
// Make newform 289.10.a.b in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_289_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_289_10_a_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_289_10_a_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 := [-675998208, -243559296, -10388768, 2252056, 8252, -2986, -1, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [1595734267008, 249666517824, 9962276152, -962897524, -21966986, 479085, 8711], [1729601433216, 980540221248, -87332865896, -1085670148, 124232878, 292545, -41053], [7069845465216, 961758589248, -93593409896, -1085670148, 124232878, 292545, -41053], [113709524082048, 13251504106944, -1752000948088, -12878937644, 2465651834, 2902635, -843359], [-59384105783424, -8853358980672, 873469755944, 10192644772, -1224135742, -2816505, 419317]];
    Rf_basisdens := [1, 1, 3478080000, 6260544000, 6260544000, 31302720000, 10434240000];
    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_289_a();"
function MakeCharacter_289_a()
    N := 289;
    order := 1;
    char_gens := [3];
    v := [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_289_a_Hecke(Kf)
    return MakeCharacter_289_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 := 10;
    raw_aps := [[0, -1, 0, 0, 0, 0, 0], [-12, -2, 0, 0, 1, 0, 0], [-198, 26, 1, 1, 2, 0, 0], [-1358, 69, -3, 3, -14, -7, -6], [-19292, -206, -2, -2, 59, 36, -28], [23312, 2444, 15, -71, -306, -22, 22], [0, 0, 0, 0, 0, 0, 0], [110184, 8144, 100, 264, 46, 572, -572], [-190922, -26063, 203, 141, -246, -1815, -702], [-135550, -40114, -869, -1525, -10978, -1840, -904], [-507130, -6735, 3979, -411, -6272, 2957, 5722], [-2617230, 45102, -6105, -5441, 4266, 5648, 7352], [-1492278, 165676, -14290, 4594, 804, 5456, -7756], [3136628, 42186, 11144, -16112, 26088, 1334, 15140], [8171072, -451462, 1104, 31664, 93354, -12878, -26028], [17409274, -446976, 21210, 74926, -132416, 27436, 4764], [4338396, -1749298, -12644, -21988, -277836, -9518, 36004], [7146054, -586486, -65505, 60195, -41082, -58500, -11900], [43085328, 1297892, 26640, 3484, 610060, -70028, -2772], [-93694086, 1768777, 112733, 19755, -594476, -91999, 102202], [-43711854, -444796, -70496, -8708, 149704, 71740, 120844], [-136620946, -2802391, 11463, -200759, -449114, 119953, 38250], [-215742436, -1909818, 129096, 177744, 965128, -401926, -259028], [-280993836, -5328572, 228211, 51165, -1024942, 452218, 169898], [-289042294, 13616496, -129756, -524064, -834488, -960136, 23180], [-482811624, 6887884, -401249, -3335, -1447098, -847654, 253830], [526081032, 20563184, -122476, -248236, 1763376, 427624, 314720], [-100810576, 10432480, 317262, -476294, -2226097, -1024002, -61636], [-36987162, 15570734, -995099, 230969, -821858, 1118652, 280484], [-320538042, -21729808, 753582, -819018, -6970356, -1164756, 23928], [1884936788, 32512130, -1600846, -1955090, 4659332, -355974, -768292], [-988407224, 37095732, 722482, -318386, 9181727, 201474, -1344172], [-451187496, 60535420, -396349, 3746129, 11737602, -5101214, -184050], [-1565592764, 21142234, -582514, 1083150, 6778201, -2412688, -452396], [-633352874, 53306736, 961996, 4961804, -5367664, 4897592, 3144384], [615261788, 33803058, 1952970, -2830602, -24344832, -4058622, 819372], [3384772914, 120082652, -2103736, -581268, 15777668, 6154540, 5203884], [-8537941144, 74376916, 1433944, -2866420, 11911921, 9254730, 5936784], [1169031430, -77029317, -6053533, -5492619, -18964758, 7524639, -3984762], [-23144802, 162165346, 4251571, 8656655, 35927946, 8811940, 121876], [-3608541224, -264732872, -2341900, -12476152, 39072298, 15881148, 4825652], [961469926, 258083874, 9165535, -8459557, 6700146, -3520916, 9135916], [347799488, 39530718, 7704616, 22355848, 25364646, -5267338, -12424076], [280720090, 223329128, 14067694, 4664810, -31044708, -2927564, 9076588], [-1341839054, -447320742, -16831, 8341065, -17437978, -10122392, -1772064], [-6413983734, -204503933, -1417047, -10785625, -123285346, -2288437, -14025450], [-10398919816, 326445692, -21799614, 23653438, 18895577, 18233814, -232188], [-9986709956, 527040264, -11017454, -10699066, -87049894, 35153096, -6473680], [-13817536872, -779660364, -4745556, 30786336, -39134619, 24370218, -30303384], [-5944600236, 120393632, 6978811, -46285295, -225343306, 27967422, 21904034], [-5006018534, -1144474308, 17964266, 23819998, -135401380, 20001144, 49700452], [18006928120, -652616678, -20398880, 26151720, -7753082, -60044470, -40140380], [22176251102, -184554400, -14785686, -4846070, -164196500, 37150180, -3740016], [-27314940768, 856324388, -20419480, -67989076, 81247784, 10191788, 2386212], [-26652927156, 473627364, -25804703, 73112987, -39628690, 3158150, 8591122], [24746780252, -426311314, 60291970, -61071042, -72488096, -11785450, 32192100], [54230943534, -1283918330, -19790315, -78564079, -71742894, 41057500, 31533100], [-23000302224, -646194542, 60287988, -6507372, -356130162, -71238726, -3893236], [5643064642, 1413525390, -33337633, -11541561, 104874058, -89332624, -9528944], [17671858166, -666066264, -14055064, -61040396, 327671832, 80696312, 78855084], [-54838355876, 575528046, 1866722, -42228582, 202132615, 76994648, 47184604], [-25107178946, -1386546536, 12765388, -78506524, -313189912, -153662272, -50190600], [11227773428, 432147134, -56557920, -188870304, 207716834, 24434830, -55884780], [-45119776402, -320992685, 47486503, -140089727, 712959398, 34126071, 49426822], [-114211705730, -1332444028, 