
// Make newform 153.10.a.f in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_153_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_153_10_a_f();".
// 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_153_10_a_f();".
// 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], [-854, 3, 1, 0, 0, 0, 0], [1595734267008, 249666517824, 9962276152, -962897524, -21966986, 479085, 8711], [-7071932313216, -961758589248, 93593409896, 1085670148, -124232878, -292545, 41053], [-13060049459328, -1407118526784, 214005649768, 1241764484, -307414574, -239985, 106349], [-59384105783424, -8853358980672, 873469755944, 10192644772, -1224135742, -2816505, 419317]];
    Rf_basisdens := [1, 1, 1, 3478080000, 2086848000, 5217120000, 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_153_a();"
function MakeCharacter_153_a()
    N := 153;
    order := 1;
    char_gens := [137, 37];
    v := [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_153_a_Hecke(Kf)
    return MakeCharacter_153_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], [0, 0, 0, 0, 0, 0, 0], [-198, 26, 1, 1, -1, 0, 0], [1349, -69, -3, 3, -6, -7, 6], [-19325, -206, -2, -2, -31, -36, -28], [23374, 2444, -71, 15, 133, 22, 22], [-83521, 0, 0, 0, 0, 0, 0], [110154, 8144, 264, 100, -294, -572, -572], [-190141, -26063, 141, 203, 640, 1815, -702], [-132294, -40114, -1525, -869, 4781, 1840, -904], [506299, 6735, 411, -3979, -1242, 2957, -5722], [2624162, -45102, 5441, 6105, 1491, 5648, -7352], [-1491302, 165676, 4594, -14290, -3618, -5456, -7756], [3116746, 42186, -16112, 11144, -3770, -1334, 15140], [-8165356, 451462, -31664, -1104, 37380, -12878, 26028], [-17494218, 446976, -74926, -21210, -10018, 27436, -4764], [-4419522, 1749298, 21988, 12644, -103114, -9518, -36004], [-7219378, 586486, -60195, 65505, -13129, -58500, 11900], [42907640, 1297892, 3484, 26640, -181172, 70028, -2772], [-93452091, 1768777, 19755, 112733, 222240, 91999, 102202], [43791474, 444796, 8708, 70496, 70912, 71740, -120844], [136645065, 2802391, 200759, -11463, -176640, 119953, -38250], [215811674, 1909818, -177744, -129096, 246982, -401926, 259028], [280768818, 5328572, -51165, -228211, -173853, 452218, -169898], [288793462, -13616496, 524064, 129756, -772896, -960136, -23180], [482048930, -6887884, 3335, 401249, -766029, -847654, -253830], [525185208, 20563184, -248236, -122476, -647588, -427624, 314720], [-100044739, 10432480, -476294, 317262, 1242131, 1024002, -61636], [36932114, -15570734, -230969, 995099, 175921, 1118652, -280484], [-318372350, -21729808, -819018, 753582, 2984710, 1164756, 23928], [1882198942, 32512130, -1955090, -1600846, -782756, 355974, -768292], [-991747215, 37095732, -318386, 722482, -3021605, -201474, -1344172], [450902206, -60535420, -3746129, 396349, 3460839, -5101214, 184050], [1566325835, -21142234, -1083150, 582514, 1816221, -2412688, 452396], [629888314, -53306736, -4961804, -961996, 1497244, 4897592, -3144384], [622842538, 33803058, -2830602, 1952970, 10411352, 4058622, 819372], [3377074666, 120082652, -581268, -2103736, -7116980, -6154540, 5203884], [8546907641, -74376916, 2866420, -1433944, 6100077, 9254730, -5936784], [1169183057, -77029317, -5492619, -6053533, 5644246, -7524639, -3984762], [-32286994, 162165346, 8656655, 4251571, -17798847, -8811940, 121876], [3635176474, 264732872, 12476152, 2341900, 14159098, 15881148, -4825652], [-954770478, -258083874, 8459557, -9165535, -1760109, -3520916, -9135916], [-356004284, -39530718, -22355848, -7704616, 14151052, -5267338, 12424076], [-295154054, -223329128, -4664810, -14067694, -9769154, -2927564, -9076588], [-1327091554, -447320742, 