# Stored data for newform 29.4.a.b, downloaded from the LMFDB on 25 April 2024. {"label": "29.4.a.b", "space_label": "29.4.a", "level": 29, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503599694479389, "dim": 5, "is_polredabs": true, "nf_label": "5.5.13458092.1", "trace_hash": 1952070524226171465, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-256, 192, 28, -33, 0, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(1-\\beta _{1}-\\beta _{3}-\\beta _{4})q^{3}+(6+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 464, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 1.7110553901664778, "hecke_ring_index": 4, "level_radical": 29, "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": [29, 1, [2], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [29], "conrey_indexes": [1], "field_disc": 13458092, "field_disc_factorization": [[2, 2], [31, 1], [108533, 1]], "field_poly": [-8, 20, 18, -14, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.056", "prec": 17}, {"__RealLiteral__": 0, "data": "4.575", "prec": 17}, {"__RealLiteral__": 0, "data": "0.267", "prec": 17}, {"__RealLiteral__": 0, "data": "57.780", "prec": 20}, {"__RealLiteral__": 0, "data": "15.528", "prec": 20}, {"__RealLiteral__": 0, "data": "1163.364", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[29, 1]], "trace_display": [0, 8, 10, 40], "traces": [0, 5, 0, 8, 26, 10, 34, 40, -84, 33, -64, 12, -224, 14, -192, -74, 146, 66, -108, 214, 6, 0, -98, 164, 314, 207, 56, 362, 540, -145, -234, 420, -652, -576, 204, -52, -260, 378, -496, -374, -80, -1158, 348, -204, 784, -1506, 580, 248, -1880, -283, 908, 228, 1482, -554, 918, 546, -608, 44, 0, 440, 636, 618, 1250, 804, 2594, -1656, 2940, 1164, 356, -1968, -2184, -692, -2648, -1950, -1832, 3074, 1376, -1616, -1302, 272, -890, 1801, 92, 512, -3208, -1628, 2446, -232, -6954, 866, -2200, 2580, 3468, -40, -5942, 2244, 7386, 1562, -3408, -238, -5128, -974, 2860, 560, 3848, -96, -4184, 2300, 864, -1094, 4698, 4076, 3900, 42, 2224, 3144, -754, -702, -3292, -768, 5430, 3273, 3396, -5432, 2916, 768, -304, -2922, -10116, 184, -6628, 2978, -6858, 2280, 3144, -11354, -5212, 162, -108, 5600, 1988, 608, 628, -7298, 5684, -290, 4952, -1528, -2368, 1758, -696, -2724, -6296, 4946, -3708, 698, -1828, -3094, 3374, -4914, -952, -2200, 13456, -760, -1872, -1548, 6932, -6452, 12444, 4327, 212, -170, -320, 2338, -986, -4556, 15784, -2896, -364, 1936, 10156, 6202, 2712, -628, -3420, -2644, -2888, 5124, 1076, 2008, -728, -6730, -6512, -4014, -836, 1206, -302, -2554, -6748, 6864, 200, 2224, 8968, -1160, -8116, 2844, -18044, -14884, 1642, 3116, -5292, 4824, 6430, 5808, -9648, -11862, -14906, 1464, 480, 1996, 404, -2276, 12736, 2912, -17520, 6095, 2552, -2908, -11480, 6778, 5716, -16316, 2436, -1458, -5624, 13450, 12900, 11912, 1352, 5764, -9820, 2214, -17868, 16762, 7884, 10770, -3496, -4452, 4298, -1472, 14672, -1184, 2040, 11072, 264, -14584, 4626, 14642, 1612, 6488, -2410, -957, 8472, -2468, 19876, -280, -16496, -4152, 752, 938, -13862, 5684, 10820, 3088, 496, 2634, -5860, -7190, -7252, -8870, 13032, 2950, 7416, 7940, -24456, 4224, -16026, -15672, 3960, -15321, 1856, -1128, -21080, 12154, -4550, -4832, -23296, 2972, -12408, 1976, 9688, -6576, 34264, 4708, 12624, -15668, 2656, -9244, 24872, -8040, -6450, -5498, 9450, -13118, -23548, 720, -10420, -21558, 12894, -348, 22182, -9520, -5560, -516, -28814, -27090, 17142, -17114, 4772, 17256, 19784, 15392, -84, 36218, 21764, 18936, -39384, -35998, 46844, 25880, 5700, -5104, -7048, -5824, 3398, 24544, 25336, -9896, 6496, 8054, 1888, 8474, -30090, 9814, 14028, 29876, 3344, -7864, -13180, -5232, 35184, -18771, 