# Stored data for newform 9.4.c.a, downloaded from the LMFDB on 16 April 2024.
{"label": "9.4.c.a", "space_label": "9.4.c", "level": 9, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 137506062345, "dim": 4, "is_polredabs": true, "nf_label": "4.0.1089.1", "trace_hash": 1287054051224146071, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(-\\beta _{1}-\\beta _{3})q^{2}+(-1+\\beta _{1}+\\beta _{2}+\\cdots)q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "c", "char_is_real": false, "Nk2": 144, "analytic_conductor": 0.5310171900516655, "hecke_ring_index": 3, "level_radical": 3, "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": [9, 3, [2], [1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [4, 7], "field_disc": 1089, "field_disc_factorization": [[3, 2], [11, 2]], "field_poly": [9, -3, -2, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.010", "prec": 17}, {"__RealLiteral__": 0, "data": "3.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.202", "prec": 17}, {"__RealLiteral__": 0, "data": "58.774", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1467.505", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [-3, -3, -15, -7], "traces": [0, 4, -3, -3, -5, -15, 9, -7, 66, 45, 12, -66, -156, 11, -60, 27, 7, 198, 216, -154, 12, 21, 33, -33, -99, 121, -528, -432, 332, 51, 288, -43, 423, 198, -297, 6, -225, -100, 561, 759, -264, -132, -486, -88, -462, -675, -528, -399, -21, 513, 429, 297, 770, 108, 1215, 1254, -66, -1221, 60, -798, -36, -439, 228, 603, -1454, -165, -990, -988, -693, 891, -318, 2736, 891, -910, -816, -363, 1529, 165, -990, 803, 192, -567, 3630, -813, 642, -594, -33, -153, -1221, -792, -756, -1562, 858, -213, -2100, 132, 1080, -736, -846, 297, -2090, 1653, 891, 2063, -66, 936, 2592, -3186, -2133, 4004, 594, 2748, 470, 2307, -1683, -561, -156, 495, -2094, -792, 792, -572, 1074, -5049, -256, -5070, -2700, -4204, 231, 264, 1518, -627, 4257, 1606, 5142, 2511, 2970, 3912, -198, -1096, -948, 1197, -4428, 3234, -1494, -798, -3327, -270, -2548, 1947, 4752, 209, -1650, 891, 1848, -273, -2310, 1037, -3894, -8100, 3024, -1650, 1701, 6272, -5181, -5544, 546, -2607, 198, 621, 2376, 2277, -154, -957, 1278, 1166, -957, 5535, -594, 8784, 2700, -7120, 2310, 1317, -858, 1266, 1116, -2079, 11004, 3429, -5808, -1083, -6483, -880, -2787, 495, 243, -13212, 1485, 1844, 1749, -4749, 978, 129, -9504, 627, -5496, -1485, 4532, -1023, 954, 1037, 7884, 5076, 1053, 1518, -7128, 598, 1452, 12711, 3036, 2772, 2448, 2585, -3852, -4950, -1608, 2310, 11352, 11, 1782, -3267, 858, -4230, -1782, 2982, 4737, -2409, -4158, -7053, -3312, -7216, -15708, -7533, -8200, 4194, 7821, -7106, -660, 2439, 2598, 11682, 1062, 7194, 2262, -1782, 3127, 6942, -1782, -2498, -9768, -999, 17292, -10659, 3663, -3078, 5874, 4158, -5737, 6372, -1296, -9064, 1683, -2244, 9861, 2013, -2574, 11495, 4278, -1935, -528, 231, -19782, 7625, -10548, 8316, 5016, 10626, 19035, -7178, 54, 2208, -10891, -10509, -10503, -8229, -3432, 0, -33792, -4521, -9273, -11, 9768, -4959, -4279, 10050, 16038, 5786, -3102, 2055, -426, -14253, 11880, 3476, 27876, -2754, 26576, 627, -7776, 1815, 2928, 6399, 1518, -15642, 18630, 8756, -8268, -16368, -561, -5901, -1782, 12791, -6528, -9144, 14916, -6321, 2784, 14186, -1791, -4509, -2376, 2046, -24354, -6314, -1551, 1683, -16896, 9120, -3546, -15235, -11220, 12177, -25542, 1914, 