
// Make newform 6018.2.a.bb in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6018_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_6018_2_a_bb();".
// 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_6018_2_a_bb();".
// 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 := [128, -6856, 29944, 16472, -44478, -838, 17621, -2260, -2773, 540, 179, -41, -4, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1768227501996184, 20860161005825920, 37358751314234452, -21507116682985566, -32386874868109258, 6716883469612343, 9899380051264956, -922973188703411, -1346976232371876, 60295853640717, 81660319298773, -1489108919712, -1796388205553], [-2559670711426040, -15147039293522512, 122348683101464684, 86711893064448398, -141537061577422086, -46501901494687967, 49539905362356236, 8262582263045907, -7291775225900956, -550253809975141, 459309915620523, 12143449436408, -10253913982431], [191018910747970, 7953201992223538, -27309473007286086, -28641901734087195, 34437813698810893, 14674795233528832, -12435310500957227, -2577999496689658, 1859746846457838, 172279045954540, -118025134245614, -3844423118131, 2643124952245], [558668664048170, -10497946895775678, 25008787374956530, 31982336352673793, -34425778503897719, -15728312750603394, 12817031913020937, 2711523524200234, -1946700518875936, -179172235132576, 124624713157090, 3962699821337, -2806630645981], [1161596938398896, -48634450370623920, 94078149732007496, 138168015452056174, -133463695266617588, -66799597776713869, 50713678365610526, 11452358170544105, -7810944784378346, -755378470856885, 504336575792465, 16698434980110, -11419786805749], [990949223000480, 9206122997578932, -63294691908648740, -50745708591403802, 76513736980135184, 26705214956593781, -27429895945466362, -4701200261840201, 4094961906303710, 311196222902321, -260080147076221, -6831410905550, 5836486040157], [228430125895582, -14039929218321888, 34418056162936816, 40631636419194187, -45999555735978216, -19652933906266972, 17159458829299488, 3357195618452128, -2617125025528437, -219681987395845, 168177451801958, 4801952864360, -3800074510933], [927871747678256, -46826258636980632, 155400440504302388, 160388343465178226, -199066645616036446, -80202504730163387, 72691678822176548, 13885279897829999, -10951008089524496, -915337629159613, 698648560224535, 20121588852528, -15713129420919], [-7276871383436880, 152599535884229776, -471173372993526552, -513197597392377970, 611770516475666996, 256417255003978799, -224213390202227058, -44446314428220947, 33840530175307542, 2937658850521943, -2160793904265883, -64814272554394, 48613352793023], [497584607825056, 200744255133819480, -1027333801147935896, -904590081886303550, 1277245628332544140, 471078241980980913, -461116336742527902, -82857036982229621, 69064662601312658, 5495632108851737, -4393285532037869, -121059374370454, 98658980574257], [7990135291149864, -313510477401767040, 1135181228111546144, 1152338156086936082, -1450584604586481880, -585411706046996443, 529363065829535614, 102183142140723143, -79766880804874594, -6771601944160655, 5090085024310823, 149510059488566, -114490409117923]];
