# Stored data for newform 882.4.g.bf, downloaded from the LMFDB on 23 April 2024. {"label": "882.4.g.bf", "space_label": "882.4.g", "level": 882, "weight": 4, "hecke_orbit": 32, "hecke_orbit_code": 139612000832455538, "dim": 4, "is_polredabs": true, "nf_label": "4.0.16281225.4", "trace_hash": 2244890771432140500, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [108900, -1650, 355, 5, 1]], [11, [617796, -52662, 3703, -67, 1]], [13, [84, 41, 1]]], "qexp_display": "q+2\\beta _{2}q^{2}+(-4+4\\beta _{2})q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "g", "char_is_real": false, "Nk2": 14112, "analytic_conductor": 52.039684625063224, "hecke_ring_index": 1, "level_radical": 42, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [882, 3, [785, 199], [3, 2]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [361, 667], "field_disc": 16281225, "field_disc_factorization": [[3, 2], [5, 2], [269, 2]], "field_poly": [112896, 336, 337, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.877", "prec": 17}, {"__RealLiteral__": 0, "data": "0.888", "prec": 17}, {"__RealLiteral__": 0, "data": "56.730", "prec": 20}, {"__RealLiteral__": 0, "data": "45.162", "prec": 20}, {"__RealLiteral__": 0, "data": "1432.536", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [4, 0, -5, 0], "traces": [0, 4, 4, 0, -8, -5, 0, 0, -32, 0, 10, 67, 0, -82, 0, 0, -32, 92, 0, 43, 40, 0, 268, 148, 0, -435, -82, 0, 0, -154, 0, -520, 64, 0, 368, 0, 0, -7, -86, 0, 40, -852, 0, -214, 268, 0, -296, -576, 0, 0, -1740, 0, 164, -243, 0, 1010, 0, 0, -154, 7, 0, 224, -2080, 0, 256, -570, 0, -687, 368, 0, 0, -944, 0, -921, 14, 0, -344, 0, 0, 526, -80, 0, -852, -442, 0, -5840, -214, 0, -536, -774, 0, 0, -1184, 0, 1152, -1910, 0, -3906, 0, 0, -1740, -704, 0, -2453, 656, 0, -972, 219, 0, 597, 1010, 0, 0, 3524, 0, -2320, 308, 0, 28, 0, 0, -255, -448, 0, -2080, 7650, 0, -5708, 256, 0, 1140, -179, 0, 0, -2748, 0, -736, -3370, 0, 3198, 0, 0, -944, -2046, 0, -7205, -3684, 0, 56, 942, 0, -933, -344, 0, 0, -90, 0, -1274, -1052, 0, -320, 0, 0, -2188, 1704, 0, -442, 5080, 0, -5762, -5840, 0, 428, -494, 0, 0, -2144, 0, 1548, 2646, 0, 5342, 0, 0, -1184, -6070, 0, -392, 4608, 0, -7640, -750, 0, 1400, -3906, 0, 0, 5980, 0, -5780, 3480, 0, -2816, 0, 0, 5100, 4906, 0, 656, 6916, 0, 11132, -972, 0, -438, -9820, 0, 0, 2388, 0, -2020, 804, 0, 17938, 0, 0, 3524, -6213, 0, 789, -9280, 0, 1232, 3826, 0, -9510, 28, 0, 0, -11988, 0, 181, 510, 0, -1792, 0, 0, -2899, 4160, 0, 7650, 186, 0, 15296, -5708, 0, -512, 4692, 0, 0, 4560, 0, 358, 10242, 0, 5250, 0, 0, -2748, -3635, 0, 4265, -2944, 0, -13480, 11210, 0, 5711, 3198, 0, 0, -9548, 0, 5733, 1888, 0, -8184, 0, 0, -5166, 14410, 0, -3684, -8046, 0, 33590, 56, 0, -1884, -5724, 0, 0, -3732, 0, 688, -2130, 0, -15330, 0, 0, -90, 2218, 0, 