# Stored data for newform 22.6.c.a, downloaded from the LMFDB on 05 May 2024.
{"label": "22.6.c.a", "space_label": "22.6.c", "level": 22, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 137539616790, "dim": 8, "is_polredabs": true, "trace_hash": 1436511363642544650, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [5823368721, 345688830, 41007546, 1298040, 129736, 100, 301, -20, 1]]], "qexp_display": "q-4\\beta _{3}q^{2}+(3+3\\beta _{3}+\\beta _{4}-\\beta _{5})q^{3}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "c", "char_is_real": false, "Nk2": 792, "analytic_conductor": 3.528444035885574, "hecke_ring_index": 16, "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": 0, "analytic_rank_proved": true, "char_values": [22, 5, [13], [4]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 11], "conrey_indexes": [3, 5, 9, 15], "field_disc": 110567853765625, "field_disc_factorization": [[5, 6], [84121, 2]], "field_poly": [27248400, 626400, 163440, 2910, 7111, -241, 121, -1, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.825", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "201.191", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9347.096", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c5", "trace_display": [8, 20, -30, 48], "traces": [0, 8, 8, 20, -32, -30, 40, 48, 128, 284, 1200, 0, -320, -1746, -192, -3578, -512, -90, 2344, -1824, -480, 10324, 0, 1640, 640, -4572, -7536, -5500, -1312, -6666, 14312, 6878, -8192, 38962, -2960, 2456, -9376, 9062, 2136, -27728, -11520, 8014, -18216, -10792, 12320, -67880, -3120, -1304, 5120, 56724, -13832, -29014, 30144, -27598, 62480, 84238, -4352, 42926, 26664, -146416, 53952, -1942, -40872, 110074, -8192, -32972, -57728, -335736, -1440, 220148, 46776, 144862, -18176, 139906, -36248, -142640, 75456, 36586, -123568, 124046, 46080, -3952, 169104, -60618, -155456, -105966, -296352, -173656, -49280, -534800, 67560, 64510, -25600, 369082, 30376, 295574, -20480, 36414, 180304, 379390, 35648, 464306, 116056, 134012, 111744, -210088, -159488, -55856, -88000, -701432, -171952, -144072, -20992, -113622, -176624, -71848, -73216, 132282, 585664, 215848, -26368, -231352, 545488, -307822, 163488, -169650, 156504, 175158, 32768, -35584, -516512, 735240, -349888, -373476, -70656, -568070, 17920, -761630, 401968, -381936, -187104, 1080602, 770592, 600578, 154624, -721154, -559624, 161978, 114112, -325086, -929880, -287424, 34176, -556880, -713064, 2651028, -443648, 242562, -136904, -1987280, 30720, 1520044, 15808, 1679546, 1096384, 1052150, 1570432, -178154, 621824, 559596, -746096, 564638, -1099072, -1051290, -878296, -1922172, -394240, 156244, -669280, -1698124, 813280, -1958366, 62640, 559182, 102400, 261542, 471552, 201234, 284736, -263520, -1182296, -66044, -40960, 1862238, 38704, -22814, 907584, 631000, -401280, -318760, -221312, -699400, 1508656, -188414, -533824, 1266622, -536048, 975020, -70656, -2211066, 3371472, 148686, 637952, -513474, -214136, -2275916, -851840, -864926, -1304992, -2261376, -1700512, 1707964, 523928, 1349296, -49152, 