    Rf_basisdens := [1, 1, 689049844074136, 689049844074136, 172262461018534, 172262461018534, 689049844074136, 344524922037068, 172262461018534, 689049844074136, 689049844074136, 689049844074136, 689049844074136];
    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_6018_a();"
function MakeCharacter_6018_a()
    N := 6018;
    order := 1;
    char_gens := [4013, 1771, 1123];
    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_6018_a_Hecke(Kf)
    return MakeCharacter_6018_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 := [[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, 1, 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, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -1, 0, 1, 0, 0, -1, 0, 0], [0, 1, 0, -1, 1, 1, -1, -1, 0, 0, 0, 0, 1], [2, -2, -1, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0], [-1, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0], [1, 1, -1, 1, 2, 1, -1, -1, -1, 0, 2, 0, 1], [3, 0, -1, 1, 2, 1, -1, 0, -1, 0, 1, 0, 1], [1, 1, 1, 0, 0, 2, 0, -1, -1, 1, 0, 1, -1], [1, 1, 1, 0, -1, 1, 0, -1, 0, 1, 0, 0, -2], [1, -2, -1, 0, -2, -2, 0, 2, 1, 0, -1, 0, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, 1, 2, 1, 1, -1, -2, 2, 1, 0, 0], [3, -1, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, -2], [1, -1, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1], [-1, -1, -1, 1, 0, -1, -1, 1, 1, -2, -1, 0, 1], [-2, 1, -2, 0, 1, 1, -3, 0, -1, -2, 0, 0, 1], [1, -2, 1, -1, -1, 0, 0, 2, 1, 0, -2, 0, -1], [1, 0, 2, 0, -1, -1, 1, 1, 1, 2, 1, -1, 0], [0, 1, 1, -1, 1, 1, -1, -1, -1, 0, 1, 0, 1], [5, -2, 1, 0, 1, 0, 0, 1, 1, -1, 0, 0, 0], [-4, 1, 2, 1, -2, -2, 1, 2, 1, 2, 0, -1, 0], [2, 2, -1, 0, 2, 1, -1, -1, -2, 1, 0, 0, 2], [2, -1, -3, 2, 1, 2, -1, 0, -1, 1, 1, -1, -1], [1, -2, -2, 1, 1, -1, 1, 0, 0, 1, -1, 0, 0], [2, 1, -1, 0, 0, 2, -1, -1, 0, 1, 2, 0, 1], [-2, -1, 1, -3, -4, -1, -1, 2, 0, 0, -3, -1, -1], [1, -1, -1, 0, 1, -1, 2, -1, 0, 1, 0, 0, -2], [-4, 1, -1, 1, -1, -3, 0, -1, 1, 2, 0, -1, 1], [2, 1, 1, -2, 1, 1, 1, -3, 1, 1, -2, 1, 0], [-2, 0, 0, 2, -1, -2, 2, 1, 0, 1, -1, 0, -1], [-3, -3, -3, 2, -3, -2, 0, 0, 0, -2, -1, -2, -1], [2, 1, 4, -2, -1, 1, 0, 1, 1, 0, 0, 1, 1], [2, 0, 3, -2, 1, 1, 1, 1, 0, 1, 2, 0, 1], [-2, -1, 3, -2, -4, 0, 0, 0, 2, -1, 0, 1, -1], [-2, -2, -2, 2, -1, -1, 0, 0, 1, 0, 0, 0, 1], [-3, 6, 4, 1, 1, 1, 0, -1, 0, 3, 1, 1, 2], [2, -2, -1, -1, 1, 2, 1, -2, 0, 2, 0, 2, -1], [0, -3, 2, 1, -5, -4, 3, 3, 3, -1, -1, 1, -3], [-1, 1, 1, -2, 1, -1, 0, -1, 0, -1, 1, -1, 0], [-4, -2, -3, -2, 0, -3, -3, 0, 0, -4, -3, 0, 2], [-1, -1, -1, 3, -3, 1, -2, 1, 0, -2, -1, 0, -1], [-2, 3, 2, -1, -1, 0, 3, -1, -1, 3, -1, 1, -1], [3, 0, 1, 0, 3, 0, 2, -2, -1, 3, 3, -1, 0], [3, 0, 2, -4, 1, -2, 2, -1, 1, 3, -2, 1, -1], [-2, 0, 1, -1, 3, 2, 0, -4, -1, 0, 3, 1, 2], [-4, 4, -1, 0, 2, 0, -2, -1, -1, -1, 1, -1, 2], [-4, 0, 0, 0, -4, -4, 0, 3, 1, 0, -1, 0, -3], [-1, -2, -3, 1, 0, -2, 0, 0, -1, -4, -1, -1, 0], [1, 4, 0, 5, -1, -1, 0, -1, -2, 1, 1, 1, 2], [5, -3, 0, 0, 0, 2, -3, 3, -1, -3, -1, 0, 0], [3, 1, 2, 1, 0, 1, -1, -1, 2, -2, 0, 0, 1], [2, -1, 1, 1, 2, 0, 4, -2, 0, 2, 3, 1, 