8341065, -16831, 6406435, 10122392, -1772064], [6379316223, 204503933, 10785625, 1417047, -45453136, -2288437, 14025450], [10395527321, -326445692, -23653438, 21799614, 20260943, 18233814, 232188], [-9976543734, 527040264, -10699066, -11017454, 20865288, -35153096, -6473680], [-13792091181, -779660364, 30786336, -4745556, -5340645, -24370218, -30303384], [-5909665138, 120393632, -46285295, 6978811, 81220393, -27967422, 21904034], [-4951671790, -1144474308, 23819998, 17964266, 30526746, -20001144, 49700452], [-18046961784, 652616678, -26151720, 20398880, -13881944, -60044470, 40140380], [-22215369162, 184554400, 4846070, 14785686, -43964130, 37150180, 3740016], [27390746676, -856324388, 67989076, 20419480, 7816832, 10191788, -2386212], [26592028318, -473627364, -73112987, 25804703, 12214149, 3158150, -8591122], [-24734157406, 426311314, 61071042, -60291970, -48448196, -11785450, -32192100], [54188795946, -1283918330, -78564079, -19790315, 36416491, -41057500, 31533100], [-22862184176, -646194542, -6507372, 60287988, 144625420, 71238726, -3893236], [-5630189790, -1413525390, 11541561, 33337633, 1333291, -89332624, 9528944], [-17495041854, 666066264, 61040396, 14055064, 115775916, 80696312, -78855084], [54959550685, -575528046, 42228582, -1866722, 78966227, 76994648, -47184604], [25003899234, 1386546536, 78506524, -12765388, -181786236, -153662272, 50190600], [11024476004, 432147134, -188870304, -56557920, -14427120, -24434830, -55884780], [-45462198043, -320992685, -140089727, 47486503, -202331914, -34126071, 49426822], [114257965498, 1332444028, 83272394, -43345470, -37012626, 131116552, -11324248], [31297850002, 1986110162, -38624427, -102179435, 10132587, 3889376, -106185224], [-12025809782, 4366454182, -11871340, 62633964, 5310050, -31391018, 62417836], [56753918926, 2777480128, -155952828, 17029712, -195396876, 113950432, 158158004], [186137974291, -1340037872, 96037992, -109699228, -3118869, 76541546, -113902632], [36870690418, 4148409816, 105695254, -19402638, -55250550, 44832684, -251206164], [-102604180550, -3403178376, 69242856, -92361324, 457513712, 161876336, -181396508], [125683689966, -2331002164, 274867238, 144050698, -209517956, -131985460, -148320632], [51349496021, -7042182375, -83640753, -163978159, 105214964, 230980567, 49803138], [333585777982, 5893826908, -8789131, -18379237, 89094929, -316357826, -9075058], [-55262660641, -3865995982, -428935180, 142549084, 228547599, -250647304, -23103720], [34378420706, 10108067962, 355081034, 73019118, -33241996, 214446254, -67598588], [27660436114, -2687299232, -180835865, -173476067, -740263569, -21932770, 104524278], [-74888613798, -5283837470, -109746827, -37466019, 46680895, 127653672, -349157272], [142194971810, 529352384, -687826390, -200317998, 331624162, 39118828, 168436680], [-102776072678, -4809719064, -106609312, 206385664, -137060736, -280884200, 724078864], [267918868703, 9612346098, -180291564, 20434812, 116501151, -359541048, 37734304], [397390818806, -7954321572, -178853115, -232074101, -109083959, 548271918, -217767138], [144133738367, -6470651947, 479857833, -31529721, -536801912, -115537549, -396427870], [130903214470, -10487216724, 229862043, -426869755, 835143683, -13177670, 104272030], [326048061859, 23245717623, -239630111, 102536367, 219391340, -304541431, 75596486], [-88021919840, 19312325088, -932589992, 257723740, 6100888, 271839304, 320208604], [204278923902, 2493303960, 159335232, -186475336, 525054936, 390377736, 717739960], [227141122110, -2159969284, -291458573, -279847995, 