43345470, -83272394, -158882036, 131116552, 11324248], [31326341842, 1986110162, -102179435, -38624427, 12116042, -3889376, -106185224], [-12019248492, 4366454182, 62633964, -11871340, -35449828, 31391018, 62417836], [-57105268630, -2777480128, -17029712, 155952828, -856093888, 113950432, -158158004], [186045055168, -1340037872, -109699228, 96037992, -10139839, -76541546, -113902632], [36820245714, 4148409816, -19402638, 105695254, 104889080, -44832684, -251206164], [103130937118, 3403178376, 92361324, -69242856, 1279907656, 161876336, 181396508], [-125618340684, 2331002164, -144050698, -274867238, -221701170, -131985460, 148320632], [-51327921810, 7042182375, 163978159, 83640753, 1023572, 230980567, -49803138], [333505472184, 5893826908, -18379237, -8789131, -574853482, 316357826, -9075058], [55062273060, 3865995982, -142549084, 428935180, 507354921, -250647304, 23103720], [-34056581668, -10108067962, -73019118, -355081034, 40908792, 214446254, 67598588], [-28581535548, 2687299232, 173476067, 180835865, -2379693802, -21932770, -104524278], [74825547866, 5283837470, 37466019, 109746827, -97357814, 127653672, 349157272], [142551174038, 529352384, -200317998, -687826390, -267927268, -39118828, 168436680], [-102532402630, -4809719064, 206385664, -106609312, 236907320, 280884200, 724078864], [267982659116, 9612346098, 20434812, -180291564, -528752937, 359541048, 37734304], [397678755880, -7954321572, -232074101, -178853115, 1054376910, -548271918, -217767138], [144190682446, -6470651947, -31529721, 479857833, 1015010354, 115537549, -396427870], [129838208744, -10487216724, -426869755, 229862043, -2748470762, 13177670, 104272030], [-326068300630, -23245717623, -102536367, 239630111, 723085340, -304541431, -75596486], [87095430736, -19312325088, -257723740, 932589992, -1186126632, 271839304, -320208604], [203594533734, 2493303960, -186475336, 159335232, -1344122304, -390377736, 717739960], [227106024152, -2159969284, -279847995, -291458573, 451147598, -1139358618, -454887482], [329681195690, 2333717136, 429961210, -309905850, 2088968360, -353711924, 439225524], [234034435416, 3204084148, 127973560, -549274016, -142173592, -596015412, -665358688], [-657878360840, 3253159748, -436364472, -307743156, 788188022, 503402848, -483504460], [-251249810886, -7139544169, 43597617, -1199789033, 2749997074, 232685599, 862236598], [-839072614674, 11576723023, -286234545, -719726775, 1369731820, -881529697, -601323338], [-125489658792, -23095896648, -122263420, -1030691856, -1341348018, 90870276, -93648956], [134338968232, 2334339564, -747236802, -1876370102, 2551299213, 62885606, -208931708], [13780244174, 43144593695, 930709619, -723514179, 1883828776, -632723953, 1230964262], [-318391402490, -34511680064, -122681120, -934908600, 4639617504, 555917088, 1847761912], [-764373185718, 26926005556, 444356282, -521018306, 4212366820, 466847248, 339086084], [-320749163632, -46676627880, -603340672, 533604820, -2959347988, -428787216, -561924316], [-130319839842, -44714505806, 647885243, -618605929, -4754789102, -703564380, 1718297308], [-540301023624, -31707308084, 1209163842, 1549996718, -4863325213, -1370521054, 11295156], [-585615887696, 32002358452, -1424248061, -1475762115, -1263066778, -1048004582, -794698994], [-1342318649004, -15778072210, -662052400, -944566272, 8670857968, 1403319554, -227418404], [-1129133151418, -20512981104, -492625976, -969614524, -2594720992, -1906889344, -1233288052], [380376204084, -19566001946, -1677044764, 833019244, 5772538443, -1062187684, -2553369360], [-344984597184, 15736745900, 1049919891, -562790079, -3372504518, 1052999666, 1532162150], [-972147712800, -29005342984, 537694876, 2036460400, -4555387094, -2636708, 1288900764], [-438394185306, -14343461584, -2769589364, 2632046960, -2053228608, -2559957800, -1290611324], [850482584480, 2818855064, 2225837572, 739462556, 2257139060, 14171816, 1560425936], [335421672014, -60865016580, 485933804, 2273084900, 15770412144, -803964260, -1351669816], [-1685588908898, 26908788717, 918782803, 152531029, 5711639744, 478858065, 1421028738], [-1217644980522, -11904721744, 853096704, -262060496, 6455475136, -1626837392, -3760100544], [1338951056602, -5005459164, 1528203318, 711898410, 977511868, 35329208, 305342180], [-3321279687608, -61217286468, 595224628, 3022780624, -5617162787, 791378386, 836384712], [101345348140, -108318283364, 357779734, -792145134, -5073835810, -3123299660, -745905336], [-601280629430, -42369717312, -3151019240, 2868669300, 760464576, -3433537776, -1680598724], [661142430388, 8921406926, -512989412, 1220724524, 20246636169, 545317144, -1496877656], [3119455745384, 12299603782, -179223724, 755273748, -14095011518, -3058316578, -206394316], [192451846302, 14738778274, 1619817051, 3339682391, -22152890866, 1593746156, 321566420], [1507106519764, 25945783998, 340136228, -1292338860, 13591645974, 2114364558, 1383801420], [1108321423398, 71279720972, 2101024958, 2737972430, 6971510724, -3492979184, -510706048], [-1846912958114, 60592808208, 1530009436, -1529924612, -2072922016, 3393125784, 2171672832], [-639435335418, 7520562702, -1257515659, -3920044847, 114030670, -4979815412, -5557327372], [1359658225596, -107774588006, -2260771876, -5767322644, -9700222439, 601089948, 1588975416], [384431634732, -16211278690, -674706722, -3949002434, 4045258635, 2406647528, 4066676740], [-128640400256, -36679040692, -3633850821, -5847311547, 