# Stored data for newform 22.4.c.b, downloaded from the LMFDB on 24 April 2024.
{"label": "22.4.c.b", "space_label": "22.4.c", "level": 22, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503737133432854, "dim": 8, "is_polredabs": true, "trace_hash": 85922300727308035, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [4748041, 368251, 224168, -11455, 1931, 185, 42, -3, 1]]], "qexp_display": "q-2\\beta _{3}q^{2}+(1+\\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": 352, "analytic_conductor": 1.2980420201262934, "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": 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": 23913322515625, "field_disc_factorization": [[5, 6], [19, 2], [29, 2], [71, 2]], "field_poly": [5856400, 169400, 75340, 2710, 2911, -141, 71, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "7.812", "prec": 17}, {"__RealLiteral__": 0, "data": "2.231", "prec": 17}, {"__RealLiteral__": 0, "data": "208.442", "prec": 24}, {"__RealLiteral__": 0, "data": "207.240", "prec": 24}, {"__RealLiteral__": 0, "data": "10926.847", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c5", "trace_display": [4, 3, 5, -1], "traces": [0, 8, 4, 3, -8, 5, 14, -1, 16, -21, -100, -155, 32, 7, 2, 211, -32, 161, 162, -272, 20, -50, 0, 628, 56, -17, 96, -528, 16, 33, -422, 323, -256, -1144, 208, -697, -324, 49, -576, 391, 240, 361, 1430, 1442, 620, 2652, -416, -1069, 48, -709, -76, -1332, -192, -281, -1144, -7, 48, -438, -66, -128, -1116, -617, 1044, 694, -128, -138, 1248, 578, 644, -310, 34, 115, 168, -1487, -98, -1852, -128, 553, -4152, 71, -480, 1630, 658, 1942, 2960, -329, 2426, 2122, 560, -2202, 1286, 4523, -2088, 6019, -1332, -793, -96, -5128, -3292, -2213, -168, 1417, 2664, -4557, -56, -4794, -828, 971, -2112, 3680, 1104, -10290, 64, 450, 1186, 5536, 2112, -1011, 256, 459, -1088, -2197, -3676, 5391, -2088, 2825, 4122, 1033, 256, 4341, 856, -7018, 2064, 2966, -436, 1618, 872, 640, -3860, 4217, -68, -487, 4820, 6627, 3264, -2263, 2974, 42, -1624, 819, -5526, -2741, -2304, -3768, -3386, -6022, 1564, -6277, 1348, -10971, -160, -4240, -3260, 3795, -256, 7353, 6056, -6687, -5920, -8205, -2092, 1072, 1968, 3039, -1094, 13364, 1120, 14938, -5146, 5482, -2732, -8827, 4434, 10129, 4176, 8093, 9192, -9574, 3224, -816, 1586, 6413, -448, 4089, -6024, -12694, -2836, -9280, -11094, 5696, -304, -18989, -444, -8029, 4632, 2955, 9114, 15498, 1312, 6057, 7188, -5088, 1656, 14087, 1758, -1528, -1936, -2403, -3280, -9860, -5308, 9938, -3950, 5523, 32, -3336, -2720, -4438, -2372, -643, -5232, 4716, 8976, 7266, 2022, -13639, -3552, -12701, -4778, -14741, -4464, -13422, -5316, -11068, -2468, -4497, 11318, 3395, -2584, 8786, -5650, 8329, 10936, -19354, 364, 16003, -512, 24569, 7048, 23655, 1988, 6982, 836, -12548, -3528, 17270, 12098, 14077, -2028, 8495, 3554, 20271, -1744, -6466, 18480, 9585, -12960, -23041, -8434, -23879, 5576, -6022, -9256, 18439, 460, -7642, -8564, -35322, 