# Stored data for newform 33.8.e.a, downloaded from the LMFDB on 19 April 2024.
{"label": "33.8.e.a", "space_label": "33.8.e", "level": 33, "weight": 8, "hecke_orbit": 1, "hecke_orbit_code": 275012124705, "dim": 28, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [74869965115833756999378534400, 56752958678298055049687859200, 27571515762117164751687516160, 7475085117526352138950410240, 1540809738324818667335909376, 102152753282923405109755904, 30699613129576828353740800, -92818137928059844280320, 781574790556839177900032, 10191885946048529793024, 7675186969274741022720, 402633713373875745792, 90388394794494254336, 805420971411167488, 751685582598174208, 23139496901245888, 4554658107971664, 188547905635968, 26873462699128, 922138087708, 94011380549, 2089735763, 234979339, 6855516, 574889, 16944, 1036, 22, 1]]], "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2112, "analytic_conductor": 10.308705840976017, "level_radical": 33, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [33, 5, [23, 13], [5, 1]], "inner_twist_count": 2, "level_primes": [3, 11], "conrey_indexes": [4, 16, 25, 31], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 7, "sato_tate_group": "7.2.3.c5", "trace_display": [-22, 189, -777, -83], "traces": [28, -22, 189, -692, -777, 594, -83, 3568, -5103, -1352, -18851, -60966, 14635, 62912, -22896, -36148, -10338, 9477, 90342, -289719, 28836, -202339, 138508, 187704, -174068, 466130, 137781, -640233, -487290, -372546, -388352, 2726322, -265923, -1543708, 742659, -504468, 670209, 2282072, -395145, 4641741, -2721357, 620676, -199784, -5887437, -103518, 3389447, 2112053, 2292111, 3927748, -3663090, 615681, -4343053, -1743854, -354294, -8387710, -6307818, 1223721, 546605, -218820, 7822413, -743157, 3996183, -60507, -21725666, 4895794, -8684037, -3235686, 961671, 4712499, 31155916, 9848757, -5068008, -6667768, -31115192, -2544939, -6535748, 8320585, 20060730, -10121851, 44592526, -3720087, 24927115, 13288897, -17477019, -28050005, 20937351, -22226400, 39687014, -40241460, -9565938, 8733043, 11607651, 10485504, -7877385, 14371097, 2790126, 30518151, -16954218, 11659626, 65179058, -65648985, -41388489, 30072538, -3500697, -20051793, -67443015, -40356445, 8601471, -4807336, 75285238, 44887392, -243830934, 33901679, 87226281, -27439045, 22172136, -19650195, -32200717, 117253542, 2733048, 182947803, -35679294, -56822661, -98126082, 28238149, -16758252, -144475234, -237534271, -15604677, 84208394, 247283618, 65396484, 34513502, -325807680, -16691184, 364337877, -19156469, -91515069, -143383463, -568762650, 26263494, 675655706, 170543564, 176477778, -260594556, 121689655, 183107574, 402946754, -341678091, -202374180, -152345190, 185628881, 48319578, 71288118, -81824364, -214163514, -291704484, 380496341, 47084058, -834099071, 164504925, 6908733, 114920176, 1198319706, 92708955, -73383556, -168727783, -195971049, 492962514, 443761911, -33040467, -476717271, -648018210, -121175190, 218307598, 486583237, 86755590, -470482269, 218659575, 149966964, 124778503, -544118715, -102997116, -1503627167, 453209929, -63163746, 530890961, -1174342914, -12144411, 471103651, 368254913, 586592982, -534384356, -500435406, -195830838, 508894759, 141656646, -201826566, -164114568, -1161464301, 60976962, 1703126711, 811903656, -25965117, -334936120, -1431022734, 76751307, 76420090, 268849476, -42199542, -1237310176, 751589466, 250478946, 1341446352, -451392345, -70228944, -468589623, -379214010, -431903664, 