# Stored data for newform 825.4.c.j, downloaded from the LMFDB on 22 March 2023.
{"level_primes": [3, 5, 11], "is_polredabs": true, "sato_tate_group": "3.2.3.c2", "rm_discs": [], "conrey_indexes": [199], "cm_discs": [], "trace_hash": 1192902852278797249, "level_radical": 165, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 2, "is_cm": false, "hecke_orbit": 10, "analytic_conductor": 48.67657575473601, "inner_twist_count": 2, "field_disc_factorization": [[2, 4], [17, 2]], "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": 1, "label": "825.4.c.j", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "165.4.a.c", "field_poly_is_cyclotomic": false, "dim": 4, "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 4, 0, 0, 14, 0, -6, 0, 0, -36, 0, -44, 0, 0, 64, 0, -78, 0, 0, 340, 0, -24, 0, 0, -18, 0, 124, 0, 0, 316, 0, 120, 0, 0, 732, 0, -126, 0, 0, 540, 0, 76, 0, 0, -154, 0, 1144, 0, 0, 1084, 0, -96, 0, 0, 54, 0, 736, 0, 0, -496, 0, 144, 0, 0, -1538, 0, 66, 0, 0, 744, 0, 4120, 0, 0, -2276, 0, 816, 0, 0, -1284, 0, 324, 0, 0, -288, 0, 2624, 0, 0, -488, 0, 224, 0, 0, 3896, 0, 738, 0, 0, 396, 0, 1180, 0, 0, 644, 0, 2860, 0, 0, 2016, 0, -2232, 0, 0, -1632, 0, 1684, 0, 0, -3056, 0, 484, 0, 0, 624, 0, -576, 0, 0, 3096, 0, -2344, 0, 0, -472, 0, 8180, 0, 0, 92, 0, 1344, 0, 0, 702, 0, -500, 0, 0, 7180, 0, -124, 0, 0, -704, 0, 1788, 0, 0, -2832, 0, -3584, 0, 0, 2884, 0, 7528, 0, 0, 620, 0, -3060, 0, 0, 1260, 0, 858, 0, 0, -432, 0, 4480, 0, 0, 11592, 0, 432, 0, 0, 216, 0, 1176, 0, 0, 7108, 0, 3522, 0, 0, -3248, 0, -4464, 0, 0, -2580, 0, -10784, 0, 0, -3740, 0, 10732, 0, 0, -8360, 0, 162, 0, 0, 2916, 0, -56, 0, 0, 4640, 0, -340, 0, 0, -10864, 0, 264, 0, 0, -1116, 0, 2344, 0, 0, 7392, 0, 15000, 0, 0, -5684, 0, 7740, 0, 0, 1716, 0, -17152, 0, 0, 576, 0, -11182, 0, 0, 6128, 0, -2844, 0, 0, 198, 0, 5440, 0, 0, -17504, 0, 9356, 0, 0, 5748, 0, -456, 0, 0, -1080, 0, 140, 0, 0, 13672, 0, -1364, 0, 0, -13516, 0, -1008, 0, 0, -2442, 0, -22060, 0, 0, -13200, 0, -6368, 0, 0, -12240, 0, -6588, 0, 0, 2208, 0, -17288, 0, 0, 7644, 0, -9696, 0, 0, -3476, 0, -17316, 0, 0, 1134, 0, -17544, 0, 0, -13792, 0, -11472, 0, 0, 4800, 0, -2592, 0, 0, -2040, 0, -1320, 0, 0, 24736, 0, 1484, 0, 0, -11376, 0, -4860, 0, 0, 12984, 0, -3884, 0, 0, -2184, 0, 9692, 0, 0, 3776, 0, -18780, 0, 0, -684, 0, -15216, 0, 0, -8052, 0, 41064, 0, 0, -13512, 0, -16128, 0, 0, 12750, 0, 6652, 0, 0, -40248, 0, -42896, 0, 0, -8508, 0, 1386, 0, 0, 2448, 0, 7488, 0, 0, 4572, 0, 5056, 0, 0, 1280, 0, -192, 0, 0, -10296, 0, -8996, 0, 0, -11408, 0, 5952, 0, 0, 35236, 0, -8424, 0, 0, -5940, 0, 4856, 0, 0, 1920, 0, 15284, 0, 0, -18180, 0, -9756, 0, 0, -2100, 0, 