11223, -7884, -2574, 2376, -1836, 5580, -11880, 2550, 17814, 25278, 5368, 7422, -1458, 1667, 5412, -5940, 10392, 7830, 768, -5929, -1485, 7416, -5082, 66, -648, -12034, 8448, 5826, 15288, 9813, -693, 2409, -17754, 1089, 13778, -2469, 6138, 1188, 8811, -24057, 6048, -22242, -16929, -10036, -12966, -4818, -2651, 7608, 25497, 979, 744, -10935, -2796, 8778, 2673, -12760, -10098, -11736, 4118, -7878, -4158, 15726, -4554, -3129, 8085, 3621, -3996, -2923, -29148, 22491, 7128, 8217, 13284, 3661, -27, -24750, 330, 11556, -8775, 2222, -1686, 2232, 8360, -7194, 9981, 12359, 23760, 23085, -34452, 18780, -6792, 4158, -3300, 44847, 10118, -882, 19305, -17160, -2202, -627, -7095, 4719, -18909, -11428, 49368, -21384, -12936, -19497, -198, -6523, -30, 819, -22815, -52038, -25344, 13450, -10206, -44925, -15411, -3696, -8910, -11341, 21780, 25272, 45480, -11199, -9072, 13090, -27951, 396, 24706, 7674, -7290, 42884, -8976, 5988, -540, 9948, 15543, 2376, 45276, 27918, -1192, -11916, -11358, -1150, 2724, -14553, -15741, 17208, 8316, -27798, 7128, -1863, 2582, -5379, 14256, -10436, 5106, 16632, -19374, 15819, 5907, -1155, -5628, 2871, -4488, 27774, 2700, -28072, -24684, 13332, -22836, -2574, 11880, 17833, -31752, -35910, -28820, 24981, 1782, 13284, -15213, -20844, 21060, -39402, 16524, 42884, 1452, -32082, 22275, -19470, -6930, 2396, -43518, -5715, -6402, -1518, 15048, -12485, 32340, -19386, -4225, 24120, -1296, 2002, 2832, 6237, 29436, 26400, 32634, 19959, -14460, 3969, 40392, -5916, -11088, -21994, 18282, 3249, -16896, 5412, 6363, -10414, -9318, 29271, -636, 2451, -29970, -23166, -23034, -12177, 13080, 15504, -729, 2992, 11070, 21492, 7844, 4104, -22275, 5940, 46794, 33366, -4422, -4983, -5247, -1870, 3696, -44460, -57772, -13002, 35622, -5335, -20295, 3807, 9078, -49434, -31185, -86284, 23727, -1881, 3894, -2814, -45378, 2720, 1464, 20493, 43320, -2178, 1650, 5092, 23133, 3069, -43888, 11088, 11610, 9296, 18348, 40611, -44220, 16656, 27864, 2376, 2376, 9396, 13728, -42708, -3159, 49610, 2904, -5544, 39501, 50868, -2673, 88572, -22902, 3264, -18532, -4065, -4356, 3003, -30030, -46323, 47964, 31119, -30492, 11405, 426, 43362, -15180, -17160, 26676, -2310, -17160, -7755, -9498, -28347, -30078, 803, -67110, -26433, 13230, -42879, -43938, -7625, -9504, -6930, -330, -3978, 68805, -50694, 33198, -74085, -583, -39798, 594, 12143, 97548, 7425, -68082, -7725, -2574, -21087, 3234, 81135, 14498, 66528, 57024, -44264, 3795, 21672, 32703, 1281, -14211, -35647, 36720, 27819, -15444, 231, -39204, -19569, 3276, -47061, -15174, 37080, 11664, -12362, -36216, 21648, 46322, -2838, -13266, 38117, -23496, 14580, 45384, -3465, 25752, -18025, -19230, -12582, 4158, 47784, 9207, 40238, -18120, -46596, 19764, -11769, -2376, 627, -2904, 2403, 594, 1566, -7794, 4925, 14910, 12177, -6270, 15774, -35856, 39536, 14817, -42966, -528, 5547, -6786, 6358, -96060, -26730, -97188, -29271, -11496, -13921, -6534, 8235, 28391, -18216, -1485, -6688, -10461, 7494, -8472, 48741, 6336, -26136, -29700, -4617, -2646, 23271, 37224, 1793, 4932, 31977, -28182, -210, 2970, 47146, 38712, 56862, -37054, -29319, 64152, -33264, 55638, -19602, 50502, 47091, 17211, 5907, 7062, -82296, 28776, -61074, -41796, 8378, 3936, 22836, -19536, -19956, -5049, 715, 32142, -7326, 63096, 27555, 129582, 16049, 34386, 3564, -5988, -87120, -19008, 33056, 