# Stored data for newform 22.11.b.a, downloaded from the LMFDB on 25 April 2024.
{"label": "22.11.b.a", "space_label": "22.11.b", "level": 22, "weight": 11, "hecke_orbit": 1, "hecke_orbit_code": 68904026134, "dim": 10, "is_polredabs": true, "trace_hash": 1161711740269640287, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-\\beta _{1}q^{2}+(-11-\\beta _{2})q^{3}-2^{9}q^{4}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 11, "char_orbit_label": "b", "char_is_real": true, "Nk2": 2662, "analytic_conductor": 13.97785955882193, "hecke_ring_index": 2210716975104, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.502", "prec": 17}, "analytic_rank_proved": true, "char_values": [22, 2, [13], [1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 11], "conrey_indexes": [21], "field_disc": -122936818381620100448600129772003705864505774080000, "field_disc_factorization": [[-1, 1], [2, 15], [3, 4], [5, 4], [7, 4], [17, 2], [449971, 2], [726279812303, 2]], "field_poly": [8800385848545417604236, 216833564330959154376, 719974580168244048, -20333833907647600, -146480704240861, 631292713590, 6935435151, -6427236, -135903, -2, 1], "hecke_ring_index_factorization": [[2, 24], [3, 2], [11, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "9.278", "prec": 17}, {"__RealLiteral__": 0, "data": "3.222", "prec": 17}, {"__RealLiteral__": 0, "data": "521.855", "prec": 24}, {"__RealLiteral__": 0, "data": "413.387", "prec": 24}, {"__RealLiteral__": 0, "data": "46506.762", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "10.2.3.c2", "trace_display": [0, -106, 1138, 0], "traces": [0, 10, 0, -106, -5120, 1138, 0, 0, 0, 78044, 0, 95414, 54272, 0, -156288, 1441618, 2621440, 0, 0, 0, -582656, 0, -6002304, 17496838, 0, -1494468, 9714816, 54656930, 0, 0, 0, -91050970, 0, -12170158, -6879360, 0, -39958528, -82676974, -55302528, 0, 0, 0, -128221824, 0, -48851968, -124619384, 0, 352507996, -27787264, -374605478, 0, 0, 0, 571129876, 0, 1363103126, 80019456, 0, 1594048512, -1508647610, -738108416, 0, 0, 0, -1342177280, 0, 1288087680, 3146811782, 0, 5332296166, -1491609984, -328577450, 0, 0, 0, -18684358968, 0, 4256837904, 4919767680, 0, 298319872, -16957790722, 4545650304, 0, 0, 0, -12971187456, 0, 3073179648, 17791426978, 0, 40311734544, -8958381056, -11674310138, 0, 0, 0, -62585189614, 0, 48880194572, 765167616, 0, 38092454784, -50008013140, -4973985792, 0, 0, 0, -27984348160, 0, 40149757824, 61949802226, 0, 161573928322, -57760799616, -49759982654, 0, 0, 0, -134822153424, 0, 99277806298, 29223428352, 0, 46618096640, -187256697082, -21720410112, 0, 0, 0, -145722009216, 0, 6231120896, 79520833488, 0, 111035642014, 3522232320, 1940117170, 0, 0, 0, -339685299212, 0, 79276762224, 20458766336, 0, 110272414080, -125199796954, 42330610688, 0, 0, 0, 28314894336, 0, -9152068992, 389753618786, 0, 33533014418, 3777891840, 106342527052, 0, 0, 0, -28289885908, 0, 81441591286, -224638150656, 