929254, 978608, 236564, 706496, 1683582, 2001952, -1573308, -1438976, 939478, -529128, -459862, 2211104, 1854866, 1625288, -56944, 863232, -293896, -802472, 1794340, -31072, 1365062, -3135752, 1837772, -440192, -1777170, 678600, -4166034, -2270336, 2142272, -2317952, -176070, -131072, 503494, -745584, -316594, -1802272, -559748, -2280080, -414120, 484352, -5869380, 1224824, 555260, 2403264, 2153342, 1185960, 2303408, -71680, -1573136, -4828560, -2569710, -3828992, 3447254, 1527744, 3806954, -157184, -1879930, 5689792, 904928, 2317792, 7423204, 4838328, -5401232, -290816, 2132156, -2668904, 4120800, -2770944, -3235994, -647912, -2814704, 2072832, 3773330, -2257776, -236328, 3719520, -1877824, -860824, -1096540, -466944, -1064882, 1150120, -2957080, 1484736, -4961540, 2757688, 1514856, -786048, -527618, 200592, -8914232, 547616, -2685754, -2182480, 8488876, -1228800, -5749510, -6080176, 148922, 2352128, -1656216, 3282856, 10601588, 2705664, 12577212, 8759080, 3680976, -969888, -508024, -1471224, 8644340, 1165824, -3319330, -2238384, -6732554, -2577856, -9797722, -4570912, 2133032, 4396288, -15240680, -3147840, -3053946, -2123936, 6283258, 1593808, -1055960, 0, -6970104, 727464, -3115896, 1601280, -1623444, -3028824, 530736, -3253120, -1130628, -3252816, -7806920, -1563200, 1249666, -2236728, 3328056, 199680, 4917962, 2176872, 8910402, 5905312, -1531088, 5712784, 18756732, 486016, 3636398, -185320, 5436830, -4680576, 2169254, 264176, -1952154, 327680, 11175098, -3878192, 1113564, -154816, 836314, -4501384, -4547304, 2187904, 219604, 3896720, 16000564, -3924800, -10723960, 357920, -10449806, -1170432, -1136510, 4462320, -11418728, -6034624, -2795040, -6391424, -5864188, -7984384, 6513458, -5066488, 7575646, 373472, 4049386, 10545040, -18734860, 1787904, -9150876, 4941904, 19639448, -3361408, 12441406, 2200296, -3796222, 1766272, 9004490, 2053896, -5786716, 74304, -12468434, 6465984, -11502142, 3407360, 11015762, -893256, 2735766, 391488, -11303884, 320184, -12608472, -1012352, 6014972, 8782224, -5622656, 3248288, -7712280, 1886296, 1403814, 196608, 4943486, -14787616, -6842968, 11464768, -13389790, -946256, 565146, -2747264, 9615418, 8266752, -3621730, -1149568, 9613688, -10793288, -6395208, -1171456, 25275552, 3719168, -6862158, -1056608, -4642776, 1839448, 7593078, -1052416, -23085216, 4552256, 11705556, -6501152, -8628114, -7693624, 165790, 3663872, -8992742, 456224, 18578968, 5997728, 17345460, -5607200, -31274796, -4488192, 567554, 5069672, -12381568, 12543008, 16530358, 12974512, -5591256, -8753152, 8978170, 7108680, 37816108, 1578720, 23025142, -8208264, 10325020, 2504064, -14709860, -18587888, 38782532, 2802528, 2921266, -11123320, -9252282, 524288, 16780550, -2013976, -8132820, -4825984, 13658678, 11135296, -27527402, 7209088, -30970262, -2670808, -25689366, -15002240, -19477166, 829120, -22986436, -6133248, -8316696, -21552560, -10932578, 7887104, -15269246, -7834000, -3016230, -9613056, 21553846, 16583152, 7655802, 27665920, 387006, -9213632, 2243398, 92160, 4991412, -14697976, 