# Stored data for newform 144.3.o.c, downloaded from the LMFDB on 25 April 2024.
{"label": "144.3.o.c", "space_label": "144.3.o", "level": 144, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9008161377747088, "dim": 8, "is_polredabs": true, "nf_label": "8.0.856615824.2", "trace_hash": 2288730277138409455, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [1296, -324, 2133, 729, 3186, 189, 66, -3, 1]], [7, [2566404, 446958, -161487, -32643, 12366, -351, -114, 3, 1]]], "qexp_display": "q+(-\\beta _{3}+\\beta _{4})q^{3}+(1-\\beta _{2}+\\beta _{3}-\\beta _{4}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 36, "char_orbit_label": "o", "char_is_real": false, "Nk2": 1296, "analytic_conductor": 3.9237158067882754, "hecke_ring_index": 324, "level_radical": 6, "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": {"__RealLiteral__": 0, "data": "0.174", "prec": 17}, "analytic_rank_proved": true, "char_values": [144, 6, [127, 37, 65], [3, 6, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [31, 79], "field_disc": 856615824, "field_disc_factorization": [[2, 4], [3, 6], [271, 2]], "field_poly": [4, 0, 32, 0, 36, 0, 11, 0, 1], "hecke_ring_index_factorization": [[2, 2], [3, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "7.540", "prec": 17}, {"__RealLiteral__": 0, "data": "1.421", "prec": 17}, {"__RealLiteral__": 0, "data": "227.106", "prec": 24}, {"__RealLiteral__": 0, "data": "162.895", "prec": 24}, {"__RealLiteral__": 0, "data": "10864.412", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 3, 3, -3], "traces": [0, 8, 0, 3, 0, 3, 0, -3, 0, -3, 0, -18, 0, 5, 0, 21, 0, 6, 0, 0, 0, -33, 0, 81, 0, -23, 0, -108, 0, 69, 0, -45, 0, 72, 0, 0, 0, -20, 0, 141, 0, 54, 0, 0, 0, -117, 0, -207, 0, 41, 0, 141, 0, -252, 0, 0, 0, -273, 0, 306, 0, 7, 0, -441, 0, 93, 0, -12, 0, 189, 0, 0, 0, 74, 0, 387, 0, 207, 0, -33, 0, 117, 0, -549, 0, -30, 0, 87, 0, -168, 0, 0, 0, -27, 0, 684, 0, -10, 0, -585, 0, 315, 0, 273, 0, 576, 0, 0, 0, -148, 0, 348, 0, 69, 0, -189, 0, -147, 0, -684, 0, -88, 0, 315, 0, -834, 0, 0, 0, -666, 0, 495, 0, 150, 0, -819, 0, -150, 0, -204, 0, 315, 0, 0, 0, 6, 0, 564, 0, 501, 0, 705, 0, 207, 0, -621, 0, 91, 0, 216, 0, -54, 0, 0, 0, 396, 0, 387, 0, 69, 0, -405, 0, 249, 0, -246, 0, 297, 0, 0, 0, 296, 0, 45, 0, -354, 0, -279, 0, -765, 0, -207, 0, -338, 0, 111, 0, -876, 0, 0, 0, -759, 0, 63, 0, -387, 0, -135, 0, -99, 0, 687, 0, -72, 0, 0, 0, -558, 0, -105, 0, 420, 0, -567, 0, 1038, 0, 522, 0, 53, 0, 99, 0, 1290, 0, 0, 0, 1005, 0, 45, 0, 146, 0, 243, 0, 678, 0, -642, 0, -315, 0, 0, 0, 270, 0, -234, 0, -600, 0, 858, 0, -621, 0, 81, 0, 702, 0, -438, 0, -132, 0, 0, 0, -780, 0, -693, 0, 281, 0, 999, 0, -1011, 0, -261, 0, -432, 0, 0, 0, 994, 0, -486, 0, 453, 0, -873, 0, 162, 0, 891, 0, -189, 0, -531, 0, 1878, 0, 0, 0, 1101, 0, -927, 0, -470, 0, 1440, 0, 57, 0, 1413, 0, -801, 0, 0, 0, -1124, 0, -276, 0, -1251, 0, -849, 0, -924, 0, 1827, 0, 20, 0, -363, 0, -1134, 0, 0, 0, -567, 0, -1836, 0, 55, 0, 1503, 0, -792, 0, -1980, 0, -1692, 0, 0, 0, -574, 0, -1470, 0, -294, 0, 2175, 0, 1998, 0, 1674, 