0], [2, 1, 2, 0, -3, -2, 0, 1, 0, 1, -1, 2, 1], [2, -2, 3, 0, -1, -4, 3, 1, 3, 3, 2, 0, 1], [-7, -3, -5, 3, 0, -4, 2, -1, 1, -2, -3, -2, 0], [8, 0, 4, 2, 0, -1, 4, -2, -1, 2, 2, 2, 0], [0, -1, 1, -3, 1, 5, 1, -1, 3, 0, -1, 0, -1], [-1, -2, 0, -3, -5, -2, 1, 3, 2, -1, -2, -2, -3], [-5, -1, 0, 2, 1, -2, 2, 3, -1, -2, -2, -1, 1], [2, -6, -2, 1, 1, -2, 0, 3, 1, -3, 0, -3, -1], [4, -4, -2, -4, -1, 1, -1, 1, 1, 0, 2, -1, -3], [3, -3, 2, -2, -2, -1, 3, -1, 3, -2, -1, 0, 1], [2, -5, -1, -4, -3, 1, 0, 1, 0, -3, -1, 0, -1], [-7, 2, -3, 1, 2, 2, -3, -1, 1, 1, 4, -1, 2], [2, -2, -5, 0, -2, -2, -3, 3, 1, -1, -1, -1, 0], [3, 6, 1, 0, 2, 5, 0, -6, -4, 4, 2, 1, -1], [2, -1, 3, -1, -2, -1, 6, 1, 0, 2, 0, 1, -1], [-1, 4, 4, -1, 2, 4, -2, -3, 0, 1, 5, -1, 4], [-1, 3, 0, -1, 3, 0, -5, -3, 2, -1, 2, 0, 3], [5, -3, 2, 3, 1, -1, 5, 2, -1, 2, -3, 3, -1], [5, -1, 3, 0, -3, 4, 1, -1, 2, 1, -1, 1, -1], [-5, 5, 0, 0, 3, -1, 0, -1, -4, 0, -4, 1, 3], [5, 2, 2, 3, -1, -1, 0, 3, -4, -1, -1, -1, 2], [-5, 2, 3, -2, 0, -1, 1, -3, 0, 1, -1, 3, -1], [0, 3, 3, 1, -3, 1, -2, 3, -1, -2, 0, -1, -1], [4, 6, 2, 1, 6, 7, 1, -6, -4, 4, 4, 1, 0], [-4, 3, 0, 0, 0, -1, 1, 0, -1, 3, 1, 0, 2], [1, 4, -3, -3, 4, 5, -3, -1, -2, -2, 0, -2, 0], [-5, 5, 4, -3, -5, 0, 5, -3, -1, 7, 0, -1, -4], [6, 5, 5, 1, 5, 7, 2, -2, -3, 2, 3, 1, 3], [1, 2, 5, 1, 1, -2, 3, -2, 0, 0, -1, 1, 2], [-6, -4, -7, 3, -1, -4, -1, 4, 0, -4, 0, 0, -1], [2, 7, 2, -2, 3, 5, 1, -5, -4, 3, 2, 1, 0], [-4, -3, 3, -2, -1, 0, -3, 1, 2, -1, 0, -1, -2], [-1, 0, 1, 0, -4, -3, -2, 0, 0, -1, -1, -2, -3], [-6, -3, 1, -5, -2, 3, 1, 0, 2, -2, -4, 0, -1], [-3, 6, 5, -2, -5, 0, 1, 4, -2, 2, -2, -2, -3], [0, 2, 0, -1, -1, 5, -3, -1, -2, -1, 3, -1, 1], [2, -2, 0, 0, 5, 3, 2, -2, -3, -2, 0, 1, 3], [-4, 4, 4, -2, -2, -4, 2, 2, 2, -1, -4, 0, 0], [11, -3, -3, 0, 2, 0, -1, 3, 1, -3, 1, 1, 1], [10, 2, 1, 6, 6, 4, 2, -1, -4, 3, 4, 2, 1], [-5, -3, -6, 0, 4, 5, -5, 0, -1, -4, 2, -2, 1], [-2, 0, -1, -6, 4, 6, -2, 0, 2, -1, 0, -1, -3], [7, 0, 1, 3, -1, 2, 3, -2, -1, 0, 1, 3, 1], [3, -1, -1, -1, -3, 0, 1, 4, 3, 0, 3, -1, 1], [5, 0, 2, 1, 0, 2, 6, 2, -2, 3, -2, 1, -4], [5, -6, -1, -1, 5, -1, 1, -4, 1, 0, 2, 2, 0], [3, 2, 0, 4, 2, 4, 3, -3, -4, 4, 1, 2, -1], [-3, -2, 4, -5, -12, -6, 3, 4, 5, 1, -3, -1, -3], [-5, -4, 2, -1, -8, 0, 3, 0, 1, 3, -1, -2, -7], [-4, 7, -1, 2, 4, 2, -4, -5, 1, -1, 5, -1, 4], [-3, 1, -5, 5, 5, -3, -4, 3, 2, -3, 0, -1, 3], [-14, 1, -2, -2, -3, -4, -2, 3, 4, -2, -3, -3, -1], [2, -5, 2, 1, 1, 3, 1, 0, 1, 0, 3, 2, 2], [-6, 1, 4, -2, 1, 1, 2, -1, 1, 5, 1, -2, -3], [2, 3, 4, -1, -2, 0, 5, -1, -3, 1, -4, 2, -4], [7, -1, 7, -1, 0, 4, 4, -2, -1, 4, 4, 2, 0], [-1, 0, 4, -2, -3, 5, 3, 0, 4, 0, 0, 0, -3], [-9, 3, 0, -2, -4, 3, -4, -2, -5, 2, 1, -1, 1], [-2, -1, -5, -2, 0, -3, -5, 1, -1, 1, -3, -3, 1], [2, 4, 1, 2, 4, 4, 2, -2, -1, 0, 2, 2, -2], [6, 1, 5, 1, -1, 0, 5, 0, 4, 2, -2, 2, -1], [4, -1, 0, -1, 4, -1, -1, -3, 2, -5, -1, 3, 6], [-2, 2, -2, 1, 4, 3, 0, 1, 0, 3, 7, -1, 2], [1, -3, -4, 3, 0, 1, -4, 2, 1, -3, 2, -1, 0], [-8, 3, -2, -1, 2, -4, 1, 1, 1, -1, 1, -2, 0], [-2, 8, 0, 3, 10, 6, -1, -7, -2, 1, 9, 1, 5], [-5, 3, 3, -4, -2, -2, 3, -2, 1, 