326556531, 1139358618, -454887482], [-328896172978, -2333717136, 309905850, -429961210, 475116862, -353711924, -439225524], [233914315740, 3204084148, -549274016, 127973560, 429154340, 596015412, -665358688], [658514053234, -3253159748, 307743156, 436364472, 327949238, 503402848, 483504460], [-253043897799, -7139544169, -1199789033, 43597617, -594297880, -232685599, 862236598], [839715166565, -11576723023, 719726775, 286234545, -77174884, -881529697, 601323338], [125759960782, 23095896648, 1030691856, 122263420, -760389866, 90870276, 93648956], [-132216659891, -2334339564, 1876370102, 747236802, 245938239, 62885606, 208931708], [12880866447, 43144593695, -723514179, 930709619, -175863548, 632723953, 1230964262], [320746519754, 34511680064, 934908600, 122681120, 1420208664, 555917088, -1847761912], [-766280269278, 26926005556, -521018306, 444356282, -1386065254, -466847248, 339086084], [-319264048684, -46676627880, 533604820, -603340672, 951510128, 428787216, -561924316], [128912792634, 44714505806, 618605929, -647885243, -2025653137, -703564380, -1718297308], [537189743723, 31707308084, -1549996718, -1209163842, -1561283183, -1370521054, -11295156], [585829371986, -32002358452, 1475762115, 1424248061, -1262277825, -1048004582, 794698994], [1346306419026, 15778072210, 944566272, 662052400, 3043203750, 1403319554, 227418404], [1128279024322, 20512981104, 969614524, 492625976, -1823741620, -1906889344, 1233288052], [-379361433327, 19566001946, -833019244, 1677044764, 1847790001, -1062187684, 2553369360], [-344586622286, 15736745900, -562790079, 1049919891, 960764977, -1052999666, 1532162150], [969270731266, 29005342984, -2036460400, -537694876, -840521134, -2636708, -1288900764], [435101758530, 14343461584, -2632046960, 2769589364, -660379816, -2559957800, 1290611324], [-850218455892, -2818855064, -739462556, -2225837572, 1003591144, 14171816, -1560425936], [-331948245986, 60865016580, -2273084900, -485933804, 5746510928, -803964260, 1351669816], [1687550720815, -26908788717, -152531029, -918782803, 2114342946, 478858065, -1421028738], [-1219429233434, -11904721744, -262060496, 853096704, -1522192416, 1626837392, -3760100544], [1339088041850, -5005459164, 711898410, 1528203318, -574913162, -35329208, 305342180], [3317655905725, 61217286468, -3022780624, -595224628, -601001259, 791378386, -836384712], [103549629874, -108318283364, -792145134, 357779734, 2996426868, 3123299660, -745905336], [-598477158830, -42369717312, 2868669300, -3151019240, -65198700, 3433537776, -1680598724], [-655025595633, -8921406926, -1220724524, 512989412, 7337559279, 545317144, 1496877656], [-3125677037248, -12299603782, -755273748, 179223724, -5466018116, -3058316578, 206394316], [201531349466, 14738778274, 3339682391, 1619817051, 5739820773, -1593746156, 321566420], [-1501009623680, -25945783998, 1292338860, -340136228, 4804557224, 2114364558, -1383801420], [1108987227838, 71279720972, 2737972430, 2101024958, -2072167990, 3492979184, -510706048], [1848372975778, -60592808208, 1529924612, -1530009436, -69906948, 3393125784, -2171672832], [-640426770402, 7520562702, -3920044847, -1257515659, 2928609863, 4979815412, -5557327372], [1358846387997, -107774588006, -5767322644, -2260771876, 4955485045, -601089948, 1588975416], [-379648331055, 16211278690, 3949002434, 674706722, 834301243, 2406647528, -4066676740], [136370118970, 36679040692, 5847311547, 3633850821, 1882407167, -560494814, 2069257162], [-1480624108642, 71796396654, -4997228511, 3144537797, 1655213163, 4121139244, 3956020516], [941460731213, -188732773855, 78332999, -644920575, -8763970500, 