5832, -5096, 0, -4208, 6753, 0, -9977, -320, 0, 0, -12184, 0, 5555, 4376, 0, 6816, 0, 0, -2917, 884, 0, 5080, -11360, 0, -4244, -5762, 0, 11680, 18765, 0, 0, 1712, 0, 988, -6288, 0, -21912, 0, 0, -2144, 3090, 0, 14630, 6192, 0, 10584, -3538, 0, 6741, 5342, 0, 0, 51680, 0, 10108, 2368, 0, -24280, 0, 0, 18717, 784, 0, 4608, 17952, 0, -20070, -7640, 0, 1500, 2354, 0, 0, 5600, 0, 7812, -23800, 0, -7904, 0, 0, 5980, -4065, 0, -5257, -23120, 0, 13920, 15288, 0, 12005, -2816, 0, 0, 11636, 0, 652, -10200, 0, 19624, 0, 0, 17365, -1312, 0, 6916, 6564, 0, 26014, 11132, 0, 1944, 33460, 0, 0, -1752, 0, 19640, 4962, 0, 16054, 0, 0, 2388, -11252, 0, 17321, -8080, 0, 3216, -9179, 0, 26310, 17938, 0, 0, 43748, 0, -10236, -7048, 0, -24852, 0, 0, 7212, -1578, 0, -9280, -30476, 0, 1914, 1232, 0, -7652, -12770, 0, 0, -38040, 0, -56, -13672, 0, 1470, 0, 0, -11988, 24902, 0, -5909, 724, 0, 2040, -18655, 0, -2320, -1792, 0, 0, -9282, 0, 26048, 5798, 0, 16640, 0, 0, 4191, -15300, 0, 186, -10452, 0, -23380, 15296, 0, 11416, -147, 0, 0, -2048, 0, -9384, 7990, 0, -22452, 0, 0, 4560, 27438, 0, -8939, 1432, 0, 40968, 18540, 0, 2622, 5250, 0, 0, 9396, 0, -29715, 5496, 0, -14540, 0, 0, -13499, -8530, 0, -2944, 62920, 0, 19384, -13480, 0, -22420, -23848, 0, 0, 22844, 0, -6396, 34025, 0, 24562, 0, 0, -9548, -41467, 0, 50740, 22932, 0, 7552, -16470, 0, -36965, -8184, 0, 0, -37480, 0, -15042, 10332, 0, 57640, 0, 0, 6123, 7368, 0, -8046, 28574, 0, -30430, 33590, 0, -112, -15522, 0, 0, -7536, 0, 11448, 9342, 0, -75764, 0, 0, -3732, 44420, 0, -14056, 2752, 0, -8520, 3738, 0, 7414, -15330, 0, 0, -632, 0, 207, 180, 0, 8872, 0, 0, -25800, -11664, 0, -5096, -49064, 0, -15562, -4208, 0, -13506, -38595, 0, 0, -39908, 0, 640, 61222, 0, 55798, 0, 0, -12184, 312, 0, -17047, 22220, 0, 17504, -24411, 0, -5155, 6816, 0, 0, -53120, 0, 24105, 5834, 0, 3536, 0, 0, -35288, -10160, 0, -11360, 20388, 0, 39992, -4244, 0, 11524, 7293, 0, 0, 46720, 0, -37530, -37557, 0, 84100, 0, 0, 1712, 2964, 0, -6803, 3952, 0, -25152, -71920, 0, -35736, -21912, 0, 0, -13258, 0, -18007, 4288, 0, 12360, 0, 0, 19628, -29260, 0, 6192, -87720, 0, -62400, 10584, 0, 7076, 7236, 0, 0, 26964, 0, -10684, -20240, 0, 10908, 0, 0, 51680, 35428, 0, -20125, 40432, 0, 9472, 30412, 0, 28483, -24280, 0, 0, -29928, 0, 6390, -37434, 0, 3136, 0, 0, -44258, -9216, 0, 17952, -74690, 0, -41312, -20070, 0, 15280, -6328, 0, 0, 6000, 0, -4708, -16956, 0, -66360, 0, 0, 5600, -13388, 0, -106375, 31248, 0, -95200, 2946, 0, -2362, -7904, 0, 0, -17840, 0, -6418, -11960, 0, -16260, 0, 0, -7282, 10514, 0, -23120, 101526, 0, -117552, 13920, 0, -30576, 7316, 0, 0, 48020, 0, 5632, 12002, 0, -22620, 0, 0, 11636, -94240, 0, -32563, 2608, 0, -40800, 7747, 0, 39936, 19624, 0, 0, -78990, 0, -17319, -34730, 0, -5248, 0, 0, -970, -13832, 