0, 65649573888, 195053479114, 92891582592, 0, 0, 0, 250610846208, 0, 25012207616, -613448310746, 0, -490820488010, 63805124608, -588615412126, 0, 0, 0, 1574025555926, 0, -499210898736, -180484093952, 0, -196966150272, 912673700422, 14227079168, 0, 0, 0, 191798004736, 0, -602906954496, -655647315652, 0, -2438617461146, 78377624448, 358704025536, 0, 0, 0, 1602183529096, 0, -1379108022864, -1353963525504, 0, -292418496512, 2315641860406, 1180261107840, 0, 0, 0, 1659379412736, 0, -697908800512, 1506284516304, 0, -3259501283578, -40969961472, 439019374884, 0, 0, 0, 1894354878050, 0, -863555547888, -816152838144, 0, 1044334539264, 3219255783196, 772427576320, 0, 0, 0, 377911508992, 0, -2405285625600, -737438452456, 0, -3482124435614, 965260523136, -665639519184, 0, 0, 0, 2835696279286, 0, 2560823243330, -2353278651264, 0, 687194767360, -744438765596, 2136433848576, 0, 0, 0, 710502029952, 0, -659500892160, -187678581884, 0, -4103506203902, -1611167632384, -6749326157900, 0, 0, 0, -2854247248368, 0, 2645598334764, -2730135636992, 0, 10213053818496, -595040062520, 763704311808, 0, 0, 0, 168231654400, 0, -2435449188480, 10340438353680, 0, 1887367711162, -9981285659136, -5647489160078, 0, 0, 0, -12842867123870, 0, 10639905867206, -9084133622400, 0, 9566391791616, 902895354912, 9873891407616, 0, 0, 0, -5803446113280, 0, -2179501006848, 19916918564356, 0, 1261699383196, -2518921052160, -360475825054, 0, 0, 0, -19720637756798, 0, 15033479812032, -152739774464, 0, 23511191344512, -9153339306096, 8682388849664, 0, 0, 0, -2327372955648, 0, -11459714825856, 25123010794406, 0, -1052600368760, -19248695220096, -21689447534878, 0, 0, 0, -23288715160094, 0, 15394777895266, -27660872424960, 0, 6641247977472, -519853209574, 17833096099584, 0, 0, 0, 2639027134464, 0, -1573467979776, 19329112050130, 0, -13716379458446, -9109210612736, -25062021156816, 0, 0, 0, -14723936706614, 0, 28848226459910, -20639608086528, 0, 62346701513472, 14233018852358, 4586691100672, 0, 0, 0, 5977246790656, 0, -23728110688128, 28651087429598, 0, -49057279190208, -23030389755264, -39110714281498, 0, 0, 0, 17740761128374, 0, 18263591030256, -61254662178048, 0, 32043617082368, 18735742918978, 56218640394624, 0, 0, 0, 15926545784832, 0, -25026659620864, 53789511267476, 0, -86529729258288, -391765819392, -10680117686972, 0, 0, 0, 29848718638030, 0, 11224743593206, -19503336849408, 0, 71870988426624, 75497845271314, 25604102727680, 0, 0, 0, 2546680725504, 0, -71446431568512, 21831203058796, 0, -114265997816908, -16605355096320, -30859863081224, 0, 0, 0, 58154669277024, 0, -16146829104912, -112214229180672, 0, 14327986257920, 71676901581650, 102219247089024, 0, 0, 0, 63384372978048, 0, -20556676005888, 67867068146588, 0, -171628244010890, -31718298739712, -68689514860826, 0, 0, 0, 18770760362722, 0, -16968198551568, -82725851300864, 0, 107975949207936, 82266974524656, 29573529403392, 0, 0, 0, 25477111118848, 