12055027862, -560494814, -2069257162], [1477282093294, -71796396654, -3144537797, 4997228511, -4152728266, 4121139244, -3956020516], [950146368714, -188732773855, -644920575, 78332999, 27589595940, -1376017439, -174678286], [2207204916240, 81500537222, -2998672848, -370001048, -11006537066, 5109183646, -424237764], [-1989956044674, -65085652620, 1022991034, 8480567610, 22045557596, 9744038560, -91153856], [-4015046875144, 67095174396, -732422436, -133274128, 588764294, -8300248000, -6578022316], [-4066934416258, 75664859933, -3873963657, -5233110495, 8512837428, 4705147953, -4309224950], [2957955344562, -109368448967, -2360680599, -111161721, 7043629360, 4327046225, -6192360014], [-863278575988, 304315906392, 1159633363, 4216426945, -10499502650, -7873349786, -2007671886], [-3366866653968, 20956276204, 2292781303, 8275796365, 20538890490, 4217504666, 1915373382], [-44229308152, 174502650572, 42939587, -3596336023, 40841820226, 6082549266, -39245754], [-1381875199404, 30064930032, -1718405925, -8869725743, -3934817162, 6690255022, 7461116578], [7084058245092, -76191391246, -4225020514, -5241409290, 33759284369, -4230110600, -1140282844], [645061534558, -24517473332, 451186730, -2519551094, -47981777260, 3475437432, -5844584432], [-1308290627518, -7298149868, -228864068, 4409863944, -36834732320, -7828262620, -11817173988], [4564828502216, -239837848996, 8539051928, -9059955548, 15280283467, -1586379314, 1373865232], [2322598271558, -102817938834, 8306920233, 8385297397, 15383587334, 14301576564, 11047108004], [-2976199482794, 158508581789, 2971900575, -7486096863, 6969884482, -6312465499, 10289860314], [-4635412639880, -260417932756, -732200834, 5918510450, -18093608015, -9184512498, -7371344796], [-6411137339246, -198444626500, 3518841568, -16047754460, -12302267308, -1974935268, 11836195036], [-6970194215694, -120683295303, 7755315777, -3325095065, -6387800534, 13590721069, 3677852338], [1077706362250, 167267742930, -2511514527, -9285447519, 10869330570, -18856450152, 5267785440], [-3134826639722, 227158110260, 2299401230, -1546832994, 32238162380, 23298612856, 14349204144], [-10866234351852, 104234676734, -928034104, 401300608, 27065821844, -23343917238, -7431471956], [6969433705768, 16166050176, 5756010784, 3883891464, 26951664916, -3608786056, -7567674200], [959298270126, -260981573402, 987525569, -11353334307, 47049343726, 834124748, 6864546236], [-13899020233862, 189032536312, 6647249072, 16108288044, -13781953384, 4257349816, -4169132724], [-1874852802176, -114261734480, -5661255156, 3606147656, 51421171760, -6281959528, 2316235212], [7051682413626, -32510222513, -6267506207, 3511816255, -104472461330, -2885427665, -2573310882], [9309184667604, 418322076162, -12953170490, 15146166726, 80893197835, -971768044, -14135198196], [-6790719043526, -341068801895, -3429935267, -10593131261, -46212222222, -10917511531, 335793914], [-9140497709456, 292541511034, -3361176288, 8370608072, 32584672046, 4728721226, -2817964884], [-14957491216338, -262028598392, 7706608698, 2517030170, -10955979220, 708538460, 20185671008], [-4851635688030, 87698993216, -2780540660, -17156942108, -50437907136, -9661962136, -7240940344], [-3297350257354, 291550743502, -7599404563, -26625959135, 27093365510, 101218668, -5115810996], [-1857765936252, 463727550282, -5671223090, 13973954214, -78063549183, -12747523680, -21666967660], [-13778478747316, -93299661748, -304662533, 4363326253, 104336041618, -31859645870, -5012622998], [20402476784972, 251155538012, -658099254, 11438174502, -55866169450, -38416610612, 12324119808], [-1529322791284, -420945331446, -21105833904, -17345967536, -42776432236, 21798840846, -16336178740], [-14964715215362, -372484924728, 1088253856, 7963567772, -129230220288, 4778849080, -5724653364], [-7876362446574, 569292409709, -26347536003, 15646318083, 24184207096, 17149444517, -7053648990], [-3191154905350, -412456236919, -1614692175, 10988220535, 189987438868, 17561055097, 5050811778], [-13645544519222, 83980310562, 5626078289, 10910119313, 83202526406, 14866890080, 20375675064], [-6431341452218, 596386012008, 6495859616, -19298321864, -76202809048, -22777423992, 3606801128], [7251486193166, 47937431154, 20299267295, 20986074691, -38316372966, 8349920492, 1957610628], [71761338476, -592279399222, -9126283708, 4178203348, -24723920906, 14831686162, -32694870420], [-17040415743192, 673174243988, -14060156113, -8751735519, -9394307442, -38289219102, -19568715666], [9474081924586, 479857722159, -5546294407, 11037287255, -7832663764, 40756165139, -24898578706], [-9369360406620, -786233552700, 20581839715, -15523734483, -45538906702, -17834871782, 13432957162], [562983551036, 186031054026, 21688198986, 2617023278, -37743298912, 25027332218, -3229286932], [-1012031037278, 377461795972, -4166427304, -23112943596, -20430742528, -47173698020, 3419440716], [675500858016, -704961089912, 16871551440, 1089280260, 5672735083, -24167632462, 21622742752], [889229780222, 1070934268026, 8036317119, -25673644733, -19819167910, -14569541340, 11506690004], [12440444081404, 950066346676, -7236990570, 382188978, 123645561458, -20088843500, 1480317400], [1556245639420, 162152309320, -26537097297, 11223321125, -61958238906, -37145443058, -23692663134], [17634212692288, 228913540672, 21092742060, -26318687380, 21011403128, 11952588344, 37415507856], [7061110358716, -182462673194, 44712621894, 31359251798, -45993036159, 20702677972, 13764195292], [29549652897086, -158290241446, 