# Stored data for newform 882.4.g.bj, downloaded from the LMFDB on 25 April 2024. {"label": "882.4.g.bj", "space_label": "882.4.g", "level": 882, "weight": 4, "hecke_orbit": 36, "hecke_orbit_code": 157626399341937522, "dim": 4, "is_polredabs": true, "nf_label": "4.0.335241.2", "trace_hash": 1206813944886110134, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [1296, 252, 85, -7, 1]], [11, [4875264, 55200, 2833, -25, 1]], [13, [-606, -49, 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": 335241, "field_disc_factorization": [[3, 2], [193, 2]], "field_poly": [2304, 48, 49, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "3.794", "prec": 17}, {"__RealLiteral__": 0, "data": "1.399", "prec": 17}, {"__RealLiteral__": 0, "data": "53.805", "prec": 20}, {"__RealLiteral__": 0, "data": "58.791", "prec": 20}, {"__RealLiteral__": 0, "data": "1395.542", "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, 7, 0], "traces": [0, 4, 4, 0, -8, 7, 0, 0, -32, 0, -14, 25, 0, 98, 0, 0, -32, 98, 0, -119, -56, 0, 100, -122, 0, 129, 98, 0, 0, 146, 0, 98, 64, 0, 392, 0, 0, -289, 238, 0, -56, -672, 0, 614, 100, 0, 244, 672, 0, 0, 516, 0, -196, 375, 0, 1526, 0, 0, 146, 763, 0, -406, 392, 0, 256, 654, 0, 1041, 392, 0, 0, 3304, 0, -189, 578, 0, 952, 0, 0, -524, 112, 0, -672, -574, 0, -1244, 614, 0, -200, 2394, 0, 0, 976, 0, -1344, 706, 0, 126, 0, 0, 516, 910, 0, -161, -784, 0, 1500, 1419, 0, 717, 1526, 0, 0, 6104, 0, 1778, -292, 0, 3052, 0, 0, -2379, 812, 0, 392, 1302, 0, -1376, 256, 0, -1308, 4459, 0, 0, 4164, 0, -784, 2666, 0, -6930, 0, 0, 3304, 3990, 0, 931, -756, 0, 2312, 2958, 0, -243, 952, 0, 0, 6090, 0, 4018, 1048, 0, 448, 0, 0, -226, 1344, 0, -574, -4172, 0, -1562, -1244, 0, -1228, 4774, 0, 0, -800, 0, -4788, 3768, 0, -7378, 0, 0, 976, 3038, 0, 5530, -5376, 0, 2824, -1632, 0, -3640, 126, 0, 0, 2116, 0, 4396, -1032, 0, 3640, 0, 0, -1176, 322, 0, -784, -7028, 0, -7120, 1500, 0, -2838, -952, 0, 0, 2868, 0, -3052, -2424, 0, -17570, 0, 0, 6104, 3549, 0, 105, 7112, 0, -1168, -1718, 0, -36, 3052, 0, 0, 2028, 0, 5005, 4758, 0, 3248, 0, 0, -4363, -784, 0, 1302, 9954, 0, -21964, -1376, 0, -512, 462, 0, 0, -5232, 0, -8918, -2496, 0, -9534, 0, 0, 4164, -6755, 0, -301, -3136, 0, 10664, 3116, 0, 5807, -6930, 0, 0, -17708, 0, 5607, -6608, 0, 15960, 0, 0, -4626, -1862, 0, -756, 2478, 0, 17114, 2312, 0, -5916, -9744, 0, 0, -972, 0, -1904, -1860, 0, 4242, 0, 0, 6090, -17108, 0, 924, 16072, 0, 4192, -5061, 0, 5641, 448, 0, 0, -5872, 0, -217, 452, 0, 5376, 0, 0, -5989, 1148, 0, -4172, 532, 0, -6140, -1562, 0, 2488, -20139, 0, 0, -4912, 0, -9548, -13872, 0, 10584, 0, 