0, 241, 0, -1050, 0, 3390, 0, 0, 0, 2106, 0, -1809, 0, 207, 0, 1323, 0, 801, 0, -108, 0, 81, 0, 0, 0, 1084, 0, -1782, 0, -834, 0, -1089, 0, -729, 0, 1962, 0, -562, 0, 30, 0, -450, 0, 0, 0, -231, 0, -225, 0, -889, 0, 2007, 0, -1923, 0, 2931, 0, -990, 0, 0, 0, -1202, 0, -1026, 0, 594, 0, -1665, 0, 1041, 0, 108, 0, -618, 0, -435, 0, 1278, 0, 0, 0, 2607, 0, -2007, 0, 734, 0, 1602, 0, -315, 0, -2337, 0, -1431, 0, 0, 0, 1302, 0, -987, 0, -1134, 0, 3867, 0, -2376, 0, 693, 0, 1054, 0, -810, 0, -1770, 0, 0, 0, -924, 0, -1224, 0, 1236, 0, 756, 0, -1224, 0, -1026, 0, -675, 0, 0, 0, 2358, 0, 207, 0, 63, 0, -1344, 0, 2736, 0, 927, 0, -549, 0, 879, 0, 2718, 0, 0, 0, 2400, 0, -1674, 0, -1063, 0, 936, 0, 999, 0, 3636, 0, 1908, 0, 0, 0, -3364, 0, -510, 0, -546, 0, -1704, 0, 399, 0, 306, 0, -687, 0, -1146, 0, 744, 0, 0, 0, -1611, 0, 864, 0, 537, 0, 81, 0, -750, 0, -1794, 0, 531, 0, 0, 0, -830, 0, -1869, 0, 1413, 0, 3078, 0, -459, 0, 1440, 0, 1260, 0, -264, 0, -600, 0, 0, 0, 1074, 0, 1323, 0, 436, 0, -738, 0, 282, 0, -1689, 0, -1647, 0, 0, 0, 676, 0, 1647, 0, -2148, 0, -1896, 0, -1701, 0, -1098, 0, -1870, 0, -1449, 0, -4056, 0, 0, 0, -1383, 0, -1080, 0, -2056, 0, -72, 0, 318, 0, 4878, 0, -1836, 0, 0, 0, -1800, 0, 594, 0, 657, 0, -2493, 0, 1437, 0, -1665, 0, 175, 0, 1986, 0, 2736, 0, 0, 0, 315, 0, 1899, 0, 601, 0, -1845, 0, 531, 0, -4083, 0, 2124, 0, 0, 0, 3270, 0, 2985, 0, 774, 0, 4959, 0, 999, 0, -1449, 0, 2061, 0, 2199, 0, -600, 0, 0, 0, -3600, 0, 999, 0, 1451, 0, -693, 0, -351, 0, -1359, 0, 2997, 0, 0, 0, 3306, 0, 522, 0, 2946, 0, -2763, 0, -1080, 0, -2889, 0, -283, 0, -402, 0, -828, 0, 0, 0, -624, 0, 1269, 0, -939, 0, -3573, 0, 1638, 0, 4695, 0, 153, 0, 0, 0, -4312, 0, -324, 0, -807, 0, -3630, 0, -3870, 0, -495, 0, 409, 0, 1155, 0, -3936, 0, 0, 0, -1254, 0, 5103, 0, 504, 0, -2637, 0, 1725, 0, -4701, 0, -297, 0, 0, 0, -1994, 0, 4158, 0, -993, 0, 5256, 0, 2142, 0, -1881, 0, 1485, 0, -780, 0, -330, 0, 0, 0, 852, 0, 3744, 0, -513, 0, -2700, 0, 3189, 0, 411, 0, 3456, 0, 0, 0, 2816, 0, 567, 0, 2643, 0, -1737, 0, -351, 0, -3537, 0, -2555, 0, 2175, 0, 3240, 0, 0, 0, -2007, 0, 2754, 0, -3131, 0, -5436, 0, -843, 0, 4206, 0, 3510, 0, 0, 0, -2442, 0, 4290, 0, 1413, 0, -3255, 0, -1515, 0, -2529, 0, -977, 0, 1857, 0, -4104, 0, 0, 0, -2583, 0, -1845, 0, 1332, 0, -1728, 0, -558, 0, -4392, 0, 1485, 0, 0, 0, 1728, 0, 999, 0, -186, 0, 4926, 0, -945, 0, -2313, 0, 2709, 0, 3174, 0, -4230, 0, 0, 0, 873, 0, 3204, 0, 2744, 0, -3231, 0, 2481, 0, -2721, 0, -2835, 0, 0, 0, 6136, 0, -1710, 0, -597, 0, -1863, 0, 1080, 0, -324, 0, -352, 0, 795, 0, -618, 0, 0, 0, -2907, 0, 5445, 0, -1171, 0, 171, 0, 69, 0, 6549, 0, 1035, 0, 0, 0, -5514, 0, 2022, 0, 2646, 0, -1908, 0, 3444, 0, -4653, 0, -570, 0, -2601, 0, -1674, 0, 0, 0, -987, 0, -684, 0, 715, 0, -1404, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 36, 6, -1, 6, 0]], "char_orbit_index": 15, "prim_orbit_index": 6, "minimal_twist": "144.3.o.a", "char_is_minimal": true, "conrey_index": 31, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 0, 0, 0, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 