# Stored data for newform 315.3.w.a, downloaded from the LMFDB on 24 April 2024. {"label": "315.3.w.a", "space_label": "315.3.w", "level": 315, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 1511878820155, "dim": 8, "is_polredabs": true, "nf_label": "8.0.523596960000.16", "trace_hash": 1847180632831430695, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [100, -100, 190, 50, 91, 2, 13, 2, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(-1+\\beta _{1}-\\beta _{3}-\\beta _{4}+\\beta _{5}+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "w", "char_is_real": false, "Nk2": 2835, "analytic_conductor": 8.583128327349351, "hecke_ring_index": 1, "level_radical": 105, "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": "0.169", "prec": 17}, "analytic_rank_proved": true, "char_values": [315, 6, [281, 127, 136], [6, 6, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [136, 271], "field_disc": 523596960000, "field_disc_factorization": [[2, 8], [3, 6], [5, 4], [67, 2]], "field_poly": [100, 100, 190, -50, 91, -2, 13, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.099", "prec": 17}, {"__RealLiteral__": 0, "data": "8.053", "prec": 17}, {"__RealLiteral__": 0, "data": "2.159", "prec": 17}, {"__RealLiteral__": 0, "data": "278.380", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16036.330", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [-2, 0, 0, -16], "traces": [0, 8, -2, 0, -6, 0, 0, -16, 32, 0, 0, -20, 0, 0, 16, 0, -2, 18, 0, 0, 0, 0, -16, -62, 0, 20, -120, 0, -120, 100, 0, -126, -36, 0, 0, 0, 0, -80, -114, 0, 90, 0, 0, 352, 18, 0, -82, 72, 0, 38, -20, 0, -48, 76, 0, 0, -196, 0, -40, 54, 0, -396, 0, 0, -4, 60, 0, 184, 312, 0, 0, -164, 0, 348, 140, 0, 0, -152, 0, -206, 0, 0, 204, 0, 0, -60, -178, 0, 124, -282, 0, -114, 288, 0, 30, 120, 0, 0, 592, 0, 30, 402, 0, 24, 0, 0, 20, -98, 0, -62, -210, 0, 16, -32, 0, 0, -480, 0, 0, -240, 0, 210, -24, 0, 804, 0, 0, -440, 148, 0, -270, -258, 0, -144, 20, 0, -420, 310, 0, 0, -300, 0, 644, -522, 0, 390, 0, 0, 480, 328, 0, 316, 1212, 0, 488, -360, 0, 228, -226, 0, 0, 496, 0, 496, 378, 0, -768, 0, 0, -976, 300, 0, -384, 132, 0, 80, -724, 0, -456, 154, 0, 0, 30, 0, -866, -300, 0, -492, 0, 0, -720, 172, 0, -8, -1020, 0, 846, -68, 0, 240, 80, 0, 0, 370, 0, -210, -702, 0, -1692, 0, 0, 124, -504, 0, -628, 30, 0, 504, -556, 0, -60, -534, 0, 0, -642, 0, 440, 510, 0, 1050, 0, 0, 160, -560, 0, -90, -156, 0, -1440, 1696, 0, 582, 90, 0, 0, -480, 0, -612, -804, 0, 0, 0, 0, -616, 1544, 0, 390, 414, 0, 940, 540, 0, 1032, -740, 0, 0, 942, 0, 744, -132, 0, -72, 0, 0, 1352, 100, 0, 460, 1734, 0, 600, 820, 0, -312, 636, 0, 0, 78, 0, -52, 480, 0, 1320, 0, 0, -540, -1190, 0, 596, -2760, 0, -1154, -2752, 0, -1686, 180, 0, 0, -84, 0, -30, 558, 0, -948, 0, 0, 144, -14, 0, -760, -360, 0, -1504, -1644, 0, -60, 1256, 0, 0, -234, 0, -776, 2832, 0, 1386, 0, 0, -56, -1328, 0, 240, 870, 0, -1216, 3088, 0, 906, 16, 0, 0, -290, 0, -516, 1062, 0, 90, 0, 0, 1520, -1202, 0, 248, -1758, 0, 930, -780, 0, 828, -1420, 0, 0, 586, 0, 1216, -360, 0, -30, 0, 0, 904, 480, 0, 152, 1884, 0, 270, 1964, 0, -24, 1354, 0, 0, -772, 0, -1534, 360, 0, 180, 0, 0, -20, -122, 0, 1044, -2304, 