3922817603, 3292663559, -156990502818, 8454549940, 11219193908], [27844396682898, -270027793976, 6635623016, 47000663216, -129084259248, 8251196776, -1682078520], [9716038211092, 660269319962, -20981371414, 15110352006, 66937629560, 30846934522, -9183123516], [13472436128528, 82707060492, -22231726461, -46402943019, 129145398734, -25309396430, -31177220426], [-17137798746286, -615639688098, 24627902979, -31740684077, -3090545362, 30898407744, -8831955840], [32941982074884, -181186848478, 7355359684, -24629519020, -43999846450, 48900646010, 1004880324], [-22645383858478, -1101442448908, 159251424, 11977705596, -6603648648, 10963078668, -33350459044], [-50070204817618, 331671788781, 36455439719, 16974476537, -6875865960, -21222919463, -9036684878], [16341589590954, 576052740232, -14878601968, 16615508812, 110224372976, 51126119544, -9987070932], [-33533375031140, -544524085190, 5578652268, 8832648604, 210018432559, -19428269120, -44295399912], [5280471175496, -1131416086532, 5410021964, 28713748176, 341149214570, -36469503128, -60315441428], [-3871499797220, -476409927384, 21177193199, -10952390475, -46436558738, -36876153154, -18397424862], [-17455601435376, 129041138944, 46060525328, 69642741004, 39697633671, -51013653646, -10761020176], [9935238415678, -2714485482164, 4153417868, -21137857980, 284197572752, 26061433036, 15180606312], [32056574132178, 193936331392, -72285379706, -38028999062, 284519184244, -67399314596, -47272115180], [23845881101574, 275896252846, -56098204247, -67796220323, 61370170230, 21152399060, 22567188748], [-48831519733982, -550512307496, -15932396684, 29432888552, 49800921752, -65867779408, -45275569596], [-4367378704112, 1074565486996, -2940879772, 34382035068, 74777264300, -39538318340, 16465260408], [13902300039486, 624431519930, 50513151023, 5524135899, -373662355182, -7254846924, 1710230092], [-3451815624866, 1283607187965, -34232052293, 44724933709, 234025476670, 103809383941, -8684507214], [21987869211670, -1277254922072, -51723227196, 42318335716, -307476728024, 4153017664, -75928038400], [24946860365492, 537794058516, -9584294063, -71710075309, -97234137698, 102972525750, 76218162922], [7804284804196, 614746941738, 21706717940, -91700210244, -245026343418, 56203307874, 11467488876], [-26751496702660, -990107081288, 31153463807, -31426631739, 126904120726, -14430890050, 60419189282], [25151082116696, -1387870369032, -41473825228, -32771104468, -288153498084, -28607977976, 32491700088], [-5583355298320, 1496493838028, -10798446828, -9460929840, 64372076430, 9281872896, -31550055884], [34036036040578, -1490881195388, -52664674408, -55124421212, 405432606184, -5792616500, -37159308548], [18556554365260, 458888913290, -30732878368, 35311699056, 483289788070, 55729522442, 18538736180], [-7658894472574, 534324640304, 59548099356, 2653855616, -445372132000, 1794193208, 42721688548], [-53001039039324, 156065135912, -10436813637, -65606165807, -685533306146, 27507813190, 12594529858], [20846166559338, -632939715149, 8680307213, 92059004315, -164859345128, -89747303409, -5812228778], [-171309082528, -1369726729484, 34065795420, 41530585056, 114973090690, -70819375504, 52087416724], [7587965873674, 936141108875, -60785265835, -1896176781, -207286134940, -52620129329, -52213969146], [27644398399094, -253562887844, 45780538358, 60068892662, 282068870516, 39081491312, -12914423824], [58995708417064, 1343273031860, -35391207516, -1158779348, -348791145100, -71298607284, 35162139848], [-52903498041270, -2772221310112, -11998491052, 66589244428, 66042896936, 11704554888, -26887694440], [45784132834282, -2228504994821, -44039285319, -12316036537, -108611183892, -114749732633, -92921715146], [-52000070251136, 2613531618116, 4612200571, 17191995717, -147567028162, 47169689914, 47012779702], [-30752589089390, -1359696566876, -122422257384, -41180199468, -2426999204, 27370170932, -83869143356], [-17945145395042, 3846825368919, -50775241673, -57552246623, 91119643954, 70119379579, -673911042], [93109198537514, 538758280592, 16510178320, 173379244760, -75479217904, -102061831312, -74992828408], [-43421642546650, -654063618217, 2329561927, -124404615231, 85561823158, -221932020541, 38966948518], [-2198053806312, 230414259964, -120302982484, -82495047824, 361681032332, -109530267900, -65778515884], [78434289664544, -659254582444, 82295853543, -35929026487, 390109076790, -67814275118, 149605243526], [-56043634668766, 277660737100, -15506815544, -60494795164, -316728343368, 172342100068, -43665241972], [125158282718478, -710505075305, -41258886093, 105903239973, 61607628536, 148942433239, -92130045522], [88383620834756, 2875333763422, 65356076854, -63777656678, 552504980932, 18272494678, -17668162404], [61113917598676, 458957880742, 4940577528, 150481056544, -49404145305, 111533711756, 33081212232], [65934908932270, 446357525908, 88985582942, 49467463070, 27237777980, -85544815528, -75035570240], [-146583924056004, 1668177836514, -5545522120, 22772017120, -159168059787, -78924530668, -13637009112], [-5351738687988, -1767545459964, -3356904894, 69083905302, 128802139138, -33649843156, 5101981712], [45933899143552, -1016902804892, -9841640475, -1888835477, -222971850594, -67928439730, 87531641430], [-8468085607872, -428327094684, 115364768328, -84054080932, -653058576240, -35108024996, 94944385684], [-96277713113012, 126859550024, 1494220926, 59682999650, 579726847534, 193207404504, -68477230568], [-60176756422414, 