0, -1, 2, 2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 0, 3, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, -9, 0, 1, 1, 3, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -3, 1, 3, -2, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -3, 4, -3, 6, -1, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 3, 1, 1, 3, 6, 3], [0, 0, 0, 0, 0, 0, 0, 0], [13, -5, -1, -3, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 6, -1, 6, -9, 0, -5, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 3, -6, 0, -3, 0, -3, -3], [0, 0, 0, 0, 0, 0, 0, 0], [15, -14, -4, -9, 2, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 5, 1, 3, -6, -2, -2, -4], [0, 0, 0, 0, 0, 0, 0, 0], [6, 6, 3, 3, -3, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-15, 33, 1, 8, -4, -1, -4, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 6, 3, -12, 3, 3, -3, 3], [0, 0, 0, 0, 0, 0, 0, 0], [6, 24, 0, 0, -1, -6, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [6, 12, -6, 9, -12, -3, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 3, 0, -9, -4, 4, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-9, -21, 9, -6, 3, 0, 9, 6], [0, 0, 0, 0, 0, 0, 0, 0], [-18, -15, -2, 2, 2, -10, -7, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 12, 5, 0, 9, -6, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [42, -42, -6, 2, -4, -9, -6, -6], [0, 0, 0, 0, 0, 0, 0, 0], [-33, -6, -3, 0, 9, 9, 3, 9], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 15, 0, 6, -3, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-45, 24, 3, -4, -1, -12, -3, -9], [0, 0, 0, 0, 0, 0, 0, 0], [54, -21, 2, 1, -11, -2, -5, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -2, 10, 3, 0, 0, 5, 12], [0, 0, 0, 0, 0, 0, 0, 0], [-63, 6, 9, 3, 3, 0, 9, 6], [0, 0, 0, 0, 0, 0, 0, 0], [27, -22, -8, -3, -2, 0, -5, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -8, 6, 12, 3, 3, 12, 6], [0, 0, 0, 0, 0, 0, 0, 0], [24, -3, 0, -12, 6, 3, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-27, 66, -11, -4, -7, 5, -1, -5], [0, 0, 0, 0, 0, 0, 0, 0], [11, 1, -1, 3, -3, -6, -2, -6], [0, 0, 0, 0, 0, 0, 0, 0], [21, 57, -9, 5, -3, 15, 0, 12], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 54, 3, -3, 3, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-13, 4, 3, -15, 21, -4, -11, -2], [0, 0, 0, 0, 0, 0, 0, 0], [54, -63, -9, 21, -15, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-52, -43, 6, -14, 10, 10, 3, 5], [0, 0, 0, 0, 0, 0, 0, 0], [14, -19, -14, 9, -12, 21, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [54, -84, 6, -13, 2, 3, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0], [-19, 4, 3, 2, -9, -7, -1, -7], [0, 0, 0, 0, 0, 0, 0, 0], [14, -17, -14, -12, -3, 8, 3, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-24, 51, -12, 6, -6, 9, -6, 3], [0, 0, 0, 0, 0, 0, 0, 0], [104, -70, 0, -2, 28, 10, 18, 20], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -13, -9, 9, 0, -2, -15], [0, 0, 0, 0, 0, 0, 0, 0], [-84, 6, 0, -9, 18, 3, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0]]}