1, -4, 3, -1], [6, 4, 2, 1, 4, 1, -2, -3, -4, 3, -1, -1, 4], [-3, -1, 1, -1, 3, 3, 2, -4, -1, -2, 2, 2, 2], [-2, 7, 2, 4, 2, -1, 4, -3, 2, 6, 1, 2, -1], [1, -4, -5, 1, 2, 1, 0, -2, -2, -2, 0, 0, 4], [-5, -1, 1, -1, 2, -2, 0, 4, 1, -2, -4, 0, -2], [-8, 5, -5, 1, 0, -3, 0, -2, -3, 2, -2, -2, 0], [-7, -6, -3, 6, -10, -6, 0, 9, 4, -3, -4, -2, -6], [-14, 1, 0, 2, 1, -1, -1, 3, 2, 4, 4, -1, 0], [-2, -1, 0, 0, 1, 3, 0, -4, -2, 0, 5, 1, 4], [-2, 8, 5, -2, -3, 0, -4, -1, 2, 1, 1, -1, -2], [-10, -2, -1, 4, -5, -4, -1, -3, 3, -5, -2, 0, 1], [-8, 3, 0, 4, 0, -5, 3, 4, 0, 6, -1, 1, -1], [0, -3, -1, -1, -5, -3, -2, 5, 0, 2, 2, -2, -2], [8, 2, -1, -3, -1, 3, 5, -2, -1, 4, -1, 1, -5], [13, 2, -4, 5, 1, 1, -2, -3, 0, 1, 3, -1, 2], [-14, 1, 3, 5, 1, 1, -3, -1, 1, -6, 1, 0, 7], [3, -1, 2, -1, -8, -5, -4, 5, 5, -6, 1, -3, 0], [5, -1, 6, -1, 6, 6, 3, 0, -2, 5, 1, 2, 0], [-4, 9, 2, 6, -2, 7, 0, -4, -4, 2, 4, 0, 3], [-2, -5, -2, 3, -6, -7, 6, 3, 3, -1, 0, -1, -3], [-7, -1, -5, 3, 5, -1, -5, 5, 1, -4, 2, -1, 2], [-2, 11, 5, -1, 6, 8, 1, -6, -1, 2, 8, 0, 5], [3, 1, 3, -4, -3, -1, -2, -3, 2, -3, 0, 2, 4], [5, -14, -9, 1, 0, 6, -4, 2, 1, -4, 1, 1, -2], [-1, -3, -6, 5, -8, -5, 0, 5, 3, -3, -5, -3, -4], [8, 4, 0, 6, 6, 6, -3, -3, -4, 1, 8, 1, 6], [-3, 1, -4, 5, -4, -1, -1, -1, -2, -3, -4, 0, -1], [5, -10, -11, 1, 1, -2, -1, 2, 0, -6, -1, 1, 0], [-7, 3, 7, 3, -6, 0, 4, 4, -2, 3, 0, -1, 1], [-7, -5, 5, -4, -5, -6, 0, 6, 4, 1, 0, -1, 1], [4, 6, 6, -2, -2, 5, 0, -2, 1, 4, 2, 2, 0], [-17, 0, 2, 0, 3, 1, 3, 0, 2, 0, -1, 1, -1], [-6, -1, 5, -2, -6, -4, 2, -3, 3, 1, -7, 1, -8], [-1, 5, -1, 2, 1, -1, -1, -3, -5, -3, -3, -1, 1], [-3, 6, -2, 4, 9, 7, -1, -2, -4, -1, 6, -4, 5], [-2, 2, -3, 1, 6, 1, 1, -4, -5, 0, 0, 0, 2], [-10, 7, 8, -4, -7, -2, 4, -4, 1, 8, -4, 2, -2], [-5, -7, -6, 5, 0, -2, -3, -4, -2, -4, -3, 0, -4], [2, -2, -5, -5, 4, 1, -5, 6, -3, -8, 0, -1, 2], [13, -1, -2, 1, 1, 0, 0, -1, -2, -1, -1, 2, 1], [-12, -2, 2, -1, 2, -3, -2, 1, -2, -2, 3, 1, 4], [0, -4, -4, -3, -2, -5, -3, -2, 4, -5, -4, 1, -2], [-3, 1, 3, -2, -3, -3, -4, 4, 1, -2, -3, 4, 1], [-14, 0, -3, -4, -3, 2, 1, 4, 0, 1, -1, -2, -8], [8, 6, 11, -1, -1, -2, 6, -1, -4, 6, -4, 1, 3], [19, 6, 10, -1, 0, 6, 6, -7, -8, 5, 1, 3, 0], [-10, -1, 4, -2, 1, 9, 1, -5, -4, 1, -2, 1, 0], [0, 7, -5, 4, 6, 5, -3, 1, -3, -3, 2, -2, 5], [12, -4, -8, 0, 2, 2, 2, -2, -4, 2, -4, 0, -2], [4, -4, -5, 1, 9, 2, -3, -2, 0, 2, 8, 0, 3], [-2, -4, 4, 3, -2, -6, 7, 3, 2, 3, -3, 0, -3], [-5, -4, -1, -3, 2, -1, -2, 1, 3, -2, -1, -4, -5], [5, 6, 5, -2, 4, 7, -4, -5, -3, -4, 2, 2, 2], [-3, 4, 6, 3, -5, 5, 3, 1, -3, 5, 0, 2, -7], [-11, 3, -2, -5, 0, 10, -6, -3, -4, -3, -2, 0, -2], [3, 0, -3, 4, 6, -3, -4, -7, -1, -1, 4, -2, 8], [-4, 0, 4, -7, 5, 5, 1, -1, -1, 1, 1, 1, 2], [3, -7, -11, 3, 0, -1, -6, 3, -1, -6, 1, -4, -1], [-1, -9, -4, 6, 2, -13, 2, 6, 4, -2, -1, -1, 0], [8, 0, -5, 2, 3, 2, 0, -6, -5, 2, 3, 0, 3], [7, -7, -7, 2, -3, -2, 3, 1, 6, -1, 4, -2, -3], [-8, -7, 0, 0, 1, -5, 2, 9, 1, -4, -3, -2, 5], [-8, 4, 3, 7, 5, 3, -2, -2, -4, 2, 6, 2, 2], [-6, 0, -3, 6, -5, -8, -1, 4, 1, -1, -1, -4, -1], [-1, -11, -4, -7, -3, -4, 2, 5, 7, -2, -3, -3, -2], [0, -3, -4, -4, 