1376017439, -174678286], [2208924033348, 81500537222, -370001048, -2998672848, 2089118156, -5109183646, -424237764], [-1994898864986, -65085652620, 8480567610, 1022991034, -13423387922, -9744038560, -91153856], [-4012565229994, 67095174396, -133274128, -732422436, 2614919278, 8300248000, -6578022316], [-4074829151715, 75664859933, -5233110495, -3873963657, -2661624962, -4705147953, -4309224950], [-2954091011553, 109368448967, 111161721, 2360680599, 3753171288, 4327046225, 6192360014], [-854343340546, 304315906392, 4216426945, 1159633363, 4718808497, 7873349786, -2007671886], [3369601588110, -20956276204, -8275796365, -2292781303, 11010730507, 4217504666, -1915373382], [-62268321998, 174502650572, -3596336023, 42939587, -14442677823, -6082549266, -39245754], [1388706829186, -30064930032, 8869725743, 1718405925, -2038095961, 6690255022, -7461116578], [-7070720914309, 76191391246, 5241409290, 4225020514, 8095921493, -4230110600, 1140282844], [-658217280438, 24517473332, 2519551094, -451186730, -15675296974, 3475437432, 5844584432], [-1290463053242, -7298149868, 4409863944, -228864068, 13417710332, 7828262620, -11817173988], [-4554223897133, 239837848996, 9059955548, -8539051928, 1544649535, -1586379314, -1373865232], [2318293415190, -102817938834, 8385297397, 8306920233, -12690153765, -14301576564, 11047108004], [2981409353697, -158508581789, 7486096863, -2971900575, -2276225960, -6312465499, -10289860314], [-4622374259409, -260417932756, 5918510450, -732200834, 7119870021, 9184512498, -7371344796], [-6417076774694, -198444626500, -16047754460, 3518841568, 10108319012, 1974935268, 11836195036], [-6974811919249, -120683295303, -3325095065, 7755315777, -1292608490, -13590721069, 3677852338], [-1074178437098, -167267742930, 9285447519, 2511514527, -5757522367, -18856450152, -5267785440], [-3154370120130, 227158110260, -1546832994, 2299401230, -17996647414, -23298612856, 14349204144], [-10867207452982, 104234676734, 401300608, -928034104, -1374401738, 23343917238, -7431471956], [-6964242007124, -16166050176, -3883891464, -5756010784, 9075590108, -3608786056, 7567674200], [-935768224430, 260981573402, 11353334307, -987525569, 12176711389, 834124748, -6864546236], [-13885106507310, 189032536312, 16108288044, 6647249072, 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-260300288728, -358981649540], [-193850521930807, -1358821818878, 1334417185786, -43632230462, 878057061595, 1048360314872, -745282321900], [127139486623641, -19702790076423, -671603451581, -235430634123, 370811017668, -214161395817, -125394554110], [-244423942357522, 7210862709566, 177587853561, -114918556131, 1972509181743, 803687956980, -843383351276], [44301913492814, -38146932281594, -577780098127, 212674399981, -1190475171973, -1412449475356, 670123397900], [-140528488909394, -7139641730994, -163664410173, 157354581603, -919563919639, -776507947384, 175429780144], [-618458579187957, -13961999393153, -448517493499, 179893735515, -419728656816, -1300692171575, -102117174210], [821122607712244, -9800013961950, 112898711352, -537590384552, -3351973152, 106050679182, -186137226740], [-179084570882767, 15777846128734, 847962105392, -396520576752, -52755331395, 1105806250736, 14565061744], [452527420151895, 12206908073920, -196948442410, 209471265562, -30588535199, -848135015082, 1445169121540], [246242408102898, -7851676113304, 590082985710, -157479598326, -1943997900558, -318741012596, 11904870188], [-849732584367598, -33478640618472, -64449221338, -18243001066, -565783926034, -678423167444, 934843532240], [-555127016493378, 23660226871868, 