26075608, -12186080, 3431184, 10992520, 32244416, 6431488, -2039726, 17744224, -5365942, 4389984, 31172122, -15227816, 17715428, 4729856, 8511690, -17314480, -4368570, -22759168, 19290754, 10820168, -679452, 3106432, 8483282, -8344896, -36839336, 6909408, -41802900, 12761768, -31810540, -2400256, -29643494, 483896, -11003694, 10675616, 5223582, 25693840, 60960790, -4259584, 4974334, 12943976, -37815380, 268128, -28752210, -24597784, 8638576, 1825792, 23870224, -21919040, -30695816, -5201376, 24958280, 3169232, 2451378, 9128960, 16738858, 7511296, -18015228, 2310976, 3135110, 42752080, 41810642, 1867776, -25385734, 15573968, 14953436, 9055520, -21800210, -4371600, 30270556, 5831936, -37026112, -11248280, -21047944, -10177472, 2901140, -8229384, 17838460, 3144192, 14034048, 32177072, -17413946, -6157248, -9135554, 35656928, 36236444, -7938944, -407410, -21058144, 15648996, -31796480, -32469656, -996864, -9588804, 491520, 24415382, -12185440, 56417466, -8837696, -6626068, -595688, -18055122, 18311168, 28255546, -7367376, -16363834, -13131424, -56896910, 27034688, -28725664, 2051584, -8713332, -9154968, -46480488, -15285600, -101659288, -11071264, 28906998, -16443008, 8723396, 573176, 12015284, 5884896, 2823294, -35869440, 14764838, -10571776, 10589250, 13277320, 8495070, -5990624, 44952242, -42353064, 8133014, -11937536, 49299100, -18558672, 37699360, 9034208, 6809154, 1235992, 39031732, 18966528, -2606294, 60962720, 11734558, 8458560, 27409448, -41903616, 19948056, 8495744, 29304306, 52633488, -65495964, 21752608, -12371294, -35459560, -13537680, 0, -92344196, 24391216, 41278066, 1659904, 28200074, -16480216, 18255578, -6405120, -2743128, 2076656, -20048556, 30109376, 48894346, -2122944, 34028700, -4323840, -7401558, -14160888, -33988852, -31333856, -36445536, -24504920, -49338064, 1002240, 29957714, 11929576, 20983572, 16461312, -15806510, -13312224, -30365654, -1679360, -5911840, -44881648, 38616766, -8707488, -27217758, 6969712, 19192190, 19848832, 36235366, 32077792, -63755164, 6120224, -18164276, 19403192, -46666920, -333824, -8985110, -9310472, 1809650, 741280, -11090070, 40436800, 24964060, 388864, -11493022, -8677016, 71315812, 4326496, 13627182, 4869176, 43095938, -655360, -49007856, -14410792, 80473080, 29795808, 62495126, 20209504, 4740998, -2330496, 28940334, -3345256, -7935086, -35281024, 41689934, 33934496, -70525370, -8751616, -59747838, -8191216, -17128462, 10538880, -69371152, 18774744, -70990744, 17944960, -16959708, -83759280, -75501602, 3981760, -52735458, -22766976, -68054786, 4681728, -2068400, -45894960, -16442184, 58079360, 39519532, 45674912, -82947558, -29715584, 47834042, 2203040, -55868104, -3014624, 204210532, 27407072, 10589356, -8541184, -27481312, 49595248, 12782050, -243488, 28549710, -30302584, 2969546, 20141312, -88329318, -6174864, -17510810, -42180160, 31823354, -39993480, -4728540, 7716864, 201626, 74906424, 114801188, 24718144, 164806380, 28143408, 36275044, -40417408, -23728508, 30443056, 21375834, -8801184, 80647248, 72298208, -48382092, -6284288, -66227174, -36017960, -35374492, -18379104, 