# Stored data for newform 22.8.a.d, downloaded from the LMFDB on 16 April 2024.
{"label": "22.8.a.d", "space_label": "22.8.a", "level": 22, "weight": 8, "hecke_orbit": 4, "hecke_orbit_code": 13510799016329238, "dim": 2, "is_polredabs": true, "nf_label": "2.2.14881.1", "trace_hash": 842475210021442680, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-3588, 23, 1]]], "qexp_display": "q+8q^{2}+(-11-\\beta )q^{3}+2^{6}q^{4}+(165+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1408, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 6.872470560650679, "hecke_ring_index": 1, "level_radical": 22, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [22, 1, [13], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 11], "conrey_indexes": [1], "field_disc": 14881, "field_disc_factorization": [[23, 1], [647, 1]], "field_poly": [-3720, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.012", "prec": 17}, {"__RealLiteral__": 0, "data": "1.966", "prec": 17}, {"__RealLiteral__": 0, "data": "0.010", "prec": 17}, {"__RealLiteral__": 0, "data": "10.487", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "79.440", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [11, -1]], "trace_display": [16, -23, 331, 1794], "traces": [0, 2, 16, -23, 128, 331, -184, 1794, 1024, 3331, 2648, 2662, -1472, -5406, 14352, -11247, 8192, 15032, 26648, 16916, 21184, -124798, 21296, -51351, -11776, -94029, -43248, -159137, 114816, -207130, -89976, -19071, 65536, -30613, 120256, 401074, 213184, 351333, 135328, 940148, 169472, 123610, -998384, -159822, 170368, 722412, -410808, 451160, -94208, 1420470, -752232, -1928826, -345984, -1260832, -1273096, 440561, 918528, -3795736, -1657040, 887547, -719808, -597918, -152568, 5383748, 524288, -1772672, -244904, 2864711, 962048, -3628227, 3208592, 1306267, 1705472, -4577530, 2810664, -1381472, 1082624, 2387814, 7521184, -2946342, 1355776, -7367030, 988880, 9965450, -7987072, 4243754, -1278576, 7813560, 1362944, 10185377, 5779296, -17140888, -3286464, -9416131, 3609280, 6400800, -753664, -27765477, 11363760, 4433561, -6017856, 15763504, -15430608, -21247560, -2767872, -28526118, -10086656, 42486930, -10184768, -21762152, 3524488, 21145763, 7348224, 19093467, -30365888, -4279827, -13256320, -29197210, 7100376, 38067116, -5758464, 3543122, -4783344, 58147128, -1220544, -38958369, 43069984, -1462688, 4194304, 96198374, -14181376, 34935054, -1959232, 65590480, 22917688, -24424965, 7696384, -24341797, -29025816, -27593638, 25668736, -48105144, 10450136, -7195386, 13643776, -39711580, -36620240, -203211003, 22485312, -46746476, -11051776, -652250, 8660992, 65422830, 19102512, 6479197, 60169472, -31104109, -23570736, -54756606, 10846208, 13000842, -58936240, -89866824, 7911040, -14969757, 79723600, 22062204, -63896576, -7283094, 33950032, 111001244, -10228608, 95228712, 62508480, -49864736, 10903552, 96244443, 81483016, -101986689, 46234368, 49022281, -137127104, 97040036, -26291712, 32959519, -75329048, 20007592, 28874240, -115974970, 51206400, 56831303, -6029312, 240248038, -222123816, 185802924, 90910080, 44358420, 35468488, -85832552, -48142848, 227049215, 126108032, -261837520, -123444864, -39111188, -169980480, 11506470, -22142976, 22515196, -228208944, -240403360, -80693248, 288275031, 339895440, -120810962, -81478144, 117789578, -174097216, -165558508, 28195904, -247834540, 169166104, 259147141, 58785792, -99960773, 152747736, 142321866, -242927104, -387843279, -34238616, -166106138, -106050560, -349504062, -233577680, 117583784, 56803008, 445030082, 304536928, -419135362, -46067712, -110755270, 28344976, 236979028, -38266752, 421963383, 465177024, -470665784, -9764352, 69579462, -311666952, 