0, -160, -340, 0, -1086, 210, 0, 0, 1164, 0, -690, -2310, 0, -1476, 0, 0, 2596, 992, 0, -1310, 90, 0, -492, 2112, 0, -990, -644, 0, 0, -1470, 0, 816, -2574, 0, -408, 0, 0, -120, 748, 0, 330, 1188, 0, 1040, -140, 0, 30, -264, 0, 0, -420, 0, 400, -1758, 0, 1650, 0, 0, 1072, 1340, 0, 1328, 4368, 0, 844, 120, 0, -384, -70, 0, 0, 1416, 0, -520, -1032, 0, -660, 0, 0, -1440, 420, 0, -1496, 852, 0, 900, -2336, 0, 180, -1320, 0, 0, -2330, 0, -362, 300, 0, -60, 0, 0, 1260, 538, 0, 1044, -1440, 0, -1176, -4840, 0, 1824, 690, 0, 0, -520, 0, 180, -258, 0, 336, 0, 0, -2416, 186, 0, -1266, 1140, 0, -3828, 3156, 0, -330, 1360, 0, 0, -860, 0, -146, 1404, 0, -420, 0, 0, -3248, -1656, 0, -40, -450, 0, 1288, 4628, 0, -2640, -968, 0, 0, -630, 0, 752, 1536, 0, 720, 0, 0, 16, 16, 0, -722, 1032, 0, 258, -620, 0, 1428, 82, 0, 0, 2058, 0, 1424, -1944, 0, -2334, 0, 0, -900, -660, 0, -340, -2262, 0, -390, -408, 0, 1140, -1712, 0, 0, 2414, 0, -108, 420, 0, -84, 0, 0, -1560, -414, 0, 100, -5274, 0, 2158, -5024, 0, -1416, 780, 0, 0, 198, 0, -100, 1974, 0, 2268, 0, 0, -416, 472, 0, -172, 720, 0, 2208, -1400, 0, 1890, 340, 0, 0, 2556, 0, 2400, 2718, 0, -60, 0, 0, -3744, 898, 0, -420, 1734, 0, -480, 4648, 0, -1278, -406, 0, 0, 1710, 0, 2060, 432, 0, 150, 0, 0, 496, 338, 0, -720, 570, 0, 1668, -1320, 0, 1332, 934, 0, 0, -2396, 0, -1948, 1194, 0, 1602, 0, 0, 4952, 360, 0, 468, -2832, 0, -540, -1052, 0, -3120, -1034, 0, 0, -3756, 0, -596, 960, 0, 2448, 0, 0, -600, -1926, 0, -1024, -1332, 0, 1350, -7448, 0, 3288, 250, 0, 0, 2100, 0, 1170, -1038, 0, -2352, 0, 0, -2388, 866, 0, 2056, 1710, 0, -1720, 532, 0, -720, 962, 0, 0, 1114, 0, -434, -12, 0, -7440, 0, 0, -2312, -1270, 0, 450, -1032, 0, 736, -888, 0, -1578, 2274, 0, 0, -480, 0, -3060, -4230, 0, -630, 0, 0, -760, -360, 0, 656, 5160, 0, 2146, -2700, 0, 1092, -660, 0, 0, -2228, 0, -1380, 1614, 0, 1092, 0, 0, 912, 180, 0, 3632, -3906, 0, -720, 7620, 0, 7296, 706, 0, 0, -240, 0, 2350, 120, 0, 3540, 0, 0, -480, 2986, 0, -3536, 3936, 0, 5220, 5056, 0, -2466, -840, 0, 0, 4338, 0, -420, 438, 0, -3936, 0, 0, 6792, 1814, 0, -210, -120, 0, -2100, 3248, 0, 1200, -3100, 0, 0, 3432, 0, -3824, 1422, 0, -24, 0, 0, 2960, -656, 0, 810, -1698, 0, 276, 3932, 0, 2286, 1204, 0, 0, 150, 0, 1624, 108, 0, -360, 0, 0, 832, -4104, 0, 1184, 4338, 0, -4274, -2520, 0, -1416, -468, 0, 0, -3074, 0, -340, -8010, 0, 2484, 0, 0, 2440, -360, 0, -416, -5592, 0, -1050, -884, 0, -1008, -478, 0, 0, -4572, 0, 1498, -720, 0, 4152, 0, 0, -800, 740, 0, -3960, 3420, 0, -3534, -5736, 0, -3588, -480, 0, 0, -3490, 0, 210, 2370, 0, 2904, 0, 0, -1784, -578, 0, -1038, -570, 0, 540, 7960, 0, 120, 612, 0, 0, 424, 0, -46, 6390, 0, 1542, 0, 0, -2792, 3180, 0, -180, -1770, 0, -1656, 596, 0, -3720, 994, 0, 0, -300, 0, -1216, 1122, 0, -840, 0, 0, 5544, -5818, 0, 1798, 4704, 0, -6112, -2760, 0, -60, 1298, 0, 0], "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, 4, -1, 6, 0]], "char_orbit_index": 23, "prim_orbit_index": 4, "minimal_twist": "105.3.n.a", "char_is_minimal": true, "conrey_index": 136, "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, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, -1, -1, 1, 2, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 1, -1, 1, -4, 0, 1, 0], [5, 0, 2, 1, 1, 3, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, -1, -1, -1, 0, 0], [-4, -1, 1, 1, -5, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [2, -4, 0, 2, 0, 5, 5, -4], [5, -1, 1, 6, 11, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, -2, 0, -3, 0, 1, -2], [3, -4, -1, -4, -4, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 4, 4, 1, 4, -4, -4], [-5, 2, 0, -1, -9, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, -2, 3, -1, -5, 3, 1], [0, -3, -4, 0, 12, 0, 2, -4], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 5, 0, 0, 0], [-20, -1, 1, 2, -10, 1, 14, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-13, -3, -5, -5, 4, -14, -6, 4], [5, 0, -10, 0, -5, -1, -9, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-8, -1, 4, -1, 12, -7, 0, 0], [-5, -1, 3, 1, -8, 8, 10, -6], [0, 0, 0, 0, 0, 0, 0, 0], [-20, 4, 0, -2, -38, 14, 14, 2], [0, 0, 4, 1, -3, 7, 5, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 8, -4, 0, 22, -10, -3, -4], [-10, -7, -8, -7, 2, -22, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10, -3, -2, 6, 5, -2, -5, 2], [-4, 6, 0, -3, -5, -12, -12, 3], [0, 0, 0, 0, 0, 0, 0, 0], [49, 0, 10, 5, 5, 8, 2, -5], [0, 7, 0, 0, -1, -2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-15, 17, -2, -17, -13, 9, 22, 4], [14, 1, 1, -2, 7, 1, 5, -1], [0, 0, 0, 0, 0, 0, 0, 0], [11, 9, 2, -18, -4, -14, -7, -2], [0, 0, 0, -5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-13, 15, -3, 15, 10, 12, 0, 0], [13, 3, -5, -3, 18, 2, 14, 10], [0, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, 3, 2, 4, 4, 2], [-35, 14, 2, -3, -12, 21, 13, 6], [0, 0, 0, 0, 0, 0, 0, 0], [0, -32, -4, 0, -8, 16, 10, -4], [-3, 14, -1, 14, 2, -14, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-60, -4, 10, 8, -30, 10, -4, -10], [-5, 40, 0, -20, -3, -5, -5, 7], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, -12, -1, -6, -15, 3, 6], [0, -14, 2, 0, -21, -2, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [47, 5, -1, -5, 48, -11, -20, 2], [44, -20, 12, 40, 22, 12, -6, -12], [0, 0, 0, 0, 0, 0, 0, 0], [0, -7, 3, 13, 3, -7, -5, -5], [1, 0, 10, -28, 5, 9, 1, -5], [0, 0, 0, 0, 0, 0, 0, 0], [31, -11, -7, -11, -38, -23, 0, 0], [40, 31, -7, -31, 47, -7, 0, 14], [0, 0, 0, 0, 0, 0, 0, 0], [-31, 46, 0, -23, -56, 21, 21, 6], [-2, 13, 11, -9, 21, 7, -13, -5], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 6, 0, 52, 12, 3, 6], [5, -9, 1, -9, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [30, 5, -9, -10, 15, -9, -15, 9], [-9, -24, 0, 12, -13, -37, -37, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, -6, -14, -3, -3, -3, 3], [0, -48, -3, 0, 19, -33, -15, -3], [0, 0, 0, 0, 0, 0, 0, 0], [15, -17, -5, 17, 20, 0, 10, 10], [-46, -10, 11, 20, -23, 11, -11, -11], [0, 0, 0, 0, 0, 0, 0, 0], [-33, 15, 6, 15, -4, -35, -48, 14], [5, 0, -6, 53, -3, 23, -29, 3], [0, 0, 0, 0, 0, 0, 0, 0], [5, -1, 4, -1, -1, 5, 0, 0], [20, -14, -2, 14, 22, -3, -2, 4], [0, 0, 0, 0, 0, 0, 0, 0], [6, -28, 0, 14, 22, 16, 16, 10], [45, 19, -9, -10, -38, 14, 0, 16], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, 0, -5, 10, 5, 0]]}