6, 8, -8, -1, -2, 2, 4, 14, 8, -2, 4, -5, -3, -5], [-19, 5, 5, -3, 7, -2, 1, 5, -1, -4, 1, 2, -3, -7], [18, -1, 9, -1, 10, -6, 5, -8, -9, 6, -7, -13, 14, -1], [-9, -7, 2, 5, -9, 3, -4, 3, -5, -6, 1, 6, -7, 4], [12, 1, -5, 0, 8, -5, 3, -2, 1, 3, -4, 0, 4, -1], [2, 2, 7, -4, 12, -8, 12, 4, 4, 6, -7, -10, 5, 3], [12, 3, 2, 4, -4, 0, 8, 1, -1, -7, 1, 2, -12, 0], [-1, -7, -8, 0, -2, -1, -13, -3, -1, -10, 1, 7, 0, 1], [11, 10, 2, 4, -5, -5, 3, 4, -1, 2, 4, 1, 4, -7], [-2, 1, 1, 5, -3, 1, 9, 1, -6, -5, 6, -5, 4, 6], [-13, 7, -8, -1, 3, 8, 1, 7, -3, 4, -2, 4, 0, 8], [6, 0, 2, 3, -3, 3, -10, 2, -6, 0, 1, -3, 1, -4], [-15, -1, -4, -2, 3, 9, -9, 3, -8, -1, -7, 1, 5, 1], [-5, 1, 4, 4, -6, 5, 5, 10, 0, -6, 5, -5, 1, 4], [19, -12, -12, 1, -9, 1, -6, 0, 5, -5, 5, -1, -1, -2], [-5, -15, -2, -4, -9, 14, -15, -2, 1, -1, 3, 8, -4, -2], [-38, 5, -5, 4, -9, 6, -1, 4, 0, -2, 8, -1, 0, -1], [6, -9, -9, -3, 2, 0, -9, 3, 5, -8, -1, 6, -3, 0], [7, 6, 8, 5, -5, 9, 1, 2, 2, -2, 5, 1, -4, 4], [5, -8, -3, 2, 1, 5, -19, -9, -1, -18, -3, 9, -4, -5], [-9, -11, -11, -5, -9, 11, -10, 0, 9, -4, 5, 13, -5, -2], [6, 2, -7, 2, -10, -4, 7, 9, 7, 4, 7, -1, -6, -9], [-13, 0, 2, -1, -2, -4, -3, -7, 2, -8, 1, 1, -4, 2], [4, 8, 3, 3, 3, -3, 4, 11, 1, -1, -1, -7, -2, -1], [-4, -6, -1, -7, 1, -1, 4, 2, 1, -2, -1, 1, 1, -5], [16, -4, -2, -2, -3, 2, 6, 12, 0, 10, -1, -4, -1, -5], [-17, -1, -3, -3, -4, -5, -13, -1, 2, -14, 0, 9, -8, -5], [16, -7, -9, 1, -11, -5, -1, -5, 5, -1, 4, 0, 0, -2], [-2, -5, -13, 8, -10, 2, -7, -4, 6, -9, -5, 4, -3, 7], [-8, -7, -16, 1, -12, -4, -13, 8, 21, -25, 9, 11, -11, -2], [10, -5, 4, -2, 6, -4, 7, -5, -5, 12, -4, -9, 2, -2], [-10, -11, 4, 5, -3, -2, -6, 8, 6, -14, 0, 8, -7, -10], [11, -6, -16, -3, -6, 0, -21, -6, 4, -14, -1, 9, -4, -7], [10, 7, 10, 3, 7, -3, 10, 4, -13, 4, 4, -1, 7, 0], [2, 13, 3, 2, 4, -3, 6, -8, -7, 0, -7, 1, -2, 9], [3, -5, -2, 3, -4, 6, 9, -2, 0, 2, 7, 1, 2, 3], [36, -4, -5, 12, -12, 3, -1, -11, -7, 12, -4, -6, 6, 3], [28, -9, 3, 5, 6, -3, -6, -9, -2, 8, -7, -4, 12, -1], [-21, 6, -1, 9, -6, 3, 8, 2, -1, -6, 6, 2, -1, 11], [26, 12, -4, -4, -2, -5, 7, 0, 9, 7, -6, -7, -1, 2], [16, -13, 1, -5, -1, 6, -7, 1, -5, 14, 0, 1, 12, -2], [1, -8, 6, 4, 2, 0, 15, -4, -7, 15, 6, -2, 11, 0], [-12, 7, -3, -2, -8, -1, 3, 15, 15, -21, 2, 0, -11, -4], [-4, -8, 0, -4, 3, 1, 6, -4, 7, 1, 6, 10, 2, 3], [18, -3, 3, 1, -1, 3, 9, 10, 3, 1, 1, -7, -1, -1], [-10, -11, 4, -5, 0, -2, -9, 2, 0, -9, -2, -1, -1, -3], [-1, 8, 9, 10, 3, -3, -5, -1, 3, -6, -4, -2, -1, 3]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6024_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6024_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_6024_2_a_o(:prec:=14)
    chi := MakeCharacter_6024_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_6024_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_6024_2_a_o( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6024_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-416, -912, 10776, -8040, -25196, 20277, 16575, -9662, -4890, 1667, 679, -119, -43, 3, 1]>,<7,R![-107648, 344608, -292612, -127612, 289347, -67264, -74200, 34347, 6000, -5155, 105, 318, -32, -7, 1]>],Snew);
    return Vf;
end function;