2011958, -47765736, 89219992, -3426176, 32457000, -35309824, 74256624, -36414656, -69136730, -38644472, -127847858, 5632000, 75493802, -44063048, 3201760, 20531584, -33589226, 11309296, 1166212, -1565952, -11141398, -24179344, 35851306, 19371744, 36221886, 34453168, -72002296, -9411072, 22035640, -1739688, -30043984, 21465184, -46690564, -38096536, -67184516, -12993152, 18546670, -95749760, -2422860, -28087104, -87801934, -5615256, 102195974, 1343488, 23977204, 70426416, 54112250, 14868064, 67986980, 84144632, 171192960, 15657728, -54051878, -30290560, -76424346, 3855584, -104645682, -2260584, -13701750, -44585984, 77343310, -10137552, -29375298, -33067008, -23917828, -52050440, -43689978, -20613888, -52362124, 66131248, 1845980, 33531872, 46065352, -25423808, 5981786, 6825984, 39107546, 86113912, -22744786, -14876672, 8028670, -80877568, -104893140, 8479232, 1474434, 18571104, 104164770, -23550592, 37004606, 122181048, -125504172, 35377664, -48978480, -9534976, 114460624, 29677856, -41800246, 56780136, 26911412, -13814272, -102247198, 34512456, -32431180, -59726784, -118833044, 4343200, -28249632, -14655488, 39131708, -20387112, -3945118, 4176064, 95086254, -20299392, 4519320, 27739008, 70283692, 59978240, -5666168, -36783520, -28700514, -106559976, -66940858, 17952768, -100231650, -49950176, 57435840, -3124608, 20499004, 49526272, -40350052, 19700608, -50780136, 45314248, 39669070, 29404352, -21420064, 106251904, 32793968, -7043072, 81009680, 41153560, 49437460, -5280160, -23093510, -151264432, 42674170, -9085440], "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": 3, "prim_orbit_index": 3, "minimal_twist": "22.6.c.a", "char_is_minimal": true, "conrey_index": 3, "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], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, 0, 0, 0], [3, 0, 0, 3, 1, -1, 0, 0], [0, -16, 0, 0, 0, 0, 0, 0], [27, -48, 0, 48, -27, 0, 2, 0], [-4, 16, 0, -16, 4, 0, 0, -4], [0, -2, -1, -13, 13, -4, -5, -5], [0, 0, 0, 0, 64, 0, 0, 0], [87, -87, -2, 119, 0, -6, 0, 6], [108, 84, -8, 0, 84, 0, 0, -8], [0, -77, -11, -154, -77, 0, -22, -11], [-16, -48, 0, 0, -48, 16, 16, 0], [-363, 363, 24, -216, 0, -20, 0, 20], [-52, 0, 16, -52, 60, 20, 16, 0], [0, -399, 31, 695, -695, 23, 54, 54], [-256, 256, 0, -256, 256, 0, 0, 0], [-83, 102, 0, -102, 83, 0, -14, 50], [0, 476, -8, -348, 348, -24, -32, -32], [-129, 0, -24, -129, -525, 61, -24, 0], [-336, 336, -32, -768, 0, 32, 0, -32], [577, 1427, -32, 0, 1427, -30, -30, -32], [308, -924, 44, 308, 0, 44, 0, 44], [86, 238, -86, 0, 238, -112, -112, -86], [192, -192, -64, 256, 0, 0, 0, 0], [-803, 0, 108, -803, 123, 84, 108, 0], [0, -864, 96, 1452, -1452, -80, 16, 16], [1012, -2893, 0, 2893, -1012, 0, 117, -74], [-240, 32, 0, -32, 240, 0, 64, 80], [0, -2915, 182, 209, -209, -170, 12, 12], [2780, 0, -92, 2780, -1184, -216, -92, 0], [-334, 334, -262, -4441, 0, 217, 0, -217], [-1024, 0, 0, 0, 0, 0, 0, 0], [2453, 2200, 22, -3839, 3630, 22, 0, -220], [-332, -76, 56, 0, -76, -200, -200, 56], [1415, -1415, -167, 