0, -110259755658624, 76464256304150, 0, -185706611454214, -47960678590464, -45825449449418, 0, 0, 0, 56985055154290, 0, 119083306656864, -193760667535872, 0, 69028942553088, 109448695539928, 118104379852032, 0, 0, 0, 53243578080000, 0, -50830236824576, 46885359335222, 0, -87318102999322, -14962395316224, -194457437687516, 0, 0, 0, 81174580824768, 0, 57357323825032, -23868465479680, 0, 232957287504384, 85419696381740, 95875428905984, 0, 0, 0, 11120849977344, 0, -85225371023232, 190834662135734, 0, -168941146159166, -137068562901888, -150787201048080, 0, 0, 0, -45465329795956, 0, 74083060265060, -189447507050880, 0, 74609668718592, 45183757238098, 157543753145856, 0, 0, 0, -42789718506624, 0, -3190333898752, 137672615056044, 0, -53250723555608, -40714666745856, 96772251516912, 0, 0, 0, -286163259256682, 0, 168271354745318, -56850248711168, 0, 303848570500224, -97765213785278, -1803382947840, 0, 0, 0, -993339991040, 0, -132885151728384, 282787338722880, 0, -56405534726208, -186889219363584, -182716647919474, 0, 0, 0, -432852607623456, 0, 135524349023184, -140312835124224, 0, 173918873196544, -154254884427578, 138880145938944, 0, 0, 0, -101981932324992, 0, -40589702258688, 308010006564646, 0, -14239564965336, -10474888364032, -211895866064638, 0, 0, 0, -164714949410880, 0, 255094016405228, -56459476008960, 0, 381478148972160, -232813267630820, 64102296040448, 0, 0, 0, -21673272672256, 0, -65098228905600, 203145798103248, 0, 353369745354388, -157689324377472, -37111335781220, 0, 0, 0, -141288739505624, 0, 432364675726786, -151284909929088, 0, -14497225900032, 107558407885248, 88428624026880, 0, 0, 0, 23794018532736, 0, 4685859323904, -13000774882556, 0, 86221205683526, -199553852818432, -264700241008118, 0, 0, 0, -92393850508258, 0, -26010918335952, -17168903382016, 0, 105838905787392, 311821114656374, -1934280622080, 0, 0, 0, -54447373850624, 0, 136379184995328, 35149529495944, 0, -121496124030590, 81151634143872, -52662423215674, 0, 0, 0, 151611876035926, 0, -186603570464542, 124805705918976, 0, 14484421584896, -528300343252574, -161317845870336, 0, 0, 0, 112724446767360, 0, -41698094738432, -156392926158958, 0, -133464926462256, 115014733135872, 510482961606192, 0, 0, 0, 71739358255078, 0, -301967649357792, -33612581830656, 0, -523540405374336, 395136599961696, -99867381306368, 0, 0, 0, -47560490287104, 0, 8438079551616, -165049428703604, 0, -260119974732074, 30697678089984, -19665016283582, 0, 0, 0, 251666383551878, 0, -408811674953088, 281589430773888, 0, -128312753258496, 890474233485264, 198661785244800, 0, 0, 0, 50613920342400, 0, -12806250299392, -848904771248164, 0, -626160689281296, 314085535101952, 327586386523010, 0, 0, 0, 1200584075620982, 0, -829634935455216, 251300089861120, 0, -942770868872064, -1070253991693562, -32668223799296, 0, 0, 0, 301371091008512, 0, 57275758434048, -513139337166730, 0, 101367574496930, 973503870741120, 683879372930976, 