278084980566, -685690037198, 744791280202, 114649933832, 211358056724], [179732552581398, -15421815260432, -166548404610, 278089489610, -683385857156, 314569735416, -723173571464], [421801924559614, -8712537026196, 348183470154, 1378758871298, 1064660133878, 835199906216, 1233081646264], [437202327814230, -14483993483816, -529591177476, -301164725828, 1227058039316, 306216513632, 1012215650464], [-220461597351242, -39416097402722, 146820413627, -572741058573, -901436832743, -568222506040, -341214458168], [292875034935024, 10976164122096, -242814163376, -292240031032, 2155483874512, 760506464992, -80711891880], [-978508895362542, 16598383154012, 631727857335, 516098128017, 18370395659, 1274150117282, -574720410886], [255029423000635, 16903266179622, -36707428524, -703849164892, -713782668141, 491501747948, 97485577656], [-694321235854658, 6240304579606, -47803637025, 718090461479, 1821315716337, -867621762032, 954798634112], [-112225125493368, -40386693280972, -561813528572, -773166786808, -2758129609284, -768731671332, 161683617260], [-64746491221943, 30079374429993, 23999104297, 333139774423, -979810002718, -2059336794005, 1210156960058], [395748800624174, 13080025832970, 1004641737847, -376141243357, 745699352217, 362165612964, -43565776508], [-636180844761326, 6858426483710, -231868512844, -248257476148, -502402437086, -385884946514, 684019945828], [37956165124838, 15618964288284, -866473857236, -663361518156, 1199372856712, -744515120492, -438920419128], [279064536071966, 6210073113036, -963816713304, 187738815156, -1537299474720, 151940211260, -25870060724], [-285816369576013, 24075317400361, 807311046835, -905647688699, 1393516704270, 1606874794723, -881580756086], [-149984232647418, -6124495876288, 418761903089, 259196915523, -105699226983, 192928647986, 654188154234], [573738292740566, 9247691765684, -391684326161, 132122461, -898930189985, 213681573202, 428974878378], [-67544736804586, 15779374674740, -1349865652098, -140021176326, -200759862948, -2380668886124, 122431427920], [-229075459407599, -3444309456108, -605108926840, -60162977316, 2620313846657, 192462991738, -1179838090048], [-38167860856162, 46696821252696, 375077220350, 253559154330, -425539847986, -497875242540, 584080720660], [-1078236627083006, 157707221390, -120071270802, -480276983934, -515019621336, 1436461884674, -1173787319260], [-210844327196218, -20758863887046, 265738671817, -956130211215, -52139409185, -885118679952, 290739300648], [602979409640842, 25311902082748, -688066090542, 160776531286, 319837227318, 100841798112, -685765564052], [-873859544170136, 7381715489118, -731857174520, 180053000768, 2070608320760, 1659810669570, -1235005008092], [-246646849141085, -18571666948210, -1084499913248, 325777590872, 2157694989823, -445010487892, -665687493480], [82589208823258, -12391853798236, 272192758900, 429632126584, -1603789305834, -375091544376, -472800247372], [-398721487312186, 24379811151000, 65573753620, -1190134400016, 269411711092, 1198964660424, -350974820892], [-677423240990814, 4017338947022, -2270330830745, -1060439007873, 148818691793, -503604067880, 757932415792], [1096955042463188, -29209257208298, -178650220404, -215020259196, 626833322392, -134678173798, -13434323924], [-945410353664574, -3033220344924, -1196226211572, 570248955048, 1697890441272, -1346312785436, 88736396132], [508938408782682, -19346216550558, -703883698876, -1338411500700, -2019834644070, 909433204474, 106051832524], [606416704838237, -12301484379586, -1392568906682, -1638475596666, 1766849850683, 2467112835196, -1235567522660], [-1343893470103141, 