3017, 0, -183, 0, 183], [-1392, 0, 96, -1392, -512, 128, 96, 0], [0, 4145, -16, -193, 193, 140, 124, 124], [2100, -2616, 0, 2616, -2100, 0, -96, 244], [-5862, 1861, 0, -1861, 5862, 0, -355, -172], [0, -3072, -128, 1344, -1344, 128, 0, 0], [5029, 0, 244, 5029, -11080, 436, 244, 0], [-5708, 5708, -8, -8016, 0, 128, 0, -128], [-8488, 14278, 182, 0, 14278, 78, 78, 182], [0, 1232, 176, -1232, 3696, -176, 0, 352], [-5099, -6772, 394, 0, -6772, 684, 684, 394], [-952, 952, 104, -1296, 0, 344, 0, -344], [629, 0, -838, 629, -2539, -463, -838, 0], [0, 1024, -256, -768, 768, 0, -256, -256], [10180, -1089, 0, 1089, -10180, 0, -10, -84], [-492, -2720, 0, 2720, 492, 0, 432, 336], [0, -15377, -61, -435, 435, 117, 56, 56], [5808, 0, 320, 5808, -2352, -64, 320, 0], [-6747, 6747, 1274, -6442, 0, -1448, 0, 1448], [4048, 7524, -468, 0, 7524, 296, 296, -468], [4125, 2717, -902, -7975, 14927, -462, -297, -231], [-960, 832, -256, 0, 832, -320, -320, -256], [-123, 123, 538, -21832, 0, 288, 0, -288], [836, 0, 680, 836, 10824, -48, 680, 0], [0, -16286, -387, 28461, -28461, -62, -449, -449], [4736, 6384, 0, -6384, -4736, 0, -368, -864], [13443, -20650, 0, 20650, -13443, 0, 320, -1486], [0, -17764, -1048, 1336, -1336, 868, -180, -180], [14920, 0, -577, 14920, 10277, -1005, -577, 0], [0, 0, 0, 4096, 0, 0, 0, 0], [-16210, 24177, 750, 0, 24177, -498, -498, 750], [-14520, -836, 88, -24332, 5720, 880, 968, 176], [-35340, -13254, -974, 0, -13254, 798, 798, -974], [304, -304, 1024, 1632, 0, -224, 0, 224], [32064, 0, -660, 32064, 13882, -1030, -660, 0], [0, 12068, -668, -5660, 5660, -732, -1400, -1400], [33751, -14411, 0, 14411, -33751, 0, -679, 1285], [2048, -7616, 0, 7616, -2048, 0, 384, 512], [0, 7335, 998, -31309, 31309, 328, 1326, 1326], [-772, 0, -560, -772, -15808, -496, -560, 0], [-37511, 37511, 177, -41213, 0, 1163, 0, -1163], [8400, 2064, 384, 0, 2064, -976, -976, 384], [-14168, 26939, 1232, -39479, 8547, 990, 1166, 880], [-23448, 16004, 1420, 0, 16004, 688, 688, 1420], [8982, -8982, -1454, -35077, 0, 957, 0, -957], [5376, 0, -512, 5376, 6912, 0, -512, 0], [0, 28216, 686, 15096, -15096, 318, 1004, 1004], [44320, -24204, 0, 24204, -44320, 0, 976, 1744], [33199, -64953, 0, 64953, -33199, 0, -537, 839], [0, -32064, -32, 22832, -22832, 512, 480, 480], [-29249, 0, 506, -29249, 34764, 2068, 506, 0], [-57112, 57112, 416, -23160, 0, -728, 0, 728], [-39323, 35232, 75, 0, 35232, 2453, 2453, 75], [-14784, 9856, 704, -14784, 9856, -1408, -704, 0], [-70212, 6724, 504, 0, 6724, -2458, -2458, 504], [27088, -27088, -1160, 47484, 0, -1576, 0, 1576], [8017, 0, 1579, 8017, 8204, 2264, 1579, 0], [0, -5184, 416, 3808, -3808, 1376, 1792, 1792], [48697, 19225, 0, -19225, -48697, 0, -416, -4912], [10156, -7640, 0, 7640, -10156, 0, -3352, -1852], [0, 30165, -999, -58811, 58811, -1683, -2682, -2682], [-3072, 0, 0, -3072, -1024, 1024, 0, 0], [4609, -4609, -4628, -4380, 0, 2456, 0, -2456], [40720, -36364, 40, 0, -36364, 336, 336, 40], [27907, 38071, -1155, -5434, 34562, -2574, -3146, -2200], [-1968, 12848, -1728, 0, 12848, -1344, -1344, -1728]]}