4, -3, -6, 5, 7, -8, 1, -1, 8], [-1, -8, -10, 3, -3, 1, -1, 1, 1, -9, 0, 0, -1], [-5, -11, 3, 2, -4, -4, 1, 3, 2, -3, -1, -2, 2], [5, -4, 5, -1, -2, -8, 7, 7, 3, -1, -6, 1, 4], [2, -2, 2, -3, 4, 2, 2, -5, -1, 1, 4, -2, 2], [-10, 0, -6, -1, 2, 6, -6, -5, -5, 1, 8, 0, -2], [9, -4, 1, -2, 4, 9, 0, -1, -5, -5, 4, 2, 0], [10, -5, 2, -6, 3, 5, 0, -1, -1, 4, 1, 0, -3], [17, 0, 8, -1, -1, -1, 4, 1, 0, 7, 1, -1, -4], [10, 8, 0, 3, 4, 4, -2, -1, -3, 7, 2, 2, 2], [12, -1, -5, 1, 3, 0, -4, 2, 1, -2, -5, -1, -4], [-7, -2, -3, -6, 1, 0, -4, -3, 5, -3, -2, 0, 2], [-3, 5, 10, -2, -10, -6, 6, 4, 5, 6, -6, 0, -4], [14, -1, 1, -3, 0, -6, 7, 0, -1, 6, -2, 0, -7], [8, 4, -7, 2, 4, 1, -1, 1, -3, 1, 2, 2, 9], [3, -9, 6, -10, -13, -6, 2, 2, 7, 2, -5, 0, -3], [-10, -3, 4, 1, 3, -1, 2, 5, 5, -7, -2, 2, 10], [-2, -9, -10, 4, -2, -5, -4, 3, 5, -2, -3, 0, -2], [-3, -9, -4, -6, -4, -5, -11, 8, 3, -8, -4, -4, 1], [-1, -15, -10, 3, -5, -6, -2, 5, 3, -9, -1, -3, -4], [8, 8, 8, 0, -4, -3, 7, -5, -1, 10, -1, -2, -2], [6, 1, 8, -3, 1, 11, 6, -2, 0, 8, 5, 4, -3], [-9, 12, 6, 7, 5, -5, 4, -4, -1, 6, 6, 1, 7], [-11, 8, 2, 0, 4, 0, -1, 0, 0, 2, 4, 0, 5], [18, 4, 2, 8, 6, 1, 4, -2, -5, 4, 4, 0, 2], [7, -8, 8, -7, -1, 5, 3, 2, 5, 1, -1, 4, -3], [-11, -8, -1, -2, -8, 1, -1, -5, 2, -5, 1, -3, -1], [-5, -4, 3, -4, -6, -5, 3, 7, 6, 5, -1, -1, 1], [4, -2, -1, 3, 2, 3, -3, -1, 2, 0, 7, 1, -1], [9, 12, 5, 0, 4, 6, 1, -12, -6, 0, 8, 5, 8], [-10, -9, -8, -3, 1, -13, 1, 2, 5, 0, -2, -3, -2], [-1, 9, -1, -5, 1, 2, -4, 3, -5, -2, 1, -4, 3], [14, -6, -1, -3, 3, -2, -4, 4, 1, -6, -5, -4, 2], [-17, 1, 4, -1, -5, 4, -2, 3, -3, -3, 1, 1, -4], [6, -4, -4, -6, -7, -3, -8, 8, 3, -8, -8, -6, -3], [-5, -4, 0, -1, -1, 0, -7, 2, -3, -6, 1, 0, 4], [-9, 0, -8, 4, 2, -2, -2, -6, -2, -2, 5, 0, 1], [5, 2, 1, 9, -2, -3, 6, -4, -2, 1, 4, 6, 4], [-7, 3, -3, 5, -8, -5, 5, 3, 4, 3, 2, -1, -4], [1, -7, -4, 1, -3, -8, 5, -1, 5, 5, -4, 0, -4], [1, -7, 7, -3, -9, -8, 5, 3, 10, -1, -10, -1, -2], [-15, 0, -6, -2, -4, -2, -4, 1, -1, -4, -2, -1, 4], [-5, -6, 1, -3, -6, -4, 2, 9, 0, 3, -5, 0, -5], [-1, -2, -14, 0, 1, -5, -10, 2, 2, -10, -3, -1, 3], [16, -3, 4, -4, -2, 3, 1, 6, -1, 0, 1, 4, -2], [-2, -5, -9, 4, 6, 2, -2, 0, 2, -2, 3, -2, -1], [-17, 0, -4, 2, -2, -8, 0, 3, 6, -2, -4, -1, 1], [-9, 1, 6, -4, -12, -5, 0, 0, 4, -3, -1, -1, 0], [-9, -6, 2, -7, -7, -4, -6, 4, 2, -5, -7, -2, 3], [-12, 9, 2, 0, -7, -5, 6, -3, 1, 5, -3, 0, -5], [14, -4, -1, -3, 2, -3, 0, 2, 2, -2, -1, -3, -1], [-13, 2, 7, -1, -5, -2, 1, 10, 4, 2, -3, 2, 0], [-8, -2, 1, 10, -7, -6, 9, 7, 1, -1, -6, 0, -5], [29, -4, -8, 1, 10, 8, 1, -5, -9, 1, 0, 2, -1], [-1, 5, 3, 5, 8, 3, -2, 4, -5, -4, 1, -1, 3], [-1, 1, -3, 8, 7, 10, 2, -11, -3, 5, 8, 4, 2], [-5, -5, 2, 4, -2, -8, 7, 3, 3, 2, 3, 4, -2], [-1, 1, 3, -3, -5, -2, -1, -5, -2, -2, -1, 2, -6], [13, 3, 6, 1, 7, 8, -2, -3, -2, -1, 5, 5, 1], [1, -4, 1, 3, -9, -5, -4, 7, 6, -7, -1, 2, 5], [-1, 5, -3, 1, -1, 0, -2, -2, 0, 6, -3, 1, -6], [-5, -3, -10, 2, -2, -3, 2, -5, 1, -4, -4, -1, -7], [-17, 4, 2, -4, 1, 3, -3, -2, 6, -2, 4, 0, 5], [-4, -5, 1, -6, -12, -12, 7, 6, 5, 3, -3, -4, -6], [21, -1, 