268127207, 344559872, -68348181, -11701504, -395337018, 33554432, 473351280, 769586992, -37459594, -113451008, -469901010, 279480432, 93868594, -15673856, -139411522, 524723840, 387609363, 183341504, -736242088, -195399720, 860132964, 61571072, 1266230776, -194734376, -125152599, -232206528, -543363980, -220749104, 189852542, 205349888, 338996984, -384841152, -42926928, 83601088, -732539880, -57563088, -723082832, 109150208, -293290746, -317692640, 328640813, -292961920, 388365886, -1625688024, 40437795, 179882496, -211811347, -373971808, -359012340, -88414208, -1464406228, -5218000, -338274846, 69287936, -189119408, 523382640, 337823212, 152820096, -884644768, 51833576, 1446481804, 481355776, 369990641, -248832872, 1218005388, -188565888, 307967735, -438052848, -275690030, 86769664, -524001594, 104006736, 977024328, -471489920, -36450662, -718934592, 1504643762, 63288320, 1005525776, -119758056, -554704271, 637788800, 5864984, 176497632, 214116279, -511172608, 1377143524, -58264752, -1557146115, 271600256, -25383501, 888009952, 2412983820, -81828864, -457948791, 761829696, 951384528, 500067840, -624507756, -398917888, 204506708, 87228416, 419936829, 769955544, -87109913, 651864128, -2795785332, -815893512, -2524030012, 369874944, 98313818, 392178248, -40745903, -1097016832, -539381112, 776320288, -941268263, -210333696, -1164206334, 263676152, -161379868, -602632384, -225572940, 160060736, 971527383, 230993920, 1200797060, -927799760, -462736611, 409651200, -2248186336, 454650424, 643515609, -48234496, 533829494, 1921984304, -2436473224, -1776990528, -886286389, 1486423392, 609674070, 727280640, 2620801194, 354867360, -898766750, 283747904, 234532460, -686660416, -4865613200, -385142784, 1963946052, 1816393720, -1085433892, 1008864256, -1023469029, -2094700160, 467624223, -987558912, 1773207388, -312889504, 830341653, -1359843840, -694187610, 92051760, 1465099838, -177143808, 219127118, 180121568, 2978100120, -1825671552, -1503126916, -1923226880, 1738493472, -645545984, -125499866, 2306200248, -1798628152, 2719163520, 1251336988, -966487696, 75770794, -651825152, 756535415, 942316624, 2126182560, -1392777728, 1607554776, -1324468064, 1309858704, 225567232, 6663931539, -1982676320, -235319445, 1353328832, 1180938695, 2073177128, -938432154, 470286336, 630088437, -799686184, 164524910, 1221981888, 5052204518, 1138574928, -3905927528, -1943416832, 584614878, -3102746232, -744792486, -273908928, -1753359246, -1328849104, 4607809875, -848404480, -1598228439, -2796032496, -2050057429, -1868621440, -1070261714, 940670272, -5881437295, 454424064, -212723082, 3560240656, 396700580, 2436295424, -507023694, -3353082896, -2667208396, -368541696, 2022305816, -886042160, -1259200734, 226759808, -4604524271, 1895832224, -4857070335, -306134016, 7648965836, 3375707064, -5157991092, 3721416192, -2838638420, -3765326272, 961530372, -78114816, -3074437922, 556635696, 4066923960, -2493335616, -8836510668, 2145017656, -5997950062, 2756478976, 2765854462, -546785448, -4662598893, -93612032, 6911770289, -3162696144, -1051242968, 268435456, -420471832, 3786810240, -2387479472, 6156695936, 600493960, -299676752, 7734630210, -907608064, -6449684721, -3759208080, 5533430140, 2235843456, 3261667352, 750948752, 2130627974, -125390848, -3099149389, -1115292176, -970168842, 4197790720, 6694982044, 3100874904, 7066988814, 1466732032, 11283526599, -5889936704, 1890645570, -1563197760, 4498600070, 6881063712, -935208313, 492568576, -4856015170, 10129846208, -3406140204, -1557875008, -3069603946, -1001220792, -4380783000, -1857652224, -8398928860, -4346911840, 2482217247, -1765992832, -5864117900, 1518820336, 11566528544, 1642799104, -2567267406, 