# Stored data for newform 405.4.e.p, downloaded from the LMFDB on 25 April 2024.
{"label": "405.4.e.p", "space_label": "405.4.e", "level": 405, "weight": 4, "hecke_orbit": 16, "hecke_orbit_code": 67554269355573653, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 785466386320232218, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [4, 4, 6, -2, 1]], [7, [2304, 0, 48, 0, 1]]], "qexp_display": "q+(\\zeta_{12}-\\zeta_{12}^{2})q^{2}+(4-4\\zeta_{12}-2\\zeta_{12}^{2}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 6480, "analytic_conductor": 23.89577355232495, "hecke_ring_index": 3, "level_radical": 15, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": [405, 3, [326, 82], [2, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [3, 5], "conrey_indexes": [136, 271], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "3.829", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "54.992", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1381.485", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [2, 0, 10, 0], "traces": [0, 4, 2, 0, 8, 10, 0, 0, 24, 0, 20, -22, 0, 64, 24, 0, 8, -64, 0, -20, -40, 0, 190, -84, 0, -50, 80, 0, 96, -170, 0, 258, -104, 0, -368, 0, 0, 152, -418, 0, 60, -578, 0, -380, 496, 0, -552, -484, 0, 590, 50, 0, -304, 1088, 0, -220, -240, 0, 314, -706, 0, -668, 372, 0, 448, -320, 0, 1452, 544, 0, -120, 1948, 0, 2368, 964, 0, 776, -672, 0, -408, 80, 0, -580, -444, 0, -160, -556, 0, -1812, 2052, 0, 192, -48, 0, 580, -50, 0, 668, 1180, 0, -400, 282, 0, -460, 144, 0, -56, -4248, 0, 5084, -950, 0, 768, 32, 0, 420, -784, 0, -1076, 1344, 0, -2284, 1820, 0, -1176, -500, 0, 400, 2544, 0, 200, -2178, 0, 1632, 2280, 0, -7104, -3480, 0, -4570, 240, 0, 2150, -64, 0, -1700, 1736, 0, -1472, 892, 0, 2266, -8280, 0, -1872, -1290, 0, 1076, -216, 0, 520, 1536, 0, 464, 2888, 0, -3156, 3048, 0, 2250, -3680, 0, -6784, 2412, 0, 0, 5464, 0, 1026, 4004, 0, 2012, -672, 0, -2424, 380, 0, 9760, -3488, 0, -4180, -4526, 0, -3844, 1972, 0, -2360, -17040, 0, 9856, -300, 0, 3366, -576, 0, 2890, -1256, 0, -1024, 11534, 0, -5110, 3376, 0, -3684, -3800, 0, 576, 5038, 0, 1240, 320, 0, 4232, -2112, 0, 3472, -10952, 0, -3900, -1380, 0, -2460, 11976, 0, -4840, 3160, 0, -1728, -4960, 0, 2806, -11960, 0, -736, -2950, 0, 1312, 828, 0, -250, 1008, 0, 12600, 6248, 0, -800, 1260, 0, -3552, -3040, 0, -14580, 6412, 0, 2720, -1752, 0, -6432, 26588, 0, 2944, -10880, 0, -792, -550, 0, 5508, -8708, 0, -2400, 492, 0, 3780, 1544, 0, -5144, -2304, 0, 19004, -1570, 0, 3632, -10668, 0, 3530, 18672, 0, -4840, 1920, 0, 3744, 3998, 0, -13096, -6680, 0, -13256, 2160, 0, 930, -2802, 0, -6808, 23560, 0, -5760, -10652, 0, -5902, 1120, 0, 1776, 46016, 0, -3200, -584, 0, -588, -384, 0, -6966, -17952, 0, 16800, -7260, 0, 18520, -3786, 0, -2720, -1644, 0, 0, 7080, 0, 9084, -16096, 0, -3578, -1200, 