0, 0, 0, 1128999434786626, 0, -392980950808094, 682078074525696, 0, -805901084634112, 1458020134417968, -899235643434240, 0, 0, 0, 488925579069312, 0, 255595980152832, -1092705131267952, 0, 1432799649755030, 92407856103424, 723239108064982, 0, 0, 0, 370658480758292, 0, -742256051188190, 100846668939264, 0, -1428305969192832, 139492621133088, -467288934616064, 0, 0, 0, -7284264534016, 0, 814111279546752, -1293059482823684, 0, -889287057431804, 1198075531540992, -179884922750616, 0, 0, 0, 1918376127390000, 0, -808802260391950, 952382918423424, 0, -98200578424832, -2177384001403498, -1965539485269888, 0, 0, 0, -640940377990656, 0, 308688360701952, -1615783090377312, 0, 1669287950308676, 335691425613824, 2027446017170578, 0, 0, 0, -953698633798616, 0, -138926190196464, 1248572140106752, 0, -2311670840079744, -346415336781524, -40129343717376, 0, 0, 0, -183656461074432, 0, 994948912400256, -460333410242260, 0, 2132157310957920, -433863816320256, 350205342026112, 0, 0, 0, -1136086568410042, 0, -879039690618936, 2140572873824640, 0, -820317966897152, 922533991018178, -244101369094656, 0, 0, 0, -1262172218918784, 0, 706103307706368, -685143909014678, 0, 1293805156644934, 693229325058048, -13524586895078, 0, 0, 0, -831952097962094, 0, -1407808936487712, 149718270214144, 0, -1864160249367552, -3212272477369630, -1185608632527872, 0, 0, 0, -604293687214080, 0, 1812362455035264, 327171615781718, 0, 4590040740243984, 1264858802192256, 3832829201164828, 0, 0, 0, -1231943572250170, 0, 1948485261484608, 3414826543931904, 0, -849602259320832, -1659238542018968, -2830015866069888, 0, 0, 0, 13960043168256, 0, 357329305862144, -1523133917367854, 0, 4212825691324604, -771217672347648, 326182560215450, 0, 0, 0, -2759095828924464, 0, -1753507705828846, 1668864657191936, 0, -1564843045310592, -2114396541549518, 20976620273664, 0, 0, 0, -224777919940608, 0, 3175294576933248, -326838688941024, 0, 2550941363334662, 1463146786763520, -1489101184649716, 0, 0, 0, -160159160685572, 0, 109429255624128, 2827397071229952, 0, -969909697561600, -4089241426834608, -2994982439527296, 0, 0, 0, -1690757631532800, 0, 442140440518656, -3746506151945496, 0, 5151196254772024, 417870253129728, 4246457726676676, 0, 0, 0, -2874991043201420, 0, 2565835533644592, -534699284103168, 0, -3142067433344640, -1195029710082110, -1648258960996352, 0, 0, 0, -395482919075840, 0, 642701502279936, -1349044445476298, 0, 4253627356486416, -127083208631808, -3179041760144030, 0, 0, 0, 724049257843138, 0, -2274661783905984, 3316533101171328, 0, -193490692603904, 2135814116230284, 78672362115456, 0, 0, 0, -1163800061220480, 0, 1231506240307200, -2295786234908016, 0, -2991830809634906, 377568487657472, 370574561616720, 0, 0, 0, 2023998561899890, 0, -3005050789858810, 1782847711034368, 0, -1467386392043520, -5842538440359866, -494213387845632, 0, 0, 0, 340807433822208, 0, 83864861634048, 3190456454701628, 0, -450928166897018, 