2711975872, 5269370136, -3078729216, 4497540033, -343415424, -3867383806, 668808704, -6575283686, -5860319040, 981542464, -460504704, -10675325685, -5784662656, 3810652308, 873201664, -6431892333, -2346325968, 3577658924, -2541541120, 6360458732, 2629126504, -1678167392, -2343695360, -6756980724, 3106927088, -938559992, -13005504192, 4502254072, 323502360, -17186425194, 1439059968, 6047790622, -1694490776, 8658121196, -2991774464, 2066899232, -2872098720, 1556369088, -707313664, -2621564332, -11715249824, -1208671834, -41744000, 586386691, -2706198768, 7486480630, 554303488, 18671300640, -1512955264, -6283668352, 4187061120, -7125272834, 2702585696, 9848528976, 1222560768, -2537075588, -7077158144, -1879118271, 414668608, 5170144263, 11571854432, 2069906390, 3850846208, 374899416, 2959925128, -5052124616, -1990662976, -3303299002, 9744043104, 16899218657, -1508527104, -3833180092, 2463741880, 2022932384, -3504422784, -25890850974, -2205520240, -4800245646, 694157312, 3145431969, -4192012752, 449207395, 832053888, 17600553534, 7816194624, -1262959121, -3771919360, 1181325057, -291605296, -9004292126, -5751476736, 2003490201, 12037150096, 2759197122, 506306560, -2605273846, 8044206208, 15304224842, -958064448, -19498119985, -4437634168, 14195341848, 5102310400, 14966547120, 46919872, 2238468960, 1411981056, -1009315279, 1712930232, -795828858, -4089380864, -18075477392, 11017148192, 8114687500, -466118016, 9790965316, -12457168920, -25036362454, 2172802048, -25822359210, -203068008, 8767784836, 7104079616, -4578978391, 19303870560, 12288355199, -654630912, -4764199636, -3663590328, -3377842593, 6094637568, 7165768588, 7611076224, -4468547370, 4000542720, -13129146988, -4996062048, 6769171584, -3191343104, 5772248808, 1636053664, -9218494256, 697827328, -10133372568, 3359494632, 16337786788, 6159644352, -24301288599, -696879304, -14363517028, 5214913024, 5952956193, -22366282656, -2359426432, -6527148096, 734314422, -20192240096, 7462843529, 2958999552, -3253177408, 786510544, -322108192, 3137425984, 7940265370, -325967224, -3463591851, -8776134656, -7587351566, -4315048896, -23470281508, 6210562304, 9215349138, -7530146104, -41064993891, -1682669568, 3812930341, -9313650672, 12101216482, 2109409216, 22572651904, -1291038944, 6258639892, -4821059072, -6260525150, -1804583520, 12361267824, 1280485888, 38606402796, 7772219064, -8172703233, 1847951360, 969995031, 9606376480, -5152651018, -7422398080, 39918110528, -3701892888, -4829170137, 3277209600, -12592056466, -17985490688, -37081956540, 3637203392, 15038250768, 5148124872, 10162206012, -385875968, 4526922270, 4270635952, 12624464526, 15375874432, 16904526944, -19491785792, 4085946652, -14215924224, 4724057998, -7090291112, -27785729832, 11891387136, 1738641377, 4877392560, 15085111200, 5818245120, 1091404509, 20966409552, 30132422188, 2838938880, 55342849458, -7190134000, 35852837322, 2269983232, 12255521876, 1876259680, -5168054046, -5493283328, 19133276975, -38924905600, 13519284304, -3081142272, 5354697828, 15711568416, -6092692430, 14531149760, 3261330402, -8683471136, -13878436302, 8070914048, -25946472094, -8187752232, 12153562610, -16757601280, -20601533596, 3740993784, -21488456732, -7900471296, -47022218240, 14185659104, -53137691936, -2503116032, -12462628420, 6642733224, 6853419281, -10878750720, -1838739232, -5553500880, -6654937728, 736414080, -42129027469, 11720798704, -22941943354, -1417150464, 54778893648, 1753016944, 12234090084, 1440972544, 3993760871, 23824800960, -23954369571, -14605372416, -9083291718, -12025015328, -26426364786, -15385815040, 3541002417, 13907947776, 3178180434, -5164367872, -24376836580, -1003998928, -23301164889, 