0, -12496, -3204, 0, 4870, 4104, 0, -7094, 14508, 0, 28152, -9554, 0, 1920, 5920, 0, 1836, -12960, 0, 9640, 2400, 0, 13288, -16144, 0, -3864, -9728, 0, 400, -3880, 0, 13334, 10272, 0, 3360, -19160, 0, 15904, 3276, 0, 12096, 3540, 0, -6888, -4080, 0, -4376, 3488, 0, 200, -12900, 0, -8544, 16848, 0, -5232, -25700, 0, -1708, -1450, 0, 1504, -1344, 0, -4440, 4384, 0, -16862, -5552, 0, 1942, -9020, 0, -5472, 800, 0, -4608, -5376, 0, 2780, 14580, 0, 12568, -2808, 0, 5176, 13476, 0, -4070, -18120, 0, -20096, -8268, 0, 5130, 1168, 0, -5952, 17468, 0, -3412, 3280, 0, 9920, 480, 0, 5428, 12072, 0, -480, 690, 0, -8100, 5288, 0, 16044, -34160, 0, 2496, -2900, 0, -2556, 22028, 0, 250, 9216, 0, 10912, 23202, 0, -1120, -18118, 0, 1744, 6680, 0, -48112, -15528, 0, 2950, 3814, 0, 10784, -23248, 0, -2544, -4704, 0, -27518, -1000, 0, 10872, 31264, 0, 2820, 15468, 0, -11296, 2084, 0, -2208, 47552, 0, -10584, 2300, 0, -8012, 4464, 0, -720, -66632, 0, -40784, -1512, 0, -1972, -96, 0, 14662, -560, 0, 12576, 19648, 0, -10620, 5592, 0, 6766, -12980, 0, 42348, 4448, 0, -13120, 12710, 0, -5600, -44928, 0, -9500, 10642, 0, 2496, 7668, 0, 18712, -33024, 0, -31808, -3840, 0, -25884, -13620, 0, -160, 35016, 0, 35208, 4458, 0, -30682, 10096, 0, 5784, 4200, 0, -1648, 20254, 0, -1960, 14400, 0, 10816, 25248, 0, -8904, 31044, 0, 3606, -2690, 0, 28720, -8216, 0, 13440, -10192, 0, -7056, 16654, 0, -14890, -1632, 0, 43184, 11420, 0, -21548, -17432, 0, -9100, -30208, 0, 112, 3836, 0, -6672, -2904, 0, -16312, -11760, 0, 35916, 0, 0, -1250, 21832, 0, 17104, -101888, 0, -32516, 3792, 0, -1156, 1000, 0, -18880, -43532, 0, 25440, 24630, 0, 5652, 1056, 0, 31216, 35720, 0, 6124, -1000, 0, 2560, 33544, 0, 10890, 13808, 0, -12384, -31576, 0, 16846, 23502, 0, 33336, 16320, 0, 23496, -1488, 0, 5700, -39604, 0, 1188, 31904, 0, 11856, 22932, 0, -10560, -17760, 0, -21702, 17952, 0, -34800, -15312, 0, -28432, 19808, 0, -25544, 65280, 0, -43136, 22850, 0, -6880, -28918, 0, -1200, -33260, 0, -121528, -44128, 0, 2460, -14592, 0, 20068, 21500, 0, 12312, 8532, 0, -160, 26200, 0, 16638, -19308, 0, 1344, 18156, 0, 25144, -4250, 0, -29584, -14208, 0, 17360, -46336, 0, 56084, -30492, 0, 4080, -14472, 0, -81164, 7360, 0, 4128, 21080, 0, -4460, 68432, 0, 52544, 6240, 0, -32336, 5008, 0, -7432, 22660, 0, 104560, -45592, 0, -20700, 6378, 0, -9984, -976, 0, -3024, 23264, 0, 49670, -4680, 0, 3904, -10824, 0, -12900, -22392, 0, 34836, -16694, 0, -43642, 58560, 0, 4720, -5380, 0, -1040, -37344, 0, 1080, -13632, 0, -33536, -24940, 0, 22592, -4976, 0, 13120, 5200, 0, 19896, -28480, 0, 3840, 3144, 0, -34788, -121244, 0, -35316, -1776, 0, 41852, 1160, 0, -61748, -59096, 0, 28880, -36906, 0, 6644, -4440, 0, 7800, 100928, 0, -7860, 15780, 0, 1216, -9440, 0, -15240, 70960, 0, 30080, -68198, 0, 30872, -28006, 0, 21640, 22500, 0, 