0, -800, -2604, 0, 3080, -19152, 0, 15072, -9106, 0, 5769, -7378, 0, 0, -20044, 0, 19222, -1952, 0, 12152, 0, 0, -11331, -11060, 0, -5376, 10332, 0, 4074, 2824, 0, 3264, -13762, 0, 0, -14560, 0, -252, 698, 0, 15064, 0, 0, 2116, -7623, 0, -25249, 17584, 0, -4128, 2844, 0, 15911, 3640, 0, 0, -35596, 0, -11564, 2352, 0, 1288, 0, 0, -9593, 1568, 0, -7028, 13944, 0, 6850, -7120, 0, -3000, -13076, 0, 0, -11352, 0, 1904, -4596, 0, 14182, 0, 0, 2868, -11312, 0, 21035, -12208, 0, -9696, -13703, 0, -13590, -17570, 0, 0, -15556, 0, -4200, -12208, 0, 14196, 0, 0, -4092, -210, 0, 7112, -16436, 0, 5178, -1168, 0, 3436, 2632, 0, 0, -144, 0, -6104, -10348, 0, -11298, 0, 0, 2028, 15764, 0, -17213, 20020, 0, 19032, -14737, 0, 5246, 3248, 0, 0, -25866, 0, -3178, 8726, 0, -3136, 0, 0, 26511, -2604, 0, 9954, -17724, 0, -33388, -21964, 0, 2752, -8715, 0, 0, -2048, 0, -924, 8380, 0, -15624, 0, 0, -5232, -3696, 0, 5215, -35672, 0, -9984, 22218, 0, -2022, -9534, 0, 0, -16464, 0, 9219, -8328, 0, -27020, 0, 0, -4745, 602, 0, -3136, 46900, 0, 25732, 10664, 0, -6232, -6370, 0, 0, 23228, 0, 13860, -3583, 0, -5222, 0, 0, -17708, -24157, 0, 13384, 22428, 0, -26432, -2022, 0, -2027, 15960, 0, 0, 3176, 0, -17094, 9252, 0, -7448, 0, 0, 37869, 1512, 0, 2478, -23506, 0, -27874, 17114, 0, -4624, 21294, 0, 0, -23664, 0, 19488, 17946, 0, -25340, 0, 0, -972, 25214, 0, 32858, -7616, 0, -7440, 4884, 0, -40640, 4242, 0, 0, 109336, 0, 5481, -12180, 0, -68432, 0, 0, 2076, -1848, 0, 16072, 12208, 0, 38618, 4192, 0, 10122, 4347, 0, 0, 22564, 0, -896, 3712, 0, -2954, 0, 0, -5872, 20244, 0, -50743, -868, 0, 1808, 30417, 0, -19177, 5376, 0, 0, 46960, 0, -28413, 11978, 0, 4592, 0, 0, -13910, 8344, 0, 532, 35784, 0, -9928, -6140, 0, 3124, 40551, 0, 0, 9952, 0, 40278, -6501, 0, 53788, 0, 0, -4912, -21210, 0, 37597, -38192, 0, -55488, -10294, 0, -16464, 10584, 0, 0, 28874, 0, -23275, 1600, 0, -10416, 0, 0, 32984, -6160, 0, -19152, -87612, 0, 73092, 15072, 0, 18212, 40362, 0, 0, 23076, 0, 14756, -20, 0, -49224, 0, 0, -20044, 35308, 0, -22183, 76888, 0, -7808, 10630, 0, 2515, 12152, 0, 0, 39948, 0, -30618, 22662, 0, -44240, 0, 0, 31324, 10752, 0, 10332, -48986, 0, -71204, 4074, 0, -5648, 8330, 0, 0, 13056, 0, 27524, 48126, 0, 51912, 0, 0, -14560, 51814, 0, 12593, -1008, 0, 2792, 19992, 0, 1736, 15064, 0, 0, -10088, 0, 33824, -4232, 0, -30492, 0, 0, 6458, 50498, 0, 17584, 38514, 0, 112176, -4128, 0, -5688, 67886, 0, 0, 63644, 0, -7280, 39776, 0, 77028, 0, 0, -35596, -19474, 0, -12187, -46256, 0, 9408, -31973, 0, 26532, 1288, 0, 0, 48558, 0, -76041, 19186, 0, 6272, 0, 0, 12578, 14056, 0, 13944, -28252, 