18080, 0, 0, -21112, 0, -836, 0, 0, -12248, 0, -13872, 0, 0, 864, 0, -45964, 0, 0, 2508, 0, -2428, 0, 0, -4064, 0, -9216, 0, 0, -13680, 0, -12736, 0, 0, 14576, 0, 37288, 0, 0, 1694, 0, -486, 0, 0, 3264, 0, 23800, 0, 0, 27744, 0, 720, 0, 0, 31552, 0, -6492, 0, 0, -6624, 0, -12584, 0, 0, -47232, 0, 5888, 0, 0, 22276, 0, 4512, 0, 0, 13392, 0, 30112, 0, 0, -792, 0, 6000, 0, 0, -27908, 0, 4464, 0, 0, -5796, 0, 760, 0, 0, -11924, 0, 4320, 0, 0, 47596, 0, 8640, 0, 0, -1296, 0, 14144, 0, 0, -6396, 0, 7360, 0, 0, -50656, 0, 1056, 0, 0, -6312, 0, 6080, 0, 0, 404, 0, -52244, 0, 0, 1216, 0, 13842, 0, 0, 31548, 0, -27824, 0, 0, -9388, 0, -56932, 0, 0, 5712, 0, 23616, 0, 0, -594, 0, 29924, 0, 0, 43480, 0, 32832, 0, 0, -944, 0, -444, 0, 0, -8832, 0, -27504, 0, 0, 25808, 0, -8096, 0, 0, -22096, 0, -6696, 0, 0, -12060, 0, 588, 0, 0, 77824, 0, 30736, 0, 0, 45028, 0, -19908, 0, 0, -37080, 0, -51176, 0, 0, -10368, 0, 67456, 0, 0, 5456, 0, -3168, 0, 0, 21660, 0, 37788, 0, 0, 98336, 0, -27896, 0, 0, 80520, 0, 20484, 0, 0, 26064, 0, -1584, 0, 0, -49820, 0, 5230, 0, 0, -29776, 0, -55740, 0, 0, -7344, 0, 39296, 0, 0, 35816, 0, 67640, 0, 0, -10360, 0, 17652, 0, 0, -31296, 0, 79868, 0, 0, 16918, 0, 36988, 0, 0, -3720, 0, 11556, 0, 0, -1536, 0, 11272, 0, 0, -11384, 0, 46080, 0, 0, 41588, 0, -726, 0, 0, -2916, 0, -84496, 0, 0, 70464, 0, 46968, 0, 0, -68764, 0, 48144, 0, 0, 6192, 0, -15364, 0, 0, 10352, 0, 34528, 0, 0, -16792, 0, 2592, 0, 0, -8184, 0, -25492, 0, 0, -5336, 0, 96200, 0, 0, -25168, 0, 79392, 0, 0, -23616, 0, 79532, 0, 0, -51136, 0, -45320, 0, 0, -25218, 0, 25752, 0, 0, -14796, 0, -1360, 0, 0, 14140, 0, -37616, 0, 0, -157984, 0, 4392, 0, 0, -16440, 0, -5664, 0, 0, -18500, 0, 104356, 0, 0, 25036, 0, -31788, 0, 0, -2016, 0, 83044, 0, 0, -121568, 0, -7936, 0, 0, 54344, 0, 80148, 0, 0, 20976, 0, -8976, 0, 0, 19416, 0, -52940, 0, 0, 24064, 0, -35064, 0, 0, 92376, 0, 160368, 0, 0, 2304, 0, -68872, 0, 0, 94992, 0, -31872, 0, 0, -6642, 0, 40188, 0, 0, 14124, 0, 66416, 0, 0, 131648, 0, 13164, 0, 0, -22944, 0, -44976, 0, 0, 33192, 0, -108840, 0, 0, -23808, 0, -3564, 0, 0, 3612, 0, 12512, 0, 0, 16416, 0, -154160, 0, 0, -1020, 0, -1344, 0, 0, -10620, 0, -57832, 0, 0, -30908, 0, -62708, 0, 0, -25268, 0, 35712, 0, 0, 3168, 0, 62448, 0, 0, 1104, 0, 98124, 0, 0, -91640, 0, -5796, 0, 0, 11688, 0, 16828, 0, 0, 70872, 0, -28864, 0, 0, -41768, 0, 83712, 0, 0, -25740, 0, 27776, 0, 0, -23248, 0, -113116, 0, 0, 36860, 0, 11904, 0, 0, 41208, 0, -102576, 0, 0, -36880, 0, -95628, 0, 0, 5368, 0, -18144, 0, 0, 86052, 0, 49736, 0, 0, -190464, 0, -11336, 0, 0, 65920, 0, -15720, 0, 0, 20088, 0], "hecke_ring_index_factorization": [], "nf_label": "4.0.4624.1", "field_poly": [16, 