2, -1, -2, -2, -1, 4, -6, 0, -5, 0, -4], [1, 3, -14, 1, 7, -4, -9, 1, 1, -3, -4, -5, 0], [-26, 7, 4, 6, -7, -6, 1, 5, -1, 1, -8, 3, 0], [-12, 2, 6, 1, 0, 0, 1, 4, 5, 3, -2, 3, 4], [9, 3, 7, 2, 5, -7, 6, 1, 0, 8, 8, 0, 0], [13, 3, -2, 9, -9, -5, 1, 0, 3, -1, 0, -1, -3], [5, 10, -5, 11, 4, 10, -6, -7, -10, -2, 5, 0, 1], [9, 1, -3, 1, 2, -10, 1, 6, -1, -4, -7, 2, 2], [-7, 2, 1, -1, -8, -5, 1, -1, -2, 3, -6, 3, -4], [6, 1, -6, 5, 3, 0, 0, -2, 1, -6, -5, 0, -1], [10, 12, 6, 3, 4, 8, 2, -13, -2, 1, 4, 0, 3], [13, 4, 3, -2, 11, 8, 3, 1, -2, 7, 7, 1, 5], [-15, 13, 2, 1, 4, 2, -1, -5, -1, 7, 2, -4, 5], [15, -9, -8, 4, 2, 1, -8, 0, 3, -12, -3, 1, 3], [8, 1, 2, 0, 6, 9, 5, -8, -9, 6, 1, 6, 2], [30, 6, 2, 5, 0, 5, 6, -4, -9, 6, 5, -2, -3], [-8, 7, 5, 1, 10, 0, -3, -3, -2, 0, 2, 3, 6], [5, 5, 6, 1, 2, -1, 4, -8, -2, 5, 6, 5, 5], [12, 7, -1, -3, 2, 4, -5, -4, -1, -2, 6, 0, 1], [22, 9, 8, -2, 11, 18, 1, -4, -6, 4, 7, 1, 5], [-12, 10, -8, 3, 18, 8, -4, -9, -11, 1, 4, 1, 8], [-6, 1, 9, 6, -3, -2, 15, 3, 2, 13, 2, -1, -2], [-12, -1, -7, 1, -3, -5, 0, 0, -1, 0, -3, -2, -5], [13, -6, 11, -2, -9, 2, 9, 5, 4, 7, 3, 5, -5], [5, 14, 12, -1, -1, 3, 2, -3, -4, 11, 3, 7, 2], [8, 3, 6, 2, 2, 1, 10, -2, 3, 10, 10, -2, 4], [3, 6, 5, 4, -7, -7, 9, -2, -2, 6, -2, -1, -4], [-16, -2, 0, -4, -6, -3, 5, -3, -1, 6, -2, -1, -6], [-13, -5, 2, 8, -9, -2, 7, 3, 4, 4, -1, 0, -4], [5, 8, -6, -7, 7, 0, -5, -7, -4, -1, 0, 2, 9], [20, -14, 1, -1, -11, -10, 7, 11, 9, -4, -7, 2, -12], [2, 11, 13, -4, -4, 6, 6, -5, -7, 1, -1, -1, -4], [-2, 2, 5, 3, -4, 0, 3, -5, -5, -8, -8, 7, 3], [-1, 3, -4, -7, -8, -2, -2, -3, 2, -1, -1, -5, -6], [6, -5, 7, -6, -5, 6, 6, -4, -5, 4, -8, 5, -9], [13, 6, -1, 6, -2, -5, 8, 1, 1, 5, -4, 2, -4], [-9, 0, -3, -4, 8, 3, -3, 0, 1, 3, -4, 3, 2], [0, 3, 17, 3, -3, 5, 6, 2, 1, 0, -1, 5, 1], [0, -9, 4, -5, -7, -6, 1, 7, 5, -1, -9, -3, -5], [19, 8, 2, 2, 12, 10, -1, -11, -4, 12, 9, 5, -1], [1, -3, -12, 6, 4, 5, -6, 0, -4, -6, 1, -5, 0], [-9, -10, 2, 1, -9, -7, 1, 11, 3, -8, -6, -2, -5], [-11, 14, 3, 3, -2, -3, -2, -6, -8, 6, 0, 2, 0], [8, 5, 3, 10, 2, 3, 3, -6, -2, 0, 5, 6, 2], [15, -2, -10, 2, 4, 6, -3, 2, -3, 2, 6, -1, -2], [-8, -3, 0, -1, -5, -10, 7, 5, 9, 5, -1, -5, -1], [-6, 13, 2, -6, 8, 10, -11, -6, -4, 0, 2, 0, 4], [20, -11, -2, -2, 8, -1, 3, -2, 7, -6, 1, 2, 6], [7, 10, 6, -9, -7, -2, -3, 0, -3, 3, -9, -2, -2], [-16, -16, -9, 2, -8, -15, -2, 8, 6, -9, -10, 0, -4], [12, -2, 2, -3, 5, -5, 4, -4, 0, 1, -1, 0, 9], [1, 13, -1, 10, 14, 4, 8, -4, -3, 15, 13, 2, 3], [1, 2, -8, -8, -5, 6, -11, 2, 3, -10, -5, -3, -1], [-12, -16, 3, -12, -7, -2, 2, 2, 7, -3, -9, 2, -5], [8, -4, -16, 6, -4, -14, 0, 6, 4, -6, -2, -2, 0], [-4, -1, -8, 2, 5, -9, -10, 5, -1, -9, -7, 0, 3], [-11, -2, 5, -9, -10, -6, 5, 6, 8, -2, -13, -1, -9], [3, -3, 4, -6, -1, 5, 0, 0, 0, -4, 3, -2, -5], [15, 15, 1, 5, 0, 4, 7, -8, -6, 10, 1, 1, 1], [-17, -3, -3, -3, 5, -1, -3, 6, 8, 0, 7, 1, 1], [1, 9, -10, 9, 1, 1, -4, -3, -5, -5, 3, -4, 3], [-10, 1, 1, -2, 6, 6, -1, -5, 0, -3, 2, 2, 9], [9, 3, -2, -3, 5, 12, -3, 9, -7, 1, 2, 0, -2], [0, -10, -3, 3, 9, -5, 1, 0, 3, -2, 2, 0, -1], [18, -2, -5, 2, 1, -2, -5, 4, -4, -5, -5, -2, 