1755831646712, 103576046186, 77736898478, 181469189772, -83289809588, -26519989276], [14126685206490, -4475693971874, 89498593503, -95135116401, -135888046302, 110214778464, 155485092864], [-58288345997744, 712865095712, 58273236334, -179647632934, 418685741875, -4653341082, 37582546356], [-129840460075836, 438170738804, -1550210438, 108319840286, 382373709574, 126580991652, 133525693600], [-47722130969924, -4741502060350, 106999284, -45920576740, 145486305787, -49226554464, -67166243192], [23542173683508, -1017895672734, 122068545064, 63938639120, 640853197878, 93300728770, 46956069084], [10704166531408, -766157210594, -28493678256, -107016895336, -101447970994, 103916487638, 78884083836], [192479287562508, -806641876144, 84157847839, 9634607301, -762916419250, -96737330666, 98018197090], [54005392510246, -394762629184, 50456882606, -116854428074, -338532348180, 146006519420, 32078604616], [37429283488022, 1049410140535, 190102949611, 52171128253, -934236783334, 107398124403, 252704777518], [-31295180665794, 2453582682501, 210204147819, 184586622189, -535781335204, 47109945361, 24517933858], [51714961373996, 3306548220426, -10993567704, -324763262144, -11214093869, -150419709584, -69350513920], [54227286395612, 412962814342, -43605136844, -110870059772, -38966960376, 71056163426, 38584722180], [29660276540124, 2700510390096, 186328592334, 116506974594, -610053605262, -73512549528, -118863676248], [-106016595404470, 1626324098364, 155901903460, -182491124608, -185166999884, 20122956180, 141095799940], [-157316818631486, 3036731024232, 81684157574, -162902639542, 108987793156, 19267136628, 107544560276], [40700261667052, -4284271578966, 174510578242, -266511266450, 833782488220, 6694863010, 5651746892], [106087469596554, -4445052222524, 51528791788, 69351220928, -663751687080, -40112507228, 179138561636], [-2748447448932, -4029121120328, -46861904465, 140866503317, -571436053298, -48931476258, -220069279862], [-99439893835304, 1094482404964, -32271982752, -269397533116, -504921551696, -204159015636, 188999259364], [167909432172890, 1028625713682, 4567106565, -227295657883, 264032547158, 24805940744, 47057196376], [78045811824284, -2642154212926, -119836259952, -119417427072, -1236472336227, 104537986644, 21607924064], [-197200061139490, 501660597662, -33064061247, -344712406571, -324693891490, 223317441540, 207735763388], [-104898874133124, -1946489233524, 141317482373, 15791036743, -1358298917362, 68230891302, -85042272974], [-119360673640274, 2140300452483, 198573317491, -95582449611, 312524751742, -207659734849, -80186894050], [-50617356105796, -2167124955870, -48942169360, 432711842584, -864163023786, -19666575310, -172873137540], [36300213904982, -3488806586202, 170153773173, 73626811169, -304461971578, -136006972828, 163237628356], [145711613933014, -1033738243454, -48668658497, 187138310819, -863663944754, -227165365692, -240225576980], [131248249091994, 5924250047416, -102741298640, 125245520092, 76729883064, -173372889832, -20361542388], [177154338596784, 771560317564, 78493703012, 549873834752, -428079824284, -124408693708, -253846123420], [150143990300822, -65812625484, -153452948710, -117549612094, 559217177716, 136993082928, 60003649192], [71008452530930, 7792088633848, 279957968836, -219483057348, 870724090912, 232038463136, 196221840840], [-16825871104792, -7948108177564, -54229364172, 43086829760, 1093229775657, 160040622514, -60879527576], [76305676554322, -10421895746060, -85799261908, -37049729592, -271035275924, -589061083300, -88935654828], [175283212604438, -770056283182, 109724740203, 94193490463, 1400374392910, -8668535876, 5843976924], [466872465222532, -1946535198730, -74223295344, -80887418480, -661717953754, -57814864386, 24162370412], [-171066318846802, 791562703896, 188998189932, -90836090128, 613863676544, -277551313456, 46615905668], [99982283685100, 1495703481388, 237834267434, -171149525954, -203344669118, -161712423116, 255267363360], [-231602519090558, 4970210061664, 148825601348, 312159994740, 96512920648, 187746204584, -155349201616], [24880734675324, -9870342682732, 175436168126, 800364666, -1287410045802, 113800821900, 95782866096], [249941913863636, 61984446234, -176069950604, 54115331308, 761849013484, 307272798790, -162325395884], [-143730402345136, 626569710924, -41678379481, 344815717713, 917911153830, -261299172966, -1062798770], [-212871342517316, -7061552131468, 49017089823, 118717882721, 693281815994, 308656100258, 206009597010], [118017204726404, -272119200470, 272684192068, -79622928540, -1128087063632, -392111291650, 65016106548], [-19124569927752, -5364208999942, 200809947712, -259085242792, 1690420074090, -33199882622, -358781840876], [-31664742716770, 8241647260107, 109534129079, -120272126031, 1164070242766, -208916810929, -269754934602], [307676483204434, -1323641731041, 17780524609, -613365144761, -336974087956, 115178594211, 59172909998], [-67349519275294, 6323822281760, -295145930030, 85158927614, 1745882651640, 113677676812, -375240706172], [-55807724962376, 8832690155412, 127643052562, 249885308390, -215594112977, -265815936606, 23613230428], [-155449245332040, 4657020867660, 176141886128, 19876964920, 209584446700, -271287405476, 394704502544], [28754584683942, 9083063782000, -173155563316, -254418892892, 697929847768, 593936623624, 385052285640], [17908463119426, 4955076253054, -49507702485, 439260639139, -350991406794, 251114090336, -177324274536], [9862946403972, 