30322290226205, -370774338391, 173169913807, -398296529892, -1538034166237, 1255936747570], [1681238804863274, 1736703399324, 1887202815111, 183206536353, 683763690139, 1639607670034, -836257944718], [902596366817584, 15408296681142, 629716973876, -820570957348, -1630746909732, -88432617662, -1008673400220], [728530717769210, 30378113972850, -24292996099, 335537723349, 2887047381735, 894876459288, 1388808745312], [611944201429825, -10730788473616, 678157144236, -504948633440, 3735100654565, 783970203398, 478912556448], [-903123116329601, 48719380750749, 1038424946811, 663451189597, -1627464862702, -1600803755161, 578117933106], [-1156433629524262, 7382053943012, 1757501633735, -970963805267, 318583703559, 2022944119874, -1424648571198], [-824286502016686, 12642488040848, -568360760, 84129903836, 916127510528, 1702417991976, -1733914231188], [-865103301368998, 26255216111184, -326586512272, 25098263280, -1946355846224, -867286926064, -1243283596864], [-575654717184406, -15114755342778, -1165394739387, 569840136729, 3293565328887, 18342595340, 1693839953164], [265671238135982, 43096539899872, 271393965448, 652219077176, -569218267136, 1236763185568, 675013276064], [60620164442447, -2970939343507, 566167090477, -1464632883301, 449623988524, 3400590507075, -1267939545446], [29462174387206, 37583793355800, -1184812865334, 1671086981270, -1463199318806, -1084150889796, 1468936991524], [1504927350161245, 41729675457194, -1810494634764, -288660824636, 998085782237, -2697626581468, -151869529144], [-610103212392977, 20566340753747, -2242549218817, -1395691488887, 1751604678558, 2724333891145, 132965199638], [184178674111546, -16889281856806, 494570430398, 616252687514, -2787457266544, -3326877825802, -131732970748], [-1080773860109210, -14365031856768, -1591857358215, 185915958075, -1582552845631, 1275952119746, -1435752022134], [469678865247255, -75041107841564, -2331023101124, 1072525115768, -2333745664141, -772345283754, 1049901887224], [148651412685744, 18837526812732, -367647704584, 1094524835896, 2547950182952, -442160135516, -693339601600], [145111419801310, 16705616343704, -1559377667522, -1258193686202, -240868261482, -2577716076916, -1752504625048], [955947854695374, -3410215160166, 2543996888665, 905517010929, -3625286201021, -455571352392, -133368824688], [-23896585527816, 22102246589062, -2908597791648, -1082656445264, 2801965544468, 2762808844386, -1758855043388], [-102770941470840, -22563537434338, -681941584532, -1446076532692, 1054567492600, 3181848479922, 1466155095420], [108634581550970, 14231492989166, 591919991890, 738376880038, 2399028802540, -1582215653078, 2978958571740], [-617039996901322, 58054450013404, 859739060066, 1715446073366, -1726953244930, -1921658378256, 1132944626860], [-178047151286096, -35466760570986, -2437740218504, 1026379478120, -750430919144, 47071043962, 2710809792332], [2754262051381910, -100044622176, -440722894800, -295384315960, 3328077806760, 656013145216, 23070159416], [915806465653841, -61428192169472, 617664746626, -50650514626, -141245090225, 1058580535514, -1129631079692], [177783980752154, 26627344394004, 1758634947703, -783729243999, -2389367145189, -2999899066742, -1250142596886], [1032806269884758, 61091241105626, -3191897985251, -1165642664051, 913032655339, 881329535464, 130064100608], [-269707976419858, -54394003630540, 1612601656939, -1155958110887, -2736088010669, -351771548070, -1216925920782], [929614946746524, -46012591219784, -2622870144916, -1176576556404, 2413011987984, -1966919493704, -2014633772088], [775766987735442, -62489385835228, 686922070578, 