2], [34, 3, -1, -3, 0, 4, -3, 0, -7, 8, -6, 2, -9], [-4, -19, -8, 3, -13, -7, 5, 5, 0, -7, -2, -2, -3], [-9, -7, 3, 0, 2, 4, -5, 6, -5, -7, -8, 2, -3], [28, 11, 12, 4, 11, 9, 5, -7, -4, 7, 6, 3, 10], [-14, -9, -12, -1, -3, -4, -1, 9, -1, -1, -5, -1, -5], [-14, 1, -2, 4, 6, 7, -11, 0, -5, -6, -3, 2, 0], [8, -3, -5, 1, 14, 4, -5, 2, 3, -2, 0, 2, 1], [-10, 2, 8, 0, 4, 6, -1, -5, 6, 0, 4, 1, 6], [9, 12, -5, -3, 12, 3, -2, -4, -10, 2, -2, -2, 4], [-1, -7, 2, -6, 7, 8, -2, -1, 2, 2, -2, 0, -2], [-14, 3, 4, -6, -1, 6, -1, 2, -4, -1, -5, 3, 3], [-12, -15, -10, -3, -1, -5, -5, 6, 3, -13, -4, -5, 0], [29, -2, -5, -1, 10, 7, -1, -7, 4, 0, 4, 1, 2], [7, 5, -2, 5, 10, 16, -3, -6, -8, -1, 13, 6, 4], [-1, -4, 4, -5, -8, -10, 5, 5, 5, -3, -6, 2, 3], [-8, -6, -2, 8, 1, -13, 5, 4, 2, -4, 1, 0, 0], [8, -3, -5, 12, -3, -3, -3, 9, -1, 1, 2, -2, 2], [10, -9, -4, -4, -14, -9, 1, 14, 4, 0, -1, -3, -1], [18, -9, -14, 8, 19, 8, 0, 4, -7, -4, 10, 0, 6], [-5, 3, 10, 1, -6, -5, 12, 2, 0, 3, -6, -2, -3], [6, 2, 5, -1, -1, 0, 6, 2, 7, 12, 3, 1, 0], [-10, 4, 10, -1, -13, -1, 5, -7, 1, 7, -5, 0, -4], [4, 2, 0, 4, 4, -4, 2, 1, 4, 2, -3, -2, 0], [14, 8, 2, 13, 8, 4, 2, 1, -5, 10, 0, 4, -4], [9, 2, 2, -3, 7, 7, -3, -5, 7, -5, -5, 3, 1], [17, -9, -1, -7, 4, -8, 2, 4, 5, 6, -4, 2, 0], [33, -3, 3, 2, 1, 3, 4, -6, -3, 5, -1, 4, -5], [-24, -9, -11, -1, 3, -6, -13, 3, 2, -6, 5, -7, -1], [11, -7, -9, 5, 7, 1, -7, 6, -2, -2, 5, 5, 5], [-13, 7, 3, -3, -5, 2, 3, 0, -3, 5, 4, 0, -1], [-23, 2, -5, -5, -10, 1, -7, 8, -1, -5, -9, -1, 3], [-5, 17, 2, 0, 11, 6, -4, -4, -8, -4, 3, -1, 10], [23, 8, -6, 10, 7, 11, 0, -2, -11, 8, 3, 1, -2], [26, 8, 4, 3, 20, 13, 4, -13, -10, 5, 10, 4, 4], [-5, -21, -4, -4, -10, -4, -5, 7, 1, -8, -11, -2, -6], [11, -8, -3, -5, 13, 10, -3, -6, 2, 0, 5, 0, 4], [2, -6, -12, -7, -5, -3, -15, 15, 1, -13, -7, -6, -2], [-17, -17, -13, -5, -7, -13, -7, 8, 6, -10, -7, -1, -1], [-18, -19, -6, 10, -9, -12, 0, 12, 7, -6, 0, 0, -2], [-2, -4, -7, 6, 5, 2, -7, -1, 6, -3, 4, 0, 4], [-21, -16, -11, 1, 4, -1, -5, 6, 3, -6, 4, -2, 3], [-6, -2, 9, -3, -2, 2, 7, -3, 3, 0, 7, 1, 9], [25, -7, -2, 4, -6, -1, -1, 4, 2, 2, -8, 0, -8], [3, 13, -7, 5, 12, -1, -5, -3, -1, 3, 12, -2, 5], [12, -4, 0, 1, -8, -3, 1, -2, -4, -5, -7, 0, 2], [0, -3, -10, 1, 2, 7, -8, -4, -8, -3, -3, 0, -4], [19, -1, -9, 4, 3, 1, -3, -5, 1, -3, 1, -1, -7], [0, 9, 12, 2, -1, -6, 8, -10, 3, 13, 4, 6, 8], [-2, -3, -18, 7, -1, -10, -4, -1, 4, 3, 2, -2, -2], [2, 1, 7, 1, -16, 2, -1, 1, -1, 6, 1, -4, -9], [-9, 0, 5, -2, -15, -6, 2, 1, 8, -3, 4, 1, 3], [-3, -2, 4, -1, -3, 3, 2, -6, 1, 3, -2, 1, -9], [7, 2, 0, -19, 4, 0, -3, -3, 3, -2, -2, 0, -1], [7, 3, 8, -7, -6, -2, -2, 4, 5, -2, -4, 1, -3], [-20, -6, 1, 9, -4, 0, -1, 3, -1, -7, 5, 1, 3], [11, 0, -2, 9, -9, -5, 2, 4, 1, 4, -2, -3, -13], [-1, -2, -1, -12, 5, -8, -6, -3, 6, -5, -4, 3, 9], [-12, 2, -7, 4, 9, -9, -2, 6, -2, 3, 7, -4, 5], [-9, -1, -11, 6, 7, -5, 5, -3, 1, -5, 3, -1, 3], [-11, 8, 4, -4, 9, 13, -2, -7, -10, -6, -2, 1, 11], [39, -5, -8, 13, 15, 4, -4, 4, -4, 1, 6, -3, 7], [9, -14, -9, 3, 14, 9, -10, 6, -2, -6, 11, -5, 8], [20, -3, 5, -4, -2, -12, 5, 4, 4, 