9864, -4894, 4412, -3980, 18820, -3818, 10652, -25934, -7824, 6956, -6158, -22286, -18828, -6786, -21150, -406, 11780, 15878, 1312, -16020, -15760, -16956, 23578, -33536, -44084, 12018, 22408, 11130, -2194, -672, 4636, 41836, -8928, -22314, 29952, -16062, -35928, -3072, -37024, 9790, -38880, 16070, -13984, -43006, 5568, 3868, -7348, 12554, 33196, 21468, 28912, 20008, -43848, 9672, -36304, 14376, -592, 35632, 1040, -29414, 15446, 7350, -25688, 7310, -44896, -7344, 43180, -13052, -3254, 7028, 34120, -14246, -1396, 2146, 22270, 7832, -44440, -7336, -51174, -14295, 2524, 27882, -35648, 28708, 20908, 18770, 44668, 12042, 26036, 28000, -31444, -15232, 59636, 33028, 41696, -32354, -10956, 40160, -28340, 8578, 55888, -8728, -4234, 10292, 2444, 30756, -22988, 11472, -4426, 16360, -25932, 2896, -39816, 9578, 12392, 5690, 13596, -5980, -18490, -26636, 26108, -26312, 22828, -22140, -13784, -2912, -33348, 39208, 2304, -36068, 40932, -1914, -23656, -9728, -12052, -11808, -24396, -7396, 2706, 5560, 3154, -3068, -46624, -30620, -22996, -13438, 28600, 5974, -4692, -21752, -23484, -8704, 26460, -1004, 582, -4264, -29728, 8416, 30884, -10734, 3132, -11424, -51200, 23176, 11378, 684, -69802, 3685, 2724, 15248, 37440, -18636, 25128, 2812, 68024, -41744, -39140, -11092, 39796, -6670, 25630, -17294, -9804, 9096, -1204, -10740, -46832, 23778, 72136, -6206, 42084, 29208, -6176, -64024, 24548, -7330, -31860, 19734, -1244, 3400, 24668, -61040, -28502, -29460, 3748, -26168, 78580, 26842, -3568, 43656, -44, 9908, 33720, -14668, 53076, -14366, -5376, -41832, -174, -18792, 35440, 19610, 98656, 62756, 85312, 14712, 14144, 8204, -28972, 41160, 37360, -9078, -75612, -29352, -3894, 13976, 34428, -29680, -97168, 52202, 49124, -65140, -10804, 89582, -8832, -37116, -45912, 0, -3188, -32234, -18440, -16846, -99098, 47852, -98684, 39218, 85464, 48864, -26216, -42392, -71952, -26648, -11404, -11535, 52356, -40952, -38472, 21300, 11440, 20204, 104374, 25984, -2988, -84412, -33820, -9594, 2842, -56640, 3424, 35298, 39852, 58968, 46776, -52420, 2400, -672, 3948, -3408, -73040, 2524, -84232, 45026, -57650, -4420, 4080, -34118, -91876, -59752, -32478, -10046, -21866, -19304, 39428, 6192, 65752, -4756, -99904, 75696, -25784, 38876, 107836, -51202, -17940, 24812, 4136, 8738, -75028, 23800, -4780, 37008, -2760, 1560, 29264, 5332, 25088, 20744, -40, 1216, 67348, 21832, -5108, 44824, 1980, 14752, -9106, -11604, -18616, -43062, -53248, 50102, 52710, 25788, 123392, 38596, -69064, -30824, -73124, 3126, 32316, 33266, -77860, 50152, 44984, -91622, 94672, 89048, 8102, 81272, 15004, 47040, -36176, -34266, 103826, -6003, 7516, 5246, -25304, 61401, 13920, 29972, -65740, 1490, -13560, 65654, -85996, -75008, -30112, -56592, 65648, -6432, -32280, -72206, -8304, -18896, -208, -63504, 31540, 60488, -18254, 57122, 52860, 50000, -1624, -21404, 24552, -52030, 34264, 24504, -18952, -25514, 36920, 23356, -95200, -81316, -8128, 44288, -131464, -18094, 15692, 29742, 46824, -52230, 10052, -350, -62652, 17616, 13112, -39588, 9200, -54576, -20032, -10498, 714, -5284, -30848, -6392, -81228, -33264, -96654, 54432, 60, 15124, -45504, 9402, 65140, 73098, 26912, -35356, 164936, -35678, -125356, -63172, 64344, -48648, 79394, -5060, 36976, -13622, -27440, 40504, -15660, 31456, 2208, -40006, -24836, -42740, 11384, -50256, -29704, -44834, 76352, 56470, -174508, 32388, -49336, -6384, 35768, -17382, 19220, -63144, -92630, -43518, 38364, 51524, 79576, 7636, 61012, 15848, 91028, 4205, 27404, -62326, -44608, 77506, 27724, 61156, 113758, -116752, 46520, -93352, 167780, -3654, 29560, -40956, -87072, 87178, 29280, 15772, 2948, -58712, 13604, 