4878274371742, 331157228886, -52365786838, 1054276645776, 828758217982, 585297148924], [21605511325624, -1171190262684, 59368953021, 704405110051, 181625534198, -27548554578, -61735397226], [240661632771218, 3452316818166, 53945055343, 307287103679, -981111174770, -71039569056, 334238463704], [-83036846186084, -667385208702, -47205809544, 88886645952, -686036410691, -185532076636, 371280185672], [70022745276900, 8608259628684, -267320924627, -173126623865, 986647039222, -242464842122, -643566773070], [-120017834680148, 2872241629134, -284029593862, 546604538642, -1398424457421, 232949858224, -308512303156], [59719443210766, 12414414473730, -62982723641, 181977680163, -430030182134, -306562603732, -488100676804], [182621448309294, -10174932762650, -119640571947, -565006324383, -2668792602682, -409050015500, -257552906052], [-81322928423400, -3639344506772, -238717726276, -85434426700, 1644836385440, -731806633348, -576283464928], [-156485393071840, 3673709753428, -28138291053, 290181359157, 2010283640686, 369856350122, 239282958310], [-18004129249392, 8607953875912, 288582594812, -293776417056, -2312842107103, 360679406974, 240609048448], [-96599736367284, 5028341871386, -288620302748, -130301446212, -114758027660, 399179811686, -443035497044], [-330936391889788, 1880166341532, -605743206937, -556099044735, -1219098809782, 193030668634, -417549763886], [-68687162402836, -5365431488344, 106106035055, 29416167781, -416917793306, -1031891866754, -37690739526], [-433232369472470, 3165121776267, 416927708633, 890565464063, -107412703904, -268969636401, -2016873906], [-11481265834128, -4006860742424, 241930643520, 826038482332, 2210067399407, -412279767414, -310950978776], [142787584771108, -2593070770378, 182015849160, -631401666512, -2201177955383, 655687545256, 411783621304], [321720685228902, -13101918986848, 281285228544, 228421262152, -1370918603544, 791207075120, 741001192664], [3790641389468, 7306935593934, -199969888944, -117808512672, 3066145916718, 713887993734, 293690211412], [376638486935626, -11659454050058, -239781147821, 349331429227, -7041594142, 505904439648, -441364910424], [-194038727674104, -17315478512116, 118638273452, 607165994972, 1321576041020, -143853658396, -333684871272], [-195683741773710, -8331679945308, -165960313552, -590141729748, 2881526890940, 418602047428, 408415738980], [296843625860078, 1089687289005, -179935372877, 321120308949, 2945468939010, -17693991939, -863105368158], [-807963528479542, -11468449509334, 101275085381, -41840590235, -254275021102, 313810566408, 314704895568], [-77774899468866, -12127502657752, -182419779068, -271827543868, 3501339489096, -617644049696, -452405447312], [311963159086488, -2214174022840, 446737030208, 363128541956, -4625161065870, -38373720476, 366222860804], [-414504918293536, -1512486094852, 283282257780, 255734296940, -3851243917696, 347220955196, 253864071264], [220269499732426, -2238232883744, -65476838748, -157276691644, 321749975040, 333479494744, 695838759888], [-150734592826696, -15043352329040, -655079359060, 970624406960, -4472895705582, -155943379148, -736872499652], [-398613449954762, -2704602192109, -57424144357, 939037849749, -780480661090, 171218215951, 474635060862], [270819401989922, -1627413894496, 121706008250, -702159397378, 2560546922644, 382847735892, 830929374788], [924521409233290, 5701570418864, 110581900084, -488373180820, -1749465888392, -516201961704, -352884656232], [203361490432528, -15615159924336, 633404540772, 805505336272, 1871719096473, -414726981850, -365817037568], [169321887813178, -18143474125180, -240719811658, -117191013254, -591611612564, 373707637048, 422126669204], [-159080565055154, 3607015080592, -514002461520, -323400108736, 1714750597328, -809253540112, -545812720208], [294864754996112, -13760168875256, 93386814532, -244310733948, -1752462273216, -277238304, 434178584456], [385533902565858, 33465792172036, 28650618322, -740342724594, -1269717957308, 188435913392, 559971094220], [237511608644134, 7396176315544, 255332910024, 1208293266284, 452519949584, -726817604296, -51019021740], [-160122995721420, -3920764067342, 535166326562, -295410888102, 1761634369237, -260300288728, 358981649540], [196062996178188, 1358821818878, 43632230462, -1334417185786, 2920228055699, 1048360314872, 745282321900], [127440279057554, -19702790076423, -235430634123, -671603451581, -654990997240, 214161395817, -125394554110], [-246574039392826, 7210862709566, -114918556131, 177587853561, -5291427441810, -803687956980, -843383351276], [-46070168762914, 38146932281594, -212674399981, 577780098127, -2736756138690, -1412449475356, -670123397900], [-139445260579582, -7139641730994, 157354581603, -163664410173, 2145848221706, 776507947384, 175429780144], [617590333037642, 13961999393153, -179893735515, 448517493499, -407011292372, -1300692171575, 102117174210], [-821013060974044, 9800013961950, 537590384552, -112898711352, -3207887286, 106050679182, 186137226740], [179879777656764, -15777846128734, 396520576752, -847962105392, -416110139529, 1105806250736, -14565061744], [452754957129504, 12206908073920, 209471265562, -196948442410, -559420967075, 848135015082, 1445169121540], [247596323017746, -7851676113304, -157479598326, 590082985710, 4923169703368, 318741012596, 11904870188], [-849102351220226, -33478640618472, -18243001066, -64449221338, 1083377831996, 678423167444, 934843532240], [556149892754146, -23660226871868, 685690037198, -278084980566, 