0, -82770, 6850, 0, 14240, 20909, 0, 0, -12000, 0, 26152, -46000, 0, 122206, 0, 0, -11352, 84924, 0, -728, 7616, 0, -18384, 34178, 0, 7802, 14182, 0, 0, 119298, 0, 8617, -5736, 0, -45248, 0, 0, -9870, -42070, 0, -12208, -77028, 0, 120914, -9696, 0, 27406, 10878, 0, 0, -54360, 0, 35140, 33036, 0, -38472, 0, 0, -15556, 22491, 0, -79170, -16800, 0, -48832, 10152, 0, 51169, 14196, 0, 0, -7896, 0, -63707, 8184, 0, -840, 0, 0, 32235, -14224, 0, -16436, 53928, 0, -8910, 5178, 0, 2336, -1428, 0, 0, 13744, 0, -5264, 1682, 0, 68740, 0, 0, -144, -68621, 0, 20496, -24416, 0, -41392, -47356, 0, -51433, -11298, 0, 0, -58880, 0, -10500, -4056, 0, 63056, 0, 0, -20876, 34426, 0, 20020, -17374, 0, -7528, 19032, 0, 29474, -6615, 0, 0, 20984, 0, -6496, 3180, 0, 132804, 0, 0, -25866, 37884, 0, -43582, -12712, 0, 34904, 9644, 0, 6074, -3136, 0, 0, 107200, 0, 5509, -53022, 0, -10416], "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": "126.4.g.e", "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, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-8, 0, 0, 0], [0, 0, 0, 0], [-6, -2, 8, -2], [9, 7, -16, 7], [0, 0, 0, 0], [22, 0, 0, 5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -16, 0], [54, -10, -44, -10], [0, 0, 0, 0], [0, 3, -61, 0], [-12, 0, 0, -4], [0, 0, 0, 0], [18, 0, 0, 14], [0, 14, -68, 0], [0, 0, 0, 0], [68, -7, -61, -7], [0, -10, 54, 0], [0, 0, 0, 0], [0, 0, 0, 0], [33, 0, 0, 7], [0, 0, 0, 0], [35, 28, -63, 28], [32, 0, -32, 0], [0, 0, 0, 0], [108, 0, 0, -20], [0, 0, 0, 0], [0, 0, 0, 0], [0, 21, -155, 0], [116, 6, -122, 6], [0, 0, 0, 0], [0, 8, -32, 0], [-168, 0, 0, 0], [0, 0, 0, 0], [164, 0, 0, -21], [0, -28, 64, 0], [0, 0, 0, 0], [108, 28, -136, 28], [0, 24, 324, 0], [0, 0, 0, 0], [0, 0, 0, 0], [136, 0, 0, -14], [0, 0, 0, 0], [-88, -20, 108, -20], [219, -63, -156, -63], [0, 0, 0, 0], [363, 0, 0, 37], [0, 0, 0, 0], [0, 0, 0, 0], [0, -14, 80, 0], [351, 61, -412, 61], [0, 0, 0, 0], [0, -34, -186, 0], [70, 0, 0, 56], [0, 0, 0, 0], [64, 0, 0, 0], [0, -42, 348, 0], [0, 0, 0, 0], [538, -35, -503, -35], [0, 40, 176, 0], [0, 0, 0, 0], [0, 0, 0, 0], [840, 0, 0, -28], [0, 0, 0, 0], [-46, -97, 143, -97], [268, 42, -310, 42], [0, 0, 0, 0], [232, 0, 0, 12], [0, 0, 0, 0], [0, 0, 0, 0], [0, -98, -213, 0], [48, 16, -64, 16], [0, 0, 0, 0], [0, 0, -336, 0], [-99, 0, 0, -89], [0, 0, 0, 0], [-318, 0, 0, 14], [0, 42, 286, 0], [0, 0, 0, 0], [-72, -56, 128, -56], [0, -54, 1224, 0], [0, 0, 0, 0], [0, 0, 0, 0], [216, 0, 0, 56], [0, 0, 0, 0], [-696, 48, 648, 48], [318, 70, -388, 70], [0, 0, 0, 0], [109, 0, 0, -155], [0, 0, 0, 0], [0, 0, 0, 0], [0, 28, 244, 0]]}