591759690, -408293010, -903533211, 518846511, 2475992709, 68713353, 439422613, -540277203, -274890159, 242905374, 1513263906, 1022223915, 263981202, -611735343, 339808770, 477753139, 1714977792, 273289977, -1895159279, -922631711, 1345300488, -1149654304, -1893602502, -401769396, -163815749, -1026151296, -35761500, -329596429, -2043021131, 551928681, -85563421, 1104080724, -10299312, 1020545841, 2293412412, -451138815, 2033168236, -114933998, -565308477, 1007853065, -988349925, -355234410, -1264924560, 1246836150, -153630513, -2758302528, -593723174, 557211825, -339710533, -96525534, 258280326, 1482015568, 409011117, 623898369, 742779634, 2620602554, -1142279982, -894396458, -3245263401, -17821863, -1917735336, -2742103820, -1230797565, -617136506, -2301723381, -1002964734, 1180620399, 967273916, -918410967, -132845317, 2993351154, -823990077, -33672956, 2423914811, -207350604, 3243813864, 2847534808, -44857557, 1329538784, 636449863, 1138663224, -983438703, 2671378282, 1772522595, -1341226095, -1219744035, -554807637, -636150182, -4285156260, -227179296, 449188694, -3910879969, -1728914841, -3232415387, -3980917062, -1161665874, 3532344626, -327324089, -1062581490, 1373009926, 6806001532, -283832505, 406306636, -1614607935, -232239717, 783718367, 2062232051, 1617203772, -1832769869, 5463511542, 1259917794, 1175819776, 6258944256, 488582361, -6630081381, -2041464222, 6583435218, -140688836, 2097011413, 1683776457, -2175252690, -355302036, 1382958198, 2707167951, -5428790343, -3570589620, -1662181431, 215829946, 3767603463, 3201595147, -9017128053, -484989120, -3121209232, -559027416, -144705771, -1739269307, -8176546269, -3165845634, 6049108603, -40221282, 3383829189, 1888578521, 3740465318, 2591920809, -799784202, 7185579702, 3854597463, -3834925038, -1873879591, 1534211847, 8736718427, 8350613743, 1062086904, -1401917700, -14721749115, -1374010128, 7218960962, -2848152510, -1238296896, -6961365657, -2584535883, -2230115652, 4662704326, -4973689413, -24236246358, -539882530, -3144561402, -348505011, 4834171732, -1767398001, -2273626638, 8144215502, 10873919238, 2863165239, -4350155541, -444297398, -94924548, -584327600, 20695996641, 193679586, -5586377932, -4303576032, 8796807360, -115903151, 5813667030, -412929657, -38016896876, -5519497197, 3182312826, 881973324, 10068196531, -2174680197, -4817309781, -4512148771, -2288220192, 15576136370, -7198629318, -7718986854, -4864615309, 5518550738, -453182040, -1707439610, -8792979069, -709114338, 23330517407, 7021108533, 7810630713, 2324315797, 13665467868, 4995353187, -14739370150, 6161329506, 1670948919, -12177986054, 9318438701, 7036053012, 6216716630, -3411749298, 7283448180, -15435869024, -30549493344, 4161152412, 12770565935, -6409478866, 1631357577, -1435637587, 4748389755, -1635614883, 23467502491, -8967482650, -5587420500, 3691425567, -23441559402, -4851847350, 15425720411, -7222911722, -5011979787, 11658151732, 30821833546, 448831449, -10426480825, 25051460826, -5700193641, 21579392034, 42209684982, -2923546257, -8727107437, -5754568037, 5782414878, -7097196606, -19035379264, -974215782, -36891558856, -752079117, 537025788, -7697831276, -7947775422, -611345961, 1529933109, -12309055474, -11714817078, 21763006627, 602207127, -13738248540, -5441474027, -2689124802, 315675954, -15243994179, -15102426960, -3102844752, 8166613159, -10325846941, 15797388123, 1789606628, 24942201902, -2443356495, 11598447946, -1519221753, 5647493097, 5251490690, 18231649227, 4555650141, 