2397808887340, 114649933832, -211358056724], [180582486843164, -15421815260432, 278089489610, -166548404610, 2531275711494, -314569735416, -723173571464], [420389080955582, -8712537026196, 1378758871298, 348183470154, -2706963965572, -835199906216, 1233081646264], [-436504860952390, 14483993483816, 301164725828, 529591177476, 2845366426840, 306216513632, -1012215650464], [-219706980932126, -39416097402722, -572741058573, 146820413627, 1989267578562, 568222506040, -341214458168], [290962365223888, 10976164122096, -292240031032, -242814163376, -5463130995168, -760506464992, -80711891880], [979158993615536, -16598383154012, -516098128017, -631727857335, -587311072970, 1274150117282, 574720410886], [255779913097300, 16903266179622, -703849164892, -36707428524, 2669557180895, -491501747948, 97485577656], [696094747933970, -6240304579606, -718090461479, 47803637025, 6283765274018, -867621762032, -954798634112], [-108905182355512, -40386693280972, -773166786808, -561813528572, 8067470685092, 768731671332, 161683617260], [-63790680323522, 30079374429993, 333139774423, 23999104297, 856094109852, 2059336794005, 1210156960058], [393998459534110, 13080025832970, -376141243357, 1004641737847, -2879574181534, -362165612964, -43565776508], [-635446573811396, 6858426483710, -248257476148, -231868512844, 1353190877588, 385884946514, 684019945828], [-37623266125362, -15618964288284, 663361518156, 866473857236, 3476159833392, -744515120492, 438920419128], [-281565652259990, -6210073113036, -187738815156, 963816713304, -5727655348724, 151940211260, 25870060724], [288017197327118, -24075317400361, 905647688699, -807311046835, 3380986364922, 1606874794723, 881580756086], [-150297295323524, -6124495876288, 259196915523, 418761903089, 91264425846, -192928647986, 654188154234], [-575028907256712, -9247691765684, -132122461, 391684326161, -3302156469318, 213681573202, -428974878378], [65994111289540, -15779374674740, 140021176326, 1349865652098, 428523645182, -2380668886124, -122431427920], [-231090664327416, -3444309456108, -60162977316, -605108926840, -7063369621393, -192462991738, -1179838090048], [-38117398228526, 46696821252696, 253559154330, 375077220350, 403667081068, 497875242540, 584080720660], [1077601536190868, -157707221390, 480276983934, 120071270802, -3101592019484, 1436461884674, 1173787319260], [211057926458850, 20758863887046, 956130211215, -265738671817, 994439124214, -885118679952, -290739300648], [603347638504066, 25311902082748, 160776531286, -688066090542, -170603793300, -100841798112, -685765564052], [875198295316376, -7381715489118, -180053000768, 731857174520, 3820157118190, 1659810669570, 1235005008092], [-247720044217660, -18571666948210, 325777590872, -1084499913248, -5833595544113, 445010487892, -665687493480], [83920805370192, -12391853798236, 429632126584, 272192758900, 4164083614226, 375091544376, -472800247372], [-399056472776898, 24379811151000, -1190134400016, 65573753620, 325155773528, -1198964660424, -350974820892], [-675301728851862, 4017338947022, -1060439007873, -2270330830745, 1320270687486, 503604067880, 757932415792], [1096506859361200, -29209257208298, -215020259196, -178650220404, -1836527920570, 134678173798, -13434323924], [945912017894274, 3033220344924, -570248955048, 1196226211572, 5243757897680, -1346312785436, -88736396132], [-511662127125628, 19346216550558, 1338411500700, 703883698876, -7672820835560, 909433204474, -106051832524], [-606042423894236, 12301484379586, 1638475596666, 1392568906682, 1440867810171, 2467112835196, 1235567522660], [-1343124399234858, 30322290226205, 173169913807, -370774338391, 27629761830, 1538034166237, 1255936747570], [-1678667838358024, -1736703399324, -183206536353, -1887202815111, 2298886215494, 1639607670034, 836257944718], [903597396753440, 15408296681142, -820570957348, 629716973876, 4174091137658, 88432617662, -1008673400220], [-725667963383574, -30378113972850, -335537723349, 24292996099, 7741972689818, 894876459288, -1388808745312], [607530943631024, -10730788473616, -504948633440, 678157144236, -11099488904533, -783970203398, 478912556448], [-902534076413710, 48719380750749, 663451189597, 1038424946811, 2243165886134, 1600803755161, 578117933106], [-1158509714861556, 7382053943012, -970963805267, 1757501633735, -690308624538, -2022944119874, -1424648571198], [825202061166454, -12642488040848, -84129903836, 568360760, 1045396178848, 1702417991976, 1733914231188], [-862830359010502, 26255216111184, 25098263280, -326586512272, 5298367124880, 867286926064, -1243283596864], [-577782887773906, -15114755342778, 569840136729, -1165394739387, -8696958651934, -18342595340, 1693839953164], [-265969062437670, -43096539899872, -652219077176, -271393965448, -2673024021528, 1236763185568, -675013276064], [-59604373363446, 2970939343507, 1464632883301, -566167090477, -1485551451026, 3400590507075, 1267939545446], [32110186571346, 37583793355800, 1671086981270, -1184812865334, 4490259931956, 1084150889796, 1468936991524], [-1505739759013772, -41729675457194, 288660824636, 1810494634764, 3881389293415, -2697626581468, 151869529144], [-609612267852718, 20566340753747, -1395691488887, -2242549218817, -287930925712, -2724333891145, 132965199638], [186471560947692, -16889281856806, 616252687514, 494570430398, 4540923543432, 3326877825802, -131732970748], [-1077599449905364, -14365031856768, 185915958075, -1591857358215, 7615468014854, -1275952119746, -1435752022134], [-474343634012520, 