0, 9, 0, 1], "has_non_self_twist": 1, "char_values": [825, 2, [551, 727, 376], [2, 1, 2]], "Nk2": 13200, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "c", "weight": 4, "trace_display": [0, 0, 0, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+\\beta _{1}q^{2}-3\\beta _{2}q^{3}+(3+\\beta _{3})q^{4}+(-3+\\cdots)q^{6}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 4624, "level_is_prime_power": false, "relative_dim": 4, "hecke_cutters": [[2, [16, 0, 9, 0, 1]], [7, [4096, 0, 144, 0, 1]]], "space_label": "825.4.c", "level": 825, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_degree": 1, "char_conductor": 5, "char_orbit_index": 3, "hecke_ring_generator_nbound": 3, "hecke_orbit_code": 40532534152397625, "trace_moments": [{"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "4.010", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "79.332", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2181.853", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -3, 0], [3, 0, 0, 1], [0, 0, 0, 0], [-3, 0, 0, 3], [0, -4, -4, 0], [0, 11, 4, 0], [-9, 0, 0, 0], [0, 0, 0, 0], [-11, 0, 0, 0], [0, -3, -12, 0], [0, -2, 44, 0], [16, 0, 0, 0], [0, 0, 0, 0], [-27, 0, 0, 15], [0, -44, -30, 0], [0, -9, 0, 0], [96, 0, 0, -22], [0, 0, 0, 0], [0, 0, 0, -12], [0, -11, 0, 0], [0, -60, 32, 0], [-21, 0, 0, 33], [0, 0, 0, 0], [54, 0, 0, -46], [0, 0, 27, 0], [0, -16, -32, 0], [62, 0, 0, 34], [0, 0, 0, 0], [24, 0, 0, 12], [0, 61, 92, 0], [0, 0, 33, 0], [190, 0, 0, -14], [0, 0, 0, 0], [-27, 0, 0, -9], [0, 112, -130, 0], [0, 96, -88, 0], [138, 0, 0, -6], [0, 0, 0, 0], [-58, 0, 0, 154], [0, 0, -48, 0], [0, -124, 196, 0], [-33, 0, 0, -11], [0, 0, 0, 0], [332, 0, 0, -92], [0, -216, 4, 0], [0, -45, 36, 0], [279, 0, 0, -16], [0, 0, 0, 0], [42, 0, 0, -132], [0, 38, 168, 0], [0, -196, -334, 0], [27, 0, 0, -27], [0, 0, 0, 0], [176, 0, 0, 16], [0, 66, -222, 0], [0, 62, 136, 0], [-244, 0, 0, 240], [0, 0, 0, 0], [218, 0, 0, -364], [0, 24, 48, 0], [0, 36, 36, 0], [-429, 0, 0, 89], [0, 0, 0, 0], [33, 0, 0, -33], [0, -16, -380, 0], [0, -162, -296, 0], [276, 0, 0, -180], [0, 0, 0, 0], [1052, 0, 0, -44], [0, -99, -36, 0], [0, 58, 272, 0], [-690, 0, 0, 242], [0, 0, 0, 0], [200, 0, 0, 8], [0, 44, 44, 0], [0, 138, -24, 0], [-168, 0, 0, -306], [0, 0, 0, 0], [81, 0, 0, 0], [0, -58, 616, 0], [0, -426, -70, 0], [-48, 0, 0, -48], [0, 0, 0, 0], [816, 0, 0, -320], [0, -102, -288, 0], [0, -121, -44, 0], [-58, 0, 0, -128], [0, 0, 0, 0], [-32, 0, 0, 176], [0, -148, -112, 0], [0, -36, -108, 0], [1084, 0, 0, -220], [0, 0, 0, 0], [93, 0, 0, 183], [0, -428, -298, 0], [0, 279, -64, 0], [99, 0, 0, 0], [0, 0, 0, 0]]}