2270035766, -10979951668, -2992018662, 27443776366, -15672346404, 10791024552, -2183672342, -4201210229, 6112108368, -19915971328, -61311012680, -1778201586, -17100712561, -3066860516, -25025792238, 16077244411, -41954845222, -11209806135, -2639068010, -17346766892, 3271730130, -5632490408, 34799835222, 12015221454, 8778830122, 68559476310, 35312606316, 9670610656, 33861492876, -159519780, 24859942067, -8443660325, 12703021263, -22597948674, -43585697250, 14295003795, -29449211060, 100983036, -3306862098, -26498758591, -6857946711, -4064841441, 1530787595, -24811428924, -4131400410, -6172650319, -19855238766, -4478321358, 23540920515, 20362567572, -24065662221, -6294325131, 39942872679, -12236668083, 14246463365, -7280325452, 2913217407, 15104717489, 119880707654, 17301209958, -23472858564, -14307389541, -859411782, -15561332554, 27091046156, 327899097, -34809781004, 8310708480, 11962919133, 12082757562, -10109702979, 5522690484, -29170809465, -30117955522, 1260771966, -17109392764, -36580565632, -10922470893, -21389513438, 4746250907, -49932747108, 31818321924, 4489566354, -7071949539, 33053332906, 5467584195, -13740158493, 8288382413, 10073520448, 6201250353, 63535345499, 62426752226, -594446283, 43898727520, -19927488027, 15357400821, 31327274268, 7401072002, 31359536127, -31182443139, -53725947426, 2825785521, -89324697438, 29332342468, -12137825052, -38841461860, -15304487115, 4390477668, 61086130337, -56434355748, -7317129006, 3659639202, -52538698533, -32756353830, -3972793957, 40263788268, -26926003827, -32883893597, 86764660638, -2072285289, 4068689921, -35629943885, -7557386940, 23550361008, 61260278644, 24354180468, 29837240744, -33613787016, 22712662764, 37405420741, 62094538981, 33407374752, 23775603688, -18813151930, 5642295408, 24572973728, -83435437005, -833624622, -110403412576, -14912196538, 7782127596, -20180233330, -86451741030, -24102710730, -53045818290, 11193959852, 3596792688, 54518820371, -59607750158, -20816481384, 83317429506, 36674666383, 10238778270, -27635047757, -16093236066, -4860802872, 23062820113, 71049218640, 33135422625, -38454823918, 24285621707, 1327012065, 20397290442, 9199565970, 24395396697, -52928667038, -123653638863, 24165513513, -101511865796, 32562896262, -14002611588, -68068643209, 34598506260, 3426180444, 56906579301, -58563177460, -1359099486, 22978940752, -34614652743, -20086892784, -1674357043, 19828716088, -5039754147, 23605848492, 71153503003, -6558445098, 87413529281, -540841265, -16629432057, 34322023388, 41465483646, 22739234085, -53787320354, -27348947451, 67313763261, -20910386583, 102424985613, 16516854261, -20088648624, -57817630300, 1862700705, 40732116850, 15695791073, -12045546288, 40366992034, -113430566149, 14192110521, -44411671520, -115322567557, 7686495081, -107859311863, 36593065588, -69057440892, 27886834983, 26250824088, -25062738498, 83120069768, 72157445089, -36323113176, 15226457314, 35295210150, 6204228588, -75358734262, 119763078348, -26793325611, -16711908874, 66327767235, -2711943423, 98277870110, 7330548180, 4423025223, 3547189178, -11606449650, -2888461458, 108547604906, 15476460651, -38274854670, -15504866011, -36379239441, -31136255172, 156472695369, -104871926031, -33100082433, 7827454366, -104806518647, 10428936948, 23223733628, 70806500560, -7525257858, -31883316260, 71019130789, -29810179548, 15012980896, 12043932524, -12740746851, 54501175915, -5493055558, 15350775183, -73694412250, -35065073715, 45770280606, -36076123044, 