5, -5, -2, -7], [5, 0, -4, 1, 6, 12, -4, -2, -3, -6, -2, 5, -3], [-19, 4, 9, 2, -16, -9, 6, 3, -3, 3, -8, 2, -2], [-10, -12, -10, -3, -20, -21, -8, 17, 8, -15, -9, -11, -4], [-8, -1, 13, -3, -7, 1, 9, -1, -1, -2, -7, 1, -9], [19, -3, 0, -2, 8, 9, -5, -4, 3, 2, 4, 2, 9], [10, -2, 9, -2, -14, -5, 6, -5, 4, 9, -9, 7, -12], [0, 6, 3, 1, 1, 5, 3, -5, 4, -2, 0, 5, 8], [5, 7, 16, -8, -2, 5, 5, -4, 1, 4, -4, 0, 1], [16, 0, 7, -8, 12, 10, 6, -2, -7, -9, 5, 0, 4], [6, 0, 8, 5, -14, -4, 7, 7, -6, 4, -5, -5, -5], [5, 4, 1, -2, -9, -8, 6, 4, 7, 7, 3, -2, -2], [27, 7, -11, 5, 15, 8, -1, -6, -9, 0, 12, -4, 3], [-21, -20, -3, -3, 0, -3, 0, 4, 4, -10, -6, 2, -4], [20, 11, 3, -5, 0, 0, 0, -1, -2, 6, -2, 5, 0], [7, 8, -5, 5, 2, -1, -4, -4, -12, 4, 6, -4, 2], [-4, 8, 4, -6, 2, 6, 4, -18, 0, 0, -6, 4, 0], [-6, 1, 15, -7, 4, 6, 4, -5, 1, -2, 0, 3, 5], [29, 13, 10, 7, -4, 8, 7, 2, -8, 10, 1, -2, -2], [-8, -18, -7, -6, -7, -4, -3, 0, 0, -16, -9, 4, 4], [12, -14, 5, -7, -13, 0, 3, 1, 3, 0, -7, 1, -16], [37, -2, 0, 3, 13, 9, 7, -9, 1, 7, 6, 4, -3], [8, -8, -20, -1, 12, -10, -12, 9, 8, -13, -2, -2, 7], [27, 6, -3, -6, 16, 14, -10, -8, -1, -4, 7, 0, 5], [-30, -8, -7, -1, -5, 3, -4, 9, -3, 2, -2, -3, -7], [-8, -4, 8, 0, -20, -13, 6, 13, 4, 7, -5, 2, -13], [3, 9, -7, -8, 5, 11, -10, -3, -8, -5, 0, 0, -2], [-5, 3, -6, 1, 0, -9, 0, -3, 3, 3, 1, -9, 4], [-9, 7, 5, 1, 2, 14, -5, -8, -7, 0, 3, -1, -6], [-17, 7, 3, -8, 13, 15, -4, -4, -3, -7, 5, 0, 7], [53, 6, 11, 0, 8, 2, 7, -1, -3, 7, -5, -1, 1], [15, 8, 1, 1, 3, 2, -6, -14, -3, 0, 0, 2, 1], [-12, 9, 2, -2, -8, -3, 1, -5, 2, 6, 0, -2, -5], [11, -23, -5, 0, -7, -9, 7, 14, 4, -11, -12, 0, -6], [-30, -8, -2, -3, -18, -14, -4, 13, 3, -9, -13, -7, -6], [23, 12, 17, -5, 5, 18, 8, -9, -12, 4, 1, 5, 2], [6, -4, 2, -2, -10, -1, -1, 1, -1, 0, -2, -3, -6], [-4, 13, -4, 2, -3, -4, 6, -3, 2, 6, 5, 4, 1], [11, 12, 6, -2, 12, 11, -6, -2, -1, 2, 11, 2, 9], [4, -4, -11, -2, -3, -2, -3, 3, 1, -7, -4, 2, -7], [-2, 6, 3, 6, -13, -16, 8, 4, 3, -2, -6, -1, 1], [-18, 6, -10, 7, 10, -3, 1, -7, -1, 9, 5, 3, 1], [14, 1, 2, 7, -10, -9, 11, -1, 2, 3, -1, 4, -4], [3, 4, -7, 1, 0, 1, -6, -8, 0, -6, 10, -2, 2], [20, -23, -4, -5, -15, -9, 8, 12, 6, -8, -9, 0, -5], [-27, -10, -12, -6, -18, -10, -9, 9, 9, -8, -15, -2, -10], [-21, 3, -13, 5, 7, 5, -5, -14, -3, -2, 1, -5, -2], [12, -7, -4, 5, -5, -6, -2, -9, 6, -5, 4, -2, 2], [28, 6, 14, 3, -2, -3, 13, -1, -3, 7, -1, 5, -3]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6018_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6018_2_a_bb();".
// 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_6018_2_a_bb(:prec:=13)
    chi := MakeCharacter_6018_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_6018_2_a_bb();".
// 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_6018_2_a_bb( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6018_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![128, -6856, 29944, 16472, -44478, -838, 17621, -2260, -2773, 540, 179, -41, -4, 1]>,<7,R![-48744, 115988, -21966, -173105, 192560, -53248, -30621, 22911, -2910, -1380, 420, -1, -11, 1]>],Snew);
    return Vf;
end function;