416802951662, -2678981444026, -2123686860376, -116402211324], [1070406249953122, 87525490788296, -311055313600, -993632062296, -1706603372368, 1945116286472, -844001395384], [-713543258776265, -74975741486589, 60621235495, -597901954743, 1962500582230, 665500605321, 1218906209878], [-893362259643714, 39966427956880, -2905174172867, -1912718326377, 1145454255685, 420763915946, 15165972314], [-167574626490842, 2374682000148, 1269652156127, 483864681341, -622833451241, 744165866578, -2841985328446], [-297517447671114, 36021463402646, -402944168272, 330341061824, -2487332119950, -3756557944154, 4094656337260], [1326797177545117, -25514625065500, 2929533386768, 1885936528108, -2687772464091, -262678779662, 1875928773896], [670271460593190, -40754223468792, -2329204466232, 1093501088324, 1033619438680, -4800053787088, 1145211325396], [-145858459654846, 33715128648640, -1943151649889, -54854008803, -130453208529, 656773037278, -497314550250], [692530711340952, 17158992539042, 42920449824, -732986533760, 2304858791684, 3017483414582, 2218275252052], [-821752413580161, 44165845547740, -1067172142986, -269271122974, 913174205905, 3367640555850, -249103920044], [-486313747881686, 87161325875544, -442067251604, 89349780356, 3212603028076, 1157274177824, 2430662012120], [-195093914791566, -54267338395746, 1179449606615, -582977435969, 2379834479153, 770172048504, 740333232440], [66584449682663, -49018547332681, -2533739485031, 822096074919, 6612641264128, -1975733967215, 1492845988174], [377434958294287, 17457593910715, 6089838630959, 58236638017, -701385748202, 3587428877905, -868603824538], [-1294366382501762, -24476218569864, -57074837188, -390225781580, -3821283240788, 696953518112, -2986599730488], [-277913018950908, -16801073655630, -770047657488, 756205941120, 4311535042620, 2341661184966, -917540555604], [-100883721520986, -39380961340376, 3090751557774, -2693846089414, 1143852231218, 6463087755468, -3536138075316], [-1000576068233086, 22586593296798, -5887144278975, 300083681877, 1889675118207, -2617981953868, 2464302765204], [2726385122105009, 26046748900849, 621777745399, 267329080121, -4227082954136, -342361711625, 680046691106], [1670517219033126, -60873713714344, -746800357100, -693949562528, -939016312006, -2820238919124, 242170261308], [1735482525737226, -43121690696716, 2232421988218, -2475829555006, 375237596078, 1621508440656, -4021725873320], [1137077761879302, 61519295350396, -2080885355592, -1494941377460, 4531268124192, 841274587772, 799498855172], [-9849398213835, 12519806886990, 172068022630, 1528092396374, 3085699068579, -2118762116996, 1711722723948], [-321594605012362, -78486395622556, -3537495633816, -1107038109652, 3857461921580, -1908213874196, -399099961028], [-1619782549288700, -28963421358356, 934505114872, 326272128124, -1600007583420, -3723269193532, 1570063541732], [-288816550986621, 45921115316745, 855713165483, -410616074123, 6002417684198, 4633746154563, -1003789753150]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_153_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_153_10_a_f();".
// 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_153_10_a_f(:prec:=7)
    chi := MakeCharacter_153_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_153_10_a_f();".
// 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_153_10_a_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_153_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,10,sign)));
    Vf := Kernel([<2,R![-675998208, -243559296, -10388768, 2252056, 8252, -2986, -1, 1]>],Snew);
    return Vf;
end function;