0, 6564, -17080, 0, 71118, 26014, 0, -22264, 34775, 0, 0, 7776, 0, -66920, -23692, 0, 121366, 0, 0, -1752, 22626, 0, -26138, 78560, 0, 19848, -39664, 0, -48310, 16054, 0, 0, 46002, 0, 21481, -4776, 0, -45008, 0, 0, 16182, -34642, 0, -8080, 50940, 0, -79462, 3216, 0, 18358, -25266, 0, 0, 105240, 0, -35876, -11826, 0, -166560, 0, 0, 43748, 34815, 0, 19248, -40944, 0, -28192, 89490, 0, -13277, -24852, 0, 0, -151596, 0, 9409, -14424, 0, -6312, 0, 0, -35373, 18560, 0, -30476, -7548, 0, 63570, 1914, 0, -2464, 92460, 0, 0, -30608, 0, 25540, -60160, 0, -53828, 0, 0, -38040, -21839, 0, -15384, -224, 0, -54688, -36862, 0, -4657, 1470, 0, 0, -47012, 0, 50580, 23976, 0, 99608, 0, 0, -78308, 11818, 0, 724, -305590, 0, -87508, 2040, 0, 37310, 52053, 0, 0, -9280, 0, 3584, 26328, 0, -108348, 0, 0, -9282, 8988, 0, 106850, 104192, 0, 23192, -48268, 0, 14996, 16640, 0, 0, 77320, 0, -36731, -8382, 0, -61200], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "42.4.e.c", "char_is_minimal": false, "conrey_index": 361, "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, 0, 2, 0], [0, 0, 0, 0], [-4, 0, 4, 0], [0, -1, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-8, 0, 0, 0], [0, 0, 0, 0], [6, -2, -4, -2], [33, 1, -34, 1], [0, 0, 0, 0], [-20, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -16, 0], [48, -4, -44, -4], [0, 0, 0, 0], [0, -3, 23, 0], [12, 0, 0, -4], [0, 0, 0, 0], [66, 0, 0, 2], [0, -4, 76, 0], [0, 0, 0, 0], [-220, 5, 215, 5], [0, 2, -42, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-33, 0, 0, -11], [0, 0, 0, 0], [-259, -2, 261, -2], [32, 0, -32, 0], [0, 0, 0, 0], [96, 0, 0, -8], [0, 0, 0, 0], [0, 0, 0, 0], [0, -9, 1, 0], [-40, -6, 46, -6], [0, 0, 0, 0], [0, 8, 16, 0], [-216, 0, 0, 6], [0, 0, 0, 0], [-46, 0, 0, -15], [0, -4, 136, 0], [0, 0, 0, 0], [-144, -8, 152, -8], [0, -12, -282, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-440, 0, 0, 10], [0, 0, 0, 0], [80, 4, -84, 4], [-123, 3, 120, 3], [0, 0, 0, 0], [237, 0, 0, 31], [0, 0, 0, 0], [0, 0, 0, 0], [0, 22, -88, 0], [-9, 25, -16, 25], [0, 0, 0, 0], [0, -4, 114, 0], [-518, 0, 0, -4], [0, 0, 0, 0], [64, 0, 0, 0], [0, 18, -294, 0], [0, 0, 0, 0], [-338, -11, 349, -11], [0, 16, 176, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-246, 0, 0, 20], [0, 0, 0, 0], [-478, 35, 443, 35], [16, -18, 2, -18], [0, 0, 0, 0], [-80, 0, 0, -12], [0, 0, 0, 0], [0, 0, 0, 0], [0, -8, 267, 0], [-48, 16, 32, 16], [0, 0, 0, 0], [0, -12, -420, 0], [-123, 0, 0, 25], [0, 0, 0, 0], [-1488, 0, 0, 56], [0, 30, -122, 0], [0, 0, 0, 0], [-264, -8, 272, -8], [0, 42, -408, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-288, 0, 0, -16], [0, 0, 0, 0], [588, -24, -564, -24], [-948, -14, 962, -14], [0, 0, 0, 0], [-959, 0, 0, -35], [0, 0, 0, 0], [0, 0, 0, 0], [0, -20, -860, 0]]}