672, 6055, -8194, -11213, 1012, -6789, -84, -11747, -5712, 15658, 7212, 4376, 11052, -11152, -1788, -2375, -4352, -9627, -10364, 35458, 5592, -25070, -19916, -1125, 11432, 17969, -1856, -4585, -2696, -7373, -16728, -14953, 3200, 18993, 8480, -6335, -920, -8208, 17090, -2210, 2632, 14114, 37794, 6426, 7768, -9416, -12396, 7654, -11440, -22222, 16410, -5212, -5736, 26103, -17484, 4719, -3936, 19172, 292, -16675, -6432, 21691, 2642, 11510, 4960, -306, 15164, 9591, -5888, 21512, 12416, 6521, 5464, -6136, -17396, 23858, -18448, -2739, -20258, -10113, 3328, 10053, 13174, 5047, 24076, -30604, -4062, -43654, -5328, -8475, -5498, -15098, -3892, -33239, -12826, -5959, -1024, -29611, -8348, -21136, 12048, 4011, -6562, -5242, 912, 34925, -5980, 34554, -4352, 47548, 28788, 22259, -272, 20572, -24762, -23611, 888, -15232, -4372, -6637, -2784, -9699, -5910, -6146, 15752, -27291, 40524, -17343, -224, 7258, 31566, -6530, -19176, 7707, -1224, 21507, 2248, 12386, -28174, 2327, -736, -28789, -10024, 9541, 3872, -28196, -34934, 47498, -13920, -35428, 28690, 52720, -11504, 31280, -9196, -6041, 12680, -5118, 28984, -829, -64, -23627, -10508, -24030, -14480, 24873, 8876, 39718, 3504, 17532, 19396, -13225, 22144, 15844, 6198, 33456, 8448, -15116, -2392, 1915, -1524, 39178, 27278, 221, -16256, -32848, 14712, -16107, 9556, 27247, -18208, -12269, -6752, 32593, -19816, -128008, -3688, 770, -17344, 6643, 2416, -63092, -3646, -18851, -22636, -20855, -26720, -42326, 6368, -13479, -17572, -19195, -6380, 9311, 6352, -18345, 16488, -4026, -10632, 43722, 4132, -18639, 26964, -10735, 1024, -14626, -49138, 34151, -6536, 46461, 13900, 15009, -3976, 39456, -4714, 33849, 15708, 1285, 13516, 51062, 12976, 47264, 32760, 1563, 18264, 14779, 18836, -889, 4056, 23988, 41500, 26373, 1272, -34461, -40542, 6719, -5152, -35030, -19878, 8478, 2560, 58456, -13520, 57866, -15440, -27803, -52648, -25214, -28392, -35473, 47758, -15254, 22848, -6007, 44664, -30144, 18512, -24621, 14132, -21722, -8720, -51940, -18376, -66280, -22552, 29374, -24306, -12002, -5184, -36243, -9470, 59229, 16388, 72363, -11084, -48225, -19744, -16521, 13578, 18046, -1832, 50825, -2986, 40014, -6496, 4550, 17474, -78306, 3276, -13836, 11968, -22991, 14816, -24311, 22304, 30305, 14776, 15715, -17680, 21953, 8704, -80751, 1864, -7067, -13192, 8449, -22406, 55322, -6224, -86770, -21290, 2620, -27788, -572, -480, -19234, -22864, 29983, -5328, 75158, 42792, -5461, 9170, -12061, -568, -39155, -20304, -10241, -43884, 13716, -22974, -28396, -640, 50685, 21694, 22164, 34080, 66786, 12670, -31489, 22400, 62253, 44116, 27416, -34180, 53657, 45300, -45826, 5776, -41587, -16798, -10902, 8412, -50616, 26738, -46116, 3424, 43714, -26578, 39912, 24792, -39595, 37072, 52773, 1600, 98269, 44444, 10717, 36040, -21627, -84066, -17629, -8368, -85078, 7224, -38648, 4288, 73227, 2802, 66313, -19408, 34501, -38344, -12529, -23144, -18180, -96840, -33717, 12864, -16198, 