75041107841564, -1072525115768, 2331023101124, -8559914809793, -772345283754, -1049901887224], [-146471110207376, -18837526812732, -1094524835896, 367647704584, 7718362979788, -442160135516, 693339601600], [-146911665730314, -16705616343704, 1258193686202, 1559377667522, 295733624948, -2577716076916, 1752504625048], [957029144007730, -3410215160166, 905517010929, 2543996888665, 7876290362006, 455571352392, -133368824688], [23789953280636, -22102246589062, 1082656445264, 2908597791648, 2734489997370, 2762808844386, 1758855043388], [-103143567378908, -22563537434338, -1446076532692, -681941584532, 700087586654, -3181848479922, 1466155095420], [-105643632756540, -14231492989166, -738376880038, -591919991890, 9371222052588, -1582215653078, -2978958571740], [616172782716458, -58054450013404, -1715446073366, -859739060066, -2399462296468, -1921658378256, -1132944626860], [-174858980148448, -35466760570986, 1026379478120, -2437740218504, 4736104019898, -47071043962, 2710809792332], [-2751374696469950, 100044622176, 295384315960, 440722894800, 8887497380264, 656013145216, -23070159416], [-915330045997440, 61428192169472, 50650514626, -617664746626, -864651059563, 1058580535514, 1129631079692], [-178414712949640, -26627344394004, 783729243999, -1758634947703, -2409567421122, -2999899066742, 1250142596886], [-1035085135214670, -61091241105626, 1165642664051, 3191897985251, -1334129554698, 881329535464, -130064100608], [268584490066128, 54394003630540, 1155958110887, -1612601656939, -6243890826998, -351771548070, 1216925920782], [929824804903456, -46012591219784, -1176576556404, -2622870144916, -6583085312740, 1966919493704, -2014633772088], [777759047108890, -62489385835228, 416802951662, 686922070578, 5226335401124, 2123686860376, -116402211324], [-1072423908639090, -87525490788296, 993632062296, 311055313600, -7375981717176, 1945116286472, 844001395384], [715566380593990, 74975741486589, 597901954743, -60621235495, 5282622376864, 665500605321, -1218906209878], [-891602539726532, 39966427956880, -1912718326377, -2905174172867, -110424678242, -420763915946, 15165972314], [168221445195728, -2374682000148, -483864681341, -1269652156127, -1343014064174, 744165866578, 2841985328446], [-294627171382892, 36021463402646, 330341061824, -402944168272, 4108382583968, 3756557944154, 4094656337260], [1326555416622440, -25514625065500, 1885936528108, 2929533386768, 4871105225843, 262678779662, 1875928773896], [-671567045620742, 40754223468792, -1093501088324, 2329204466232, 5571707636896, -4800053787088, -1145211325396], [143784854796428, -33715128648640, 54854008803, 1943151649889, -2991284312754, 656773037278, 497314550250], [-690182932099444, -17158992539042, 732986533760, -42920449824, 3940013410294, 3017483414582, -2218275252052], [821598415643080, -44165845547740, 269271122974, 1067172142986, -1695290081121, 3367640555850, 249103920044], [-489084283658158, 87161325875544, 89349780356, -442067251604, -8038467654800, -1157274177824, 2430662012120], [-198653198877334, -54267338395746, -582977435969, 1179449606615, -7548780995570, -770172048504, 740333232440], [62505547903566, -49018547332681, 822096074919, -2533739485031, -19279918274568, 1975733967215, 1492845988174], [-372046505411530, -17457593910715, -58236638017, -6089838630959, 398252508448, 3587428877905, 868603824538], [-1290488024423786, -24476218569864, -390225781580, -57074837188, 12217878077664, -696953518112, -2986599730488], [281454506336040, 16801073655630, -756205941120, 770047657488, 9822896285406, 2341661184966, 917540555604], [105118325309978, 39380961340376, 2693846089414, -3090751557774, 59220495960, 6463087755468, 3536138075316], [996578599072318, -22586593296798, -300083681877, 5887144278975, 2399863029514, -2617981953868, -2464302765204], [2729990427313746, 26046748900849, 267329080121, 621777745399, 11717109405384, 342361711625, 680046691106], [-1672203035702232, 60873713714344, 693949562528, 746800357100, -743610373994, -2820238919124, -242170261308], [-1732874866152930, 43121690696716, 2475829555006, -2232421988218, 1736626335796, 1621508440656, 4021725873320], [-1134627379110702, -61519295350396, 1494941377460, 2080885355592, 10671644429212, 841274587772, -799498855172], [-13107165305044, 12519806886990, 1528092396374, 172068022630, -11547927345363, 2118762116996, 1711722723948], [-321914571300126, -78486395622556, -1107038109652, -3537495633816, -9943104005120, 1908213874196, -399099961028], [-1619117046820152, -28963421358356, 326272128124, 934505114872, 142248441856, 3723269193532, 1570063541732], [-295674681836302, 45921115316745, -410616074123, 855713165483, -14229220063514, -4633746154563, -1003789753150]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_289_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_289_10_a_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_289_10_a_b(:prec:=7)
    chi := MakeCharacter_289_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 10));
    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_289_10_a_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_289_10_a_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_289_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,10,sign)));
    Vf := Kernel([<2,R![675998208, -243559296, 10388768, 2252056, -8252, -2986, 1, 1]>,<3,R![-2458538542080000, -24964560910080, 298088384256, 3088987488, -9882840, -105728, 88, 1]>],Snew);
    return Vf;
end function;