1535910320750976, 7564145763206396, 0, 0, 0, 2404344887538430, 0], "weight_parity": -1, "has_non_self_twist": 1, "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], [1, 1, 11, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "22.11.b.a", "char_is_minimal": true, "conrey_index": 21, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, -1, 0, 0, 0, 0, 0, 0, 0], [-512, 0, 0, 0, 0, 0, 0, 0, 0, 0], [113, 0, -2, 0, -1, 0, 0, 0, 0, 0], [0, 11, 0, 0, 0, 0, 1, 0, 0, 0], [0, -30, 0, 0, 0, 2, 1, 1, 0, 0], [0, 512, 0, 0, 0, 0, 0, 0, 0, 0], [7775, 0, -74, -1, 3, 0, 0, 0, 0, 0], [0, -121, 0, 0, 0, 0, -3, 16, 0, 0], [9550, -1168, 20, -3, -14, -2, 0, -14, 0, -1], [5632, 0, 512, 0, 0, 0, 0, 0, 0, 0], [0, 1857, 0, 0, 0, -27, -42, 45, 0, 0], [-15552, 0, 192, 0, 16, 0, 0, 0, 16, 0], [144174, 0, 27, -7, 213, 0, 0, 0, -15, 0], [262144, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1361, 0, 0, -7, 95, -72, 17, -7, -14], [0, -7754, 0, 0, -8, 8, 93, -48, -8, -16], [0, -10770, 0, 0, -21, -70, 145, -23, -21, -42], [-57856, 0, 1024, 0, 512, 0, 0, 0, 0, 0], [0, -25221, 0, 0, -27, 27, -24, 405, -27, -54], [-600944, -9677, -1768, 32, -452, -8, -88, 208, -44, -48], [1746344, 0, -8381, -63, 762, 0, 0, 0, 250, 0], [0, -5632, 0, 0, 0, 0, -512, 0, 0, 0], [-138319, 0, 27778, -83, 1487, 0, 0, 0, -16, 0], [968352, 0, -7824, 0, 1656, 0, 0, 0, -216, 0], [5472893, 0, 17923, -154, -1383, 0, 0, 0, -207, 0], [0, 15360, 0, 0, 0, -1024, -512, -512, 0, 0], [0, 309140, 0, 0, 85, -296, -2094, 3622, 85, 170], [0, -142191, 0, 0, -56, 1016, 1441, -3168, -56, -112], [-9097152, 0, 19775, -175, -4322, 0, 0, 0, 1066, 0], [0, -262144, 0, 0, 0, 0, 0, 0, 0, 0], [-1249548, 251133, -81474, -287, 351, 201, 1782, 3321, -924, 84], [-710848, 0, -57056, 448, -160, 0, 0, 0, 704, 0], [0, -288314, 0, 0, 218, 2174, 5211, -541, 218, 436], [-3980800, 0, 37888, 512, -1536, 0, 0, 0, 0, 0], [-8303217, 0, -88726, 146, -16001, 0, 0, 0, -1628, 0], [-5495712, 0, 87024, 1344, -8, 0, 0, 0, -728, 0], [0, 968778, 0, 0, 300, 3210, 1875, -16209, 300, 600], [0, 61952, 0, 0, 0, 0, 1536, -8192, 0, 0], [0, 897089, 0, 0, 637, -5111, 2424, -24089, 637, 1274], [-12804288, 0, 45600, 1728, 12960, 0, 0, 0, 0, 0], [0, -2555700, 0, 0, 747, -2104, -19436, 38932, 747, 1494], [-4889600, 598016, -10240, 1536, 7168, 1024, 0, 7168, 0, 512], [-12577850, 0, -290248, -938, -7806, 0, 0, 0, 1656, 0], [0, -1745437, 0, 0, -504, -15496, 6193, -16192, -504, -1008], [35455172, 0, 510868, -126, -41853, 0, 0, 0, 1051, 0], [-2883584, 0, -262144, 0, 0, 0, 0, 0, 0, 0], [-37384379, 0, 188364, -4116, 35808, 0, 0, 0, 612, 0], [0, 150286, 0, 0, -664, 1688, -19611, -23536, -664, -1328], [0, 7428462, 0, 0, -762, 13254, 8205, 46449, -762, -1524], [0, -950784, 0, 0, 0, 13824, 21504, -23040, 0, 0], [57046742, 0, -168116, -5004, 5796, 0, 0, 0, -8072, 0], [0, -5480279, 0, 0, -1232, 14480, -19047, 25440, -1232, -2464], [136256146, 7820754, -137009, -3185, -31411, -16394, 