7688, 40127, -21444, 27163, -1010, -108854, 0, -141822, 832, 21195, 452, -7031, 23508, -14531, 11776, -53156, 84756, 26572, 5808, 42001, -13042, -16351, -10288, 33805, -16188, 131269, -35308, -3052, -99056, -46844, 17736, 79191, 43018, 43033, -28844, 32157, 20226, -61160, -20096, -4041, 58544, 23139, -26348, -103465, 66106, -56715, 29768, 13841, -53212, -136246, 26524, -104146, -44492, -101047, -17104, 57853, -8130, -26223, 10996, 70225, -184, -42198, -28256, -40239, 66478, 79870, -30928, 62617, 1968, -30505, -1792, 42368, -43278, 80460, 16356, 41265, -16578, 28648, 41024, 36461, -8022, 55646, 75304, 36971, -35176, 103404, -1824, -62611, 62370, -47903, 6600, -94914, 11732, 126654, -1616, -63026, 22704, 42878, 46184, -19579, -26138, 17569, 544, 11222, 29536, 46731, 52864, 42156, 47222, 44195, -11336, 35877, -41196, -41413, -32116, 6206, -15746, 230634, 18528, -13105, -72152, -70984, 17220, 15977, 12292, -7913, -9904, -4, -34708, -147905, -81048, 25559, -62724, -108785, -3072, -21632, 60594, -78646, 20268, -30270, -70930, -54207, -52728, -76041, 16116, -118216, 2448, 24046, -55884, 3119, -4256, -113411, -24772, -2780, -40092, -48713, 43306, -51287, 7032, -16438, 69468, -67934, -6112, -44925, 73288, 36059, 16896, 50845, 56392, -8432, -120512, -88861, 25804, 60298, 27840, 71136, -59044, 116218, 77100, 66815, 91860, 343302, 7168, 119790, 10640, -72425, -38268, -111128, -8898, -81281, -25360, 79393, -58304, -41032, 71752, -55, 1658, 44663, -512, 103308, -40726, 15435, -13344, -76962, -2140, 235404, -10880, 33293, 54144, -49031, 18208, 28957, -79436, -7779, 32992, 7157, 16416, -116191, -38792, -43890, -48330, -58733, 54752, 21641, 55552, -138626, 2384, 21024, 65168, -147852, -1056, -76603, -79278, -54577, 4784, 21917, 67740, 16821, -22272, 85929, -78356, -42156, 28004, 36577, 16588, 78966, -14208, 119516, 30926, 227186, -50804, 102471, -31596, -10813, -3672, -27451, -54494, -43477, 45096, -132992, -7652, -122003, 13504, 52943, 18894, 58287, -12788, -123735, 34976, 18224, -21264, 79580, 27320, -102121, -12552, -10271, 39984, 37616, -4832, 27105, -88736, 49402, 21392, -73030, 37702, 51055, -43128, -1958, -8990, 141577, 13580, 5616, 78722, -56564, -10336, 115241, 49458, -54836, 52524, -130427, 38390, -77726, 19680], "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": "22.4.c.b", "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, -2, 0, 0, 0, 0], [1, 0, 0, 1, -1, -1, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0], [-5, 0, -8, -8, 4, 1, -1, 0], [2, 0, 0, 0, -2, 0, 0, -2], [1, 2, 0, 2, -2, 2, 1, 1], [0, 0, 0, 0, 8, 0, 0, 0], [7, -3, 7, 28, 0, -2, 0, 2], [-8, -2, 8, 0, -8, 0, 0, 2], [-13, 0, -6, 8, -15, -3, 3, 2], [8, 0, 4, 0, -4, 0, 4, 0], [4, -3, 4, 10, 0, 3, 0, -3], [-2, 6, 0, 4, -4, 4, -6, 0], [-9, 7, -12, -50, 50, 7, -9, -9], [-16, 0, -16, -16, 16, 0, 0, 0], [30, 0, 1, 1, -26, -4, 4, 3], [2, -6, -56, -14, 14, -6, 2, 2], [-55, -2, 0, -57, 36, -8, 2, 0], [16, -4, 