8154, -34485, -41866, 22275, 26145, -16005, -52602, 1971, -90492, -27489, 15840, 47461, -2058, -693, 41648, -14760, -94500, -48268, -23868, -1185, 33561, 17754, -135216, 38279, -1380, 5940, -55242, -10929, -15048, -7306, 2508, 18810, -48762, -76032, -37665, -16566, -1221, 49488, -4460, 67287, -162, 21769, 74976, 31707, 31020, 5259, -12624, -475, -10914, 11907, -11616, 3384, 23895, 107090, 46134, 24687, 34539, -63591, 47916, 4684, 11880, 37422, 30140, 55902, -85734, -37692, 26598, 13563, 41499, -2094, 9009, -42768, -31779, -5511, 40722, 14226, 62370, -55330, 51810, -23679, -18348, -33177, 12837, -40953, -25359, -57384, -74074, 50622, 88209, -169444, -11880, -88539, -6096, 43164, 9306, 10340, -8844, 92835, 21276, 49155, -7470, -10395, -72675, -22221, 62343, 34452, -2970, -41464, -38352, -10428, -27636, -21363, 23148, 28545, 34806, -648, -7062, -18768, -41316, 57640, -53493, -1881, -10098, -80226, -90396, 50070, -54114, -9009, 6648, 25671, 43200, 58509, -36696, -47871, 138842, -16797, -4554, 13079, -18150, -71577, -12306, 64152, 37665, 10642, -43746, 42438, -14056, -23100, 24804, 22572, 20016, 85140, 92190, -36273, -77616, 53406, 6534, -54243, -53702, 6666, 12474, 102608, 9540, -38373, -60048, 4668, 52020, -71071, 121458, 10800, -86064], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "9.4.c.a", "char_is_minimal": true, "conrey_index": 4, "id": 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], [1, 0, 0, 0], [0, -1, 0, -1], [-1, 1, 1, 1], [-4, 1, -3, 3], [-7, 8, 1, -1], [12, -15, 3, -3], [0, -2, 0, -3], [16, 0, -1, 0], [-3, 21, -6, 3], [6, 0, 6, 0], [0, -37, 0, 8], [-52, 22, -5, -2], [13, 2, 15, -15], [-34, 26, -8, 8], [9, -24, -15, 9], [0, -1, 0, 9], [54, 0, 9, 0], [72, 0, 27, -18], [-52, 0, -27, 0], [0, 16, 0, -20], [34, -46, 8, -7], [6, -27, -21, 21], [-7, 26, 19, -19], [-24, 9, 18, 15], [0, 53, 0, 15], [-146, 0, -28, 0], [-117, -18, -18, 36], [92, 0, 18, 0], [0, 26, 0, -1], [42, 48, -6, 12], [-23, 20, -3, 3], [216, -207, 9, -9], [-6, 165, 21, -66], [0, -117, 0, -63], [11, 0, 19, 0], [-12, -141, -60, -15], [2, 0, 54, 0], [0, 241, 0, 79], [253, -124, 11, 17], [-120, 144, 24, -24], [-115, 17, -98, 98], [-162, 12, -60, 18], [0, -47, 0, 6], [-76, 0, 79, 0], [-171, 72, 45, -45], [-138, 0, -12, 0], [0, -154, 0, -91], [-88, 145, -17, 7], [246, -267, -21, 21], [256, -173, 83, -83], [18, 117, 36, 63], [0, 358, 0, 54], [-54, 0, -162, 0], [324, -27, 54, 81], [267, 0, -93, 0], [0, -10, 0, -46], [-164, -241, 2, -79], [42, -18, 24, -24], [-331, 467, 136, -136], [168, -336, 24, 12], [0, -272, 0, 105], [70, 0, 26, 0], [192, 24, 78, -57], [-440, 0, -153, 0], [0, -136, 0, 107], [-330, 222, 33, -48], [-527, 461, -66, 66], [-432, 261, -171, 171], [297, -204, -33, 45], [0, -144, 0, -30], [756, 0, 144, 0], [0, 333, -99, 27], [-106, 0, 243, 0], [0, -380, 0, -56], [-256, 187, -83, 121], [856, -673, 183, -183], [47, -118, -71, 71], [-78, -342, -90, -174], [0, 556, 0, -309], [16, 0, -64, 0], [-351, 351, -135, -135], [1014, 0, 213, 0], [0, -460, 0, 107], [52, 218, 56, 110], [-306, 288, -18, 18], [-34, -1, -35, 35], [-42, -42, -24, 51], [0, -693, 0, 165], [-162, 0, 72, 0], [-306, 144, -18, 144], [-425, 0, -69, 0], [0, 430, 0, -2], [-71, -16, -43, 17], [-1218, 882, -336, 336], [148, 16, 164, -164], [360, 342, 423, -198], [0, -317, 0, -102], [-324, 0, -225, 0], [504, -1080, -81, 279], [-632, 0, -219, 0]]}