7403, 53003, 9449, 42], [7962624, 0, -98304, 0, -8192, 0, 0, 0, -8192, 0], [0, -11236467, 0, 0, -2319, 46005, 107448, 20187, -2319, -4638], [159237856, 0, -420208, -5440, 117592, 0, 0, 0, -1688, 0], [-150496465, 0, 920971, 462, 125164, 0, 0, 0, 18488, 0], [-73817088, 0, -13824, 3584, -109056, 0, 0, 0, 7680, 0], [0, 5618670, 0, 0, -1701, -22510, -196790, 8644, -1701, -3402], [0, 9040731, 0, 0, -1400, -66824, -67335, 52096, -1400, -2800], [0, -4187724, 0, 0, -4290, -35076, 97704, -74340, -4290, -8580], [-134217728, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -28518501, 0, 0, -4389, -40989, -161052, -56607, -4389, -8778], [129367776, 1270479, 1396176, -2688, 102032, 64120, 108317, 10512, -352, -4592], [316109071, 0, 3571591, 3718, 171860, 0, 0, 0, -38404, 0], [0, 696832, 0, 0, 3584, -48640, 36864, -8704, 3584, 7168], [531607497, 0, -4049202, 12194, 68667, 0, 0, 0, -8196, 0], [-148332928, 0, 2063200, -13952, -36448, 0, 0, 0, 19136, 0], [-34260694, 0, -3502637, 9471, 200866, 0, 0, 0, 16130, 0], [0, 3970048, 0, 0, 4096, -4096, -47616, 24576, 4096, 8192], [0, 21640047, 0, 0, 6111, 128663, -53504, -230687, 6111, 12222], [0, 8208207, 0, 0, 1168, 103024, 48837, 282064, 1168, 2336], [-1868500704, 0, -149082, 25872, -489663, 0, 0, 0, 1629, 0], [0, 5514240, 0, 0, 10752, 35840, -74240, 11776, 10752, 21504], [426183804, -1508575, 1259916, 19764, -224051, -101015, 400488, -386873, -21791, -2542], [491020992, 0, -2399040, -19200, -546768, 0, 0, 0, 28080, 0], [0, 928308, 0, 0, 15624, -12572, 532784, 87500, 15624, 31248], [29622272, 0, -524288, 0, -262144, 0, 0, 0, 0, 0], [-1697153203, 0, -3417032, 36590, -314142, 0, 0, 0, -56448, 0], [454022656, 0, -1376320, -40768, -735056, 0, 0, 0, -35792, 0], [0, -44223044, 0, 0, 5705, 146720, -700278, 292862, 5705, 11410], [0, 12913152, 0, 0, 13824, -13824, 12288, -207360, 13824, 27648], [0, 17973057, 0, 0, 13299, -186607, 144400, 512647, 13299, 26598], [-1298391264, 0, -3205200, -47808, 1256680, 0, 0, 0, -10856, 0], [0, 49145580, 0, 0, 7854, 44436, -421932, -931032, 7854, 15708], [307683328, 4954624, 905216, -16384, 231424, 4096, 45056, -106496, 22528, 24576], [1781426780, 0, 5733106, 45801, 686415, 0, 0, 0, 178624, 0], [0, 12479468, 0, 0, -7504, -98480, 213570, 98400, -7504, -15008], [4032698796, 0, 3800484, -25740, -877272, 0, 0, 0, 28308, 0], [-894128128, 0, 4291072, 32256, -390144, 0, 0, 0, -128000, 0], [-1163930719, 0, 8790010, 78546, 1785627, 0, 0, 0, -124920, 0], [0, -35811394, 0, 0, -1008, -66256, -745904, 652832, -1008, -2016], [0, -38534882, 0, 0, -34336, -367954, 133233, -7867, -34336, -68672], [0, 2883584, 0, 0, 0, 0, 262144, 0, 0, 0], [-6254692350, 0, 9577886, 22715, -709673, 0, 0, 0, 146980, 0], [0, 37646255, 0, 0, -32928, -6240, -8160, -582720, -32928, -65856], [4881790889, -117663114, -15580397, -17953, -321201, 254136, 97119, 29061, -81939, 1569], [70819328, 0, -14222336, 42496, -761344, 0, 0, 0, 8192, 0]]}