94524, -12826, 22372, 85240, 17480, 20240, -165664, 6786, 55464, 113744, 54586, -1840, -61412, 177968, -24898, 70956, 86960, 49260, -55646, -876, -21856, 23852, -16328, -68272, 67724, 13040, 11544, 82356, -17764, -126440, 69204, 49930, 15260, -174464, -38848, 117296, -12180, -61128, -5460, -26392, -16860, 192400, -99928, -116836, 21666, -78920, 30778, 26448, 31340, -149112, -32, 65208, -100176, -36520, 5528, 12388, 62656, -150364, -141512, -82848, -68116, -143244, 76102, 1780, 95948, 18908, -55850, 11028, 25702, 60854, 7316, -85826, 76328, -79168, -242, -18992, -16402, 49720, -93494, 30832, 43296, 123220, -59344, -73116, 4316, 75950, 24044, 78616, -19140, -79928, 89742, -7256, 98364, -154772, 16704, -37954, -72168, -32580, -63659, -134320, 12496, 1762, 68660, 33096, 51264, -72280, -26664, -52484, 25694, -29968, 76648, -87944, -28956, 86284, -63606, 51956, 128608, 3502, -133898, 18202, -67200, 13464, -100, -5916, 24172, 22336, -784, -70252, 74324, -43910, -18352, 7256, -53468, 59900, -11118, 33460, 134696, 14088], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "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": "29.4.a.b", "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, 0, 0, 0], [1, 0, 0, 0, 0], [0, -1, 0, 0, 0], [1, -1, 0, -1, -1], [6, 2, 0, 2, 1], [3, 1, -1, -1, 2], [6, 4, 4, 2, 1], [8, 2, -2, 0, -2], [-16, -9, -8, -4, -4], [2, 1, 5, -1, -6], [-12, 1, 4, 0, 6], [3, 7, 10, 5, 9], [-44, -13, -8, -8, -2], [5, -3, -9, 5, -6], [-40, -14, 0, 0, -4], [-5, 3, -14, -1, 11], [30, 30, 16, 18, 9], [10, 0, 10, 4, 0], [-32, -6, 4, -12, -16], [44, 8, 0, -2, 4], [-6, 8, 8, -2, -9], [-4, -16, -14, -16, -16], [-22, -28, -20, -34, -9], [46, 0, -2, 14, 24], [78, 68, 0, 26, 25], [32, -17, 11, -21, -2], [20, -25, -20, 24, -10], [51, -11, 32, 11, -27], [116, 48, 16, 28, 22], [-29, 0, 0, 0, 0], [-30, 14, 4, 22, 35], [93, -19, -14, 7, 5], [-152, -81, -8, -60, -32], [-113, -39, 9, 1, 14], [36, -26, -16, -20, -18], [-8, 14, -42, -12, -30], [-36, 68, 8, 12, 42], [48, 22, 30, -22, -28], [-104, -48, 8, -16, 4], [-75, 11, -16, -11, -11], [-44, -19, -24, -32, -78], [-216, 18, 16, 22, 44], [68, 84, 64, 60, 30], [-49, -29, 22, 25, -11], [156, 149, 56, 56, 26], [-238, 42, -78, 48, 56], [148, -78, -56, 4, 22], [45, 75, -16, -41, -7], [-396, -189, -40, -72, -54], [-47, 40, -32, -24, 4], [168, 84, 84, 12, 44], [6, -44, 54, -10, -40], [326, -52, -24, 50, 25], [-109, 75, 17, 23, 10], [154, -100, -44, -42, -97], [113, -13, 112, 41, 101], [-120, -190, -112, -128, -44], [4, -62, -42, -52, -28], [0, 29, 0, 0, 0], [90, 52, -6, 30, -16], [80, -75, 24, -28, -80], [114, -20, 66, 60, 12], [286, -78, -28, 66, 29], [144, 24, 64, 4, 20], [510, 282, 112, 34, 73], [-373, 51, -49, -15, -146], [624, 201, -4, 60, 56], [280, -88, -140, -44, 0], [100, 78, 0, 52, 46], [-334, 18, -44, 2, 104], [-448, -2, 48, 56, -8], [-122, -58, -96, -122, 6], [-464, -58, -80, -56, 112], [-384, -106, -66, -38, -32], [-448, -32, 88, -104, -64], [548, 18, 106, -2, -60], [288, 204, 64, 96, 48], [-332, 144, 158, 176, 48], [-274, 86, 44, 10, 5], [27, -139, -140, -63, -177], [-174, 68, 64, 102, 23], [241, -222, 134, -56, -136], [44, 136, -88, -68, 10], [146, -96, -42, 14, 60], [-656, -318, -128, -168, -80], [-266, 50, 20, 66, 136], [506, -4, -100, 14, -65], [-29, 29, 0, 29, 29], [-1470, -428, -64, -138, -193], [196, 66, 100, 10, 152], [-328, 18, -192, 72, 52], [552, -30, -14, -36, 94], [716, 14, 0, 156, -22], [-19, 33, 3, -45, -2], [-1274, -38, 164, -118, 9], [476, 2, -38, -68, 64], [1438, 464, 288, 250, 65], [296, 34, 48, 78, -32], [-704, 67, 96, -16, 48], [-6, 94, -96, 84, -34], [-1040, -204, -136, -168, -88]]}