29568, -17024, 0, -9200, -31608, 0, 1944, -25248, 0, -56688, 64304, 0, 33154, -16960, 0, 1842, 50512, 0, 24120, 5468, 0, 7344, 12984, 0, -47712, 80424, 0, 63144, 0, 0, 9456, 3710, 0, -27320, -65212, 0, -2800, -22016, 0, -6900, -41028, 0, -24192, 10260, 0, 55456, 8948, 0, 10010, 192, 0, 39598, -40404, 0, 49792, 43678, 0, 17232, 5030, 0, -63156, -91744, 0, -6720, -14098, 0, 95916, 47324, 0, 35472, 40896, 0, -50348, 12120, 0, 16062, 26464, 0, -1900, 54072, 0, 5008, -30110, 0, -2950, 3840, 0, -5488, 97600, 0, 161400, -16176, 0, -8720, -40820, 0, -15060, 5104, 0, 808, 37836, 0, 35680, -10450, 0, 11904, 111056, 0, -45260, 40672, 0, -48426, 17088, 0, 25436, 52768, 0, -38800, 19220, 0, -70168, -50664, 0, -9860, -66996, 0, -1728, -43424, 0, 39536, 37904, 0, -11286, -23600, 0, 764, -37704, 0, -42600, -41648, 0, -31120, -27984, 0, -134596, 16584, 0, 16392, 24640, 0, -24120, -46060, 0, -3000], "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, 9, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "405.4.a.c", "char_is_minimal": false, "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], [1, 0, 0, 0], [0, 1, -1, 0], [0, 0, 0, 0], [4, -4, -2, 2], [5, -5, 0, 0], [0, 0, 0, 0], [0, 0, 4, 0], [6, 0, 0, -10], [0, 0, 0, 0], [5, 0, 0, -5], [0, -11, 28, 0], [0, 0, 0, 0], [32, -32, -4, 4], [12, -12, 4, -4], [0, 0, 0, 0], [0, 4, -32, 0], [-16, 0, 0, 56], [0, 0, 0, 0], [-5, 0, 0, 68], [0, -20, -10, 0], [0, 0, 0, 0], [95, -95, 39, -39], [-42, 42, -32, 32], [0, 0, 0, 0], [0, -25, 0, 0], [20, 0, 0, -28], [0, 0, 0, 0], [24, 0, 0, 16], [0, -85, 24, 0], [0, 0, 0, 0], [129, -129, -12, 12], [-52, 52, 44, -44], [0, 0, 0, 0], [0, -184, 72, 0], [0, 0, 0, 20], [0, 0, 0, 0], [38, 0, 0, -148], [0, -209, 73, 0], [0, 0, 0, 0], [30, -30, 50, -50], [-289, 289, 48, -48], [0, 0, 0, 0], [0, -190, -156, 0], [124, 0, 0, 90], [0, 0, 0, 0], [-138, 0, 0, 74], [0, -242, 16, 0], [0, 0, 0, 0], [295, -295, 0, 0], [25, -25, 25, -25], [0, 0, 0, 0], [0, -152, -80, 0], [272, 0, 0, 100], [0, 0, 0, 0], [-55, 0, 0, 140], [0, -120, 24, 0], [0, 0, 0, 0], [157, -157, 109, -109], [-353, 353, 28, -28], [0, 0, 0, 0], [0, -334, 192, 0], [93, 0, 0, -117], [0, 0, 0, 0], [112, 0, 0, -248], [0, -160, -20, 0], [0, 0, 0, 0], [726, -726, -52, 52], [272, -272, -192, 192], [0, 0, 0, 0], [0, -60, 20, 0], [487, 0, 0, -196], [0, 0, 0, 0], [592, 0, 0, -92], [0, 482, -186, 0], [0, 0, 0, 0], [388, -388, -262, 262], [-336, 336, -44, 44], [0, 0, 0, 0], [0, -204, -104, 0], [20, 0, 0, -160], [0, 0, 0, 0], [-145, 0, 0, 241], [0, -222, -600, 0], [0, 0, 0, 0], [-80, 80, -280, 280], [-278, 278, 34, -34], [0, 0, 0, 0], [0, -906, 278, 0], [513, 0, 0, 0], [0, 0, 0, 0], [48, 0, 0, 128], [0, -24, -44, 0], [0, 0, 0, 0], [290, -290, 258, -258], [-25, 25, -340, 340], [0, 0, 0, 0], [0, 334, 440, 0], [295, 0, 0, -295], [0, 0, 0, 0], [-100, 0, 0, -50]]}