16, 32, 0, -4, 0, 4], [66, 3, 144, 0, -144, 0, 2, -3], [26, 6, 14, 62, -42, 0, -4, -6], [42, -6, -70, 0, 70, 0, -6, 6], [8, 8, 8, 0, 0, 0, 0, 0], [-1, -9, 0, -10, 9, -2, 9, 0], [12, -6, -20, -8, 8, -6, 12, 12], [-107, 0, -31, -31, 109, -2, 2, 4], [-4, 0, 0, 0, -8, 12, -12, -4], [-9, 10, -120, 50, -50, 10, -9, -9], [-96, -4, 0, -100, 76, 14, 4, 0], [74, 25, 74, 94, 0, 21, 0, -21], [-32, 0, 0, 0, 0, 0, 0, 0], [-50, -20, 111, 138, -124, 11, -5, 9], [46, 8, 50, 0, -50, 0, -6, -8], [-60, 3, -60, 154, 0, -16, 0, 16], [-20, -8, 0, -28, -84, -12, 8, 0], [27, -32, 80, -48, 48, -32, 27, 27], [-68, 0, 42, 42, 72, -4, 4, -12], [-160, 0, -344, -344, 164, -4, 4, 13], [0, -8, -64, -32, 32, -8, 0, 0], [57, 24, 0, 81, -35, 17, -24, 0], [288, 10, 288, 160, 0, 6, 0, -6], [255, 7, 167, 0, -167, 0, -14, -7], [84, 4, -40, 24, -56, 12, 0, -12], [313, 28, -18, 0, 18, 0, -5, -28], [-140, -24, -140, -236, 0, -12, 0, 12], [-169, -9, 0, -178, -20, 12, 9, 0], [-16, 16, 0, -16, 16, 16, -16, -16], [-234, 0, -177, -177, 239, -5, 5, -2], [0, 0, 2, 2, 18, -18, 18, 14], [2, -32, 169, 234, -234, -32, 2, 2], [-28, 12, 0, -16, -24, -12, -12, 0], [-50, -47, -50, -72, 0, -39, 0, 39], [-226, 4, -156, 0, 156, 0, -8, -4], [45, 50, 192, 118, 84, 1, -5, -14], [24, -24, 16, 0, -16, 0, 8, 24], [-8, 18, -8, 251, 0, 47, 0, -47], [98, 2, 0, 100, -340, 20, -2, 0], [-26, 40, 203, -69, 69, 40, -26, -26], [-144, 0, 48, 48, 152, -8, 8, 36], [-273, 0, -228, -228, 246, 27, -27, -28], [-8, 50, -188, -148, 148, 50, -8, -8], [311, -71, 0, 240, -468, -23, 71, 0], [0, 0, 0, 64, 0, 0, 0, 0], [69, -27, 106, 0, -106, 0, 53, 27], [270, -50, -28, 338, -26, -40, 22, 62], [91, -59, -43, 0, 43, 0, 51, 59], [100, 4, 100, -4, 0, 16, 0, -16], [-268, 88, 0, -180, 526, -18, -88, 0], [-38, 6, -308, 120, -120, 6, -38, -38], [211, 0, 334, 334, -262, 51, -51, -32], [184, 0, 224, 224, -168, -16, 16, -8], [45, 17, 418, 205, -205, 17, 45, 45], [-86, -10, 0, -96, 256, -64, 10, 0], [-461, -4, -461, -460, 0, -1, 0, 1], [-120, 8, -228, 0, 228, 0, 24, -8], [-135, -8, -118, -642, 90, -68, 11, -53], [-354, 8, 360, 0, -360, 0, -26, -8], [102, -19, 102, 206, 0, -55, 0, 55], [-48, -16, 0, -64, -64, -16, 16, 0], [-6, 30, -446, -174, 174, 30, -6, -6], [22, 0, -92, -92, -70, 48, -48, -14], [457, 0, 214, 214, -445, -12, 12, -92], [-8, 20, -320, -576, 576, 20, -8, -8], [-165, 55, 0, -110, 226, 44, -55, 0], [334, -14, 334, -204, 0, 14, 0, -14], [122, -39, -196, 0, 196, 0, -110, 39], [128, 8, 64, -56, -192, 8, 16, 16], [-521, 61, -435, 0, 435, 0, -26, -61], [-36, 46, -36, -672, 0, 56, 0, -56], [688, -28, 0, 660, 238, 3, 28, 0], [24, -48, 472, 280, -280, -48, 24, 24], [1156, 0, 122, 122, -1036, -120, 120, 69], [58, 0, 396, 396, -40, -18, 18, 42], [15, -59, 440, -40, 40, -59, 15, 15], [-32, 0, 0, -32, 32, 32, 0, 0], [-809, 10, -809, 132, 0, -10, 0, 10], [-474, 10, -124, 0, 124, 0, 4, -10], [-736, 2, -506, -770, 583, 104, 23, 57], [-64, 36, -40, 0, 40, 0, -28, -36]]}