18449601984, -11695693900, -14389025216, 25815938040, 21753308160, -30470863598, 10010695904, 17621244015, -7731901568, 55310483904, 606166352, -13968269784, -5214601216, 6930591438, 6052283320, -23022717077, 7538532992, -3921581202, 17009460480, 22935906364, -11142221824, -46458171976, 12860438208, -42274742946, -10595744512, 23288797890, 10478869632, 18689595576, 1804537856, -26404155865, 53311452312, -5900695592, -15861410560, 13850747775, -1882555560, -46943974674, 10826630656, 30398070336, 9447509560, -9805516930, 16585417024, 24587644416, -7507457232, -26989476705, 3762290688, -7010590164, 5040707496, -5058788560, -6397489472, 6868043752, 1316199280, 109806058396, 9775855104, 8484639587, 40417636144, -7252620736, 9108599424, 29864990562, -31247420224, -67130441420, -15547334656, 13264013950, 4676919024, 19321416156, -24821969856, -10979016972, -5958339888, 80971318222, -2191271424, 66548026304, -14026873968, 32258218276, -10630792832, -24854341946, 36862479000, -9421001896, -6787235840, -20564787180, -12785827512, 102462124692, -22368259968, -26788888716, -16400459432, 5648436574, -14948971520, -11714005782, -8562093712, -10298624509, 7525362176, -3350094360, -47051498360, -36949169136, 3635392512, -25767018450, -1701784656, -16932276037, 28481925248, -13374548564, 3173604640, -10429545339, 19490363392, -15601065564, -4056189552, 19427346347, -26824663168, 10399848360, -21337667168, -29540345734, -2948333568, -42365472189, 16178446528, 71576225592, -7088337280, 33420538928, -10073605872, 9039637096, 1814078464, -53154306768, -36836194168, 34838100457, 15166657792, -23376697220, -38856562680, -34201597816, -2449072128, 18346730839, 61191726688, 13556736787, 27005656512, -65095581478, -41263928736, 62568347569, 29771329536, 24017621874, -22709107360, -73557911472, -30122610176, -49398848946, 7692242976, 76958044872, -624918528, 82889053769, -24595503376, -15285112240, 4453085568, -19723740332, 32535391680, -34427865583, -19946684928], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "22.8.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [8, 0], [-11, -1], [64, 0], [165, 1], [-88, -8], [890, 14], [512, 0], [1654, 23], [1320, 8], [1331, 0], [-704, -64], [-2644, -118], [7120, 112], [-5535, -177], [4096, 0], [7398, 236], [13232, 184], [8216, 484], [10560, 64], [-61870, -1058], [10648, 0], [-25959, 567], [-5632, -512], [-47180, 331], [-21152, -944], [-79697, 257], [56960, 896], [-103200, -730], [-44280, -1416], [-10183, 1295], [32768, 0], [-14641, -1331], [59184, 1888], [198930, 3214], [105856, 1472], [177359, -3385], [65728, 3872], [468044, 4060], [84480, 512], [65808, -8006], [-494960, -8464], [-73570, -12682], [85184, 0], [358470, 5472], [-207672, 4536], [222696, 5768], [-45056, -4096], [697677, 25116], [-377440, 2648], [-959298, -10230], [-169216, -7552], [-635070, 9308], [-637576, 2056], [219615, 1331], [455680, 7168], [-1890856, -14024], [-825600, -5840], [450927, -14307], [-354240, -11328], [-292900, -12118], [-81464, 10360], [2669900, 43948], [262144, 0], [-875220, -22232], [-117128, -10648], [1449827, -34943], [473472, 15104], [-1823691, 19155], [1591440, 25712], [673515, -40763], [846848, 11776], [-2303428, 29326], [1418872, -27080], [-712340, 43208], [525824, 30976], [1184590, 18634], [3744352, 32480], [-1445542, -55258], [675840, 4096], [-3696671, 26312], [526464, -64048], [4995102, -24754], [-3959680, -67712], [2098590, 46574], [-588560, -101456], [3850800, 111960], [681472, 0], [5126607, -67837], [2867760, 43776], [-8498600, -143688], [-1661376, 36288], [-4705387, -5357], [1781568, 46144], [3156120, 88560], [-360448, -32768], [-13882111, -1255], [5581416, 200928], [2201474, 30613], [-3019520, 21184]]}