143159142624, 12180748005, 21192738758, 4659378266, 89687406303, -103047704954, -237526480179, 40090636746, -14756234218, -9421899215, -24470119926, -66724939699, -37358352003, 10225142595, -87582248261, -24670796915, -35265454380, 112559467968, 27274130940, -1489806270, -46706357792, -69156241938, 34152963120, -48459164864, 7944828021, 45423303930, -25779677989, 104893566432, 18282819906, -21886121598, 140039378271, -23541673329, -10299429232, -71770787634, 16030525698, -43678125276, 32282231850, 29712731445, 131764853732, 62761576634, -95398644024, -68880037595, 35301713573, -375451362, -156570507129, 324747225, 7332822918, 47202055323, -22397077113, 29706765174, -216748944626, 128961297652, 4392755631, -45981748236, -84241383421, -16845255963, -30673150637, -24759709193, -25979293458, 70980286525, 60109503274, 17296800372, -5387221480, -40835822362, 8461977579, -77459344647, 32945463333, 24148704366, 50069125291, 27164259150, -88716022983, -33909979894, -42763557789, -16250245434, 71262563932, -164611704975, -45260349183, -104535801687, 62286923978, -52478597250, 283771511328, 140069242600, -54977841180, 122023654712, -234874961310, 20591820972, 11060235510, -40668969659, 62146531287, 76074380289, 37915935099, 10476529713, -74899160360, 60015852324, -13302194733, 236387785708, 89417464281, -41462343747, 17337493207, -142208658646, 24797096109, 69336434187, 144377123190, 11736273924, -232859638752, 58275334916, 239632831782, 50656662903, 27369100938, -37803894426, -28927580848, 29505944719, 59091431337, 30192341765, -85404645096, 4040087868, 119730223394, -133383970234, 581346153, -63652481786, -210010487496, -87582974328, 110735924719, -76778418559, 125360041689, 53190501026, -263378788534, -4926989511, 18846237896, -10140595367, -34178326758, -55034333054, -270684047836, -17184146301, 25020924106, 176872451424, 6986140407, -55786057102, -38242980700, 46861233696, 276446574923, 41510631176, 101557314081, -149097555077, 411534163686, 37271287755, 198719865799, 105820547477, -14851730430, -51307144811, 14384516118, -7072213680, -24601302120, -161797991139, 14979806199, 3150437449, 186656404312, 17413596459, -181348167712, -283087098646, -132583506210, -72391516222, 180381114724, 21922880202, -340829220279, -238640864805, -12128094738, 113216320032, 70340004939, -77523828057, -198996958044, 259798214811, -88257385188, 123484022907, 403066996317, -19901807001, 224742988786, 96997017410, -109170529596, 186827193579, -11126076325, -33494443002, -395651999760, 88403358918, 93011929128, -31944248338, -146679124447, 8837750403, 17864119598, 139689773732, -49165957935, 3429254477, -312537379578, -21157185042, -200828146352, -19489295083, -238332268269, -244263036113, 44989313635, 7663477635, -47463315760, -5018480791, -42076523817, 88179577974, -196079705272, 149409656460, 91995941674, 11332321710, 9929443644, -94693597886, 315431775468, 58702111776, -70447757489, 64395395813, 54019853208, 49037593771, 61311435612, 45416775816, 109215488529, -101202667190, 49484786463, 53226720387, 140274417762, 106037498331, -208282532259, 41075183376, 54394318962, 212545900522, -49098499434, -4191647697, 192159857017, -52343067621, -168991494912, -125690949390, 141704681983, -3169730637, -40412751088], "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, 3, 1, 5, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "33.8.e.a", "char_is_minimal": true, "conrey_index": 4, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}