# Stored data for newform 192.5.g.b, downloaded from the LMFDB on 23 April 2024.
{"label": "192.5.g.b", "space_label": "192.5.g", "level": 192, "weight": 5, "hecke_orbit": 2, "hecke_orbit_code": 4504012028117184, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2235206874918625138, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-42, 1]]], "qexp_display": "q-3\\zeta_{6}q^{3}+42q^{5}-44\\zeta_{6}q^{7}-3^{3}q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 4, "char_orbit_label": "g", "char_is_real": true, "Nk2": 4800, "analytic_conductor": 19.84703291209811, "hecke_ring_index": 2, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.505", "prec": 17}, "analytic_rank_proved": true, "char_values": [192, 2, [127, 133, 65], [1, 2, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [127], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.922", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.126", "prec": 20}, {"__RealLiteral__": 0, "data": "0.819", "prec": 17}, {"__RealLiteral__": 0, "data": "148.111", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "4.2.3.c2", "trace_display": [0, 0, 84, 0], "traces": [0, 2, 0, 0, 0, 84, 0, 0, 0, -54, 0, 0, 0, 364, 0, 0, 0, -492, 0, 0, 0, -792, 0, 0, 0, 2278, 0, 0, 0, -156, 0, 0, 0, -216, 0, 0, 0, -1060, 0, 0, 0, -1836, 0, 0, 0, -2268, 0, 0, 0, -6814, 0, 0, 0, 9252, 0, 0, 0, -1224, 0, 0, 0, -2692, 0, 0, 0, 15288, 0, 0, 0, 7776, 0, 0, 0, -1852, 0, 0, 0, -3168, 0, 0, 0, 1458, 0, 0, 0, -20664, 0, 0, 0, 23172, 0, 0, 0, -15336, 0, 0, 0, -26236, 0, 0, 0, 10980, 0, 0, 0, -33264, 0, 0, 0, 32332, 0, 0, 0, 3684, 0, 0, 0, -9828, 0, 0, 0, 28418, 0, 0, 0, 43176, 0, 0, 0, -8856, 0, 0, 0, -17952, 0, 0, 0, -26508, 0, 0, 0, -39312, 0, 0, 0, -6552, 0, 0, 0, -876, 0, 0, 0, 13284, 0, 0, 0, -38692, 0, 0, 0, 114048, 0, 0, 0, -9072, 0, 0, 0, 9126, 0, 0, 0, 68820, 0, 0, 0, -2376, 0, 0, 0, -31412, 0, 0, 0, -44520, 0, 0, 0, 21384, 0, 0, 0, -53564, 0, 0, 0, 104964, 0, 0, 0, 11304, 0, 0, 0, -77112, 0, 0, 0, -4896, 0, 0, 0, 19008, 0, 0, 0, -224928, 0, 0, 0, -89544, 0, 0, 0, -61506, 0, 0, 0, 96940, 0, 0, 0, 97476, 0, 0, 0, 45720, 0, 0, 0, 146276, 0, 0, 0, -286188, 0, 0, 0, 124632, 0, 0, 0, 31104, 0, 0, 0, -97788, 0, 0, 0, 4212, 0, 0, 0, 388584, 0, 0, 0, 143076, 0, 0, 0, -144144, 0, 0, 0, 241036, 0, 0, 0, -6108, 0, 0, 0, -51408, 0, 0, 0, -46010, 0, 0, 0, -303324, 0, 0, 0, 5832, 0, 0, 0, -129888, 0, 0, 0, -113064, 0, 0, 0, 59256, 0, 0, 0, -257372, 0, 0, 0, 147972, 0, 0, 0, 104760, 0, 0, 0, 414596, 0, 0, 0, -576576, 0, 0, 0, 28620, 0, 0, 0, 197348, 0, 0, 0, -61344, 0, 0, 0, 326592, 0, 0, 0, -362692, 0, 0, 0, -8604, 0, 0, 0, 194832, 0, 0, 0, 232898, 0, 0, 0, -77784, 0, 0, 0, 49572, 0, 0, 0, -303556, 0, 0, 0, -28392, 0, 0, 0, 4104, 0, 0, 0, -133056, 0, 0, 0, -211500, 0, 0, 0, -3672, 0, 0, 0, 55868, 0, 0, 0, 475764, 0, 0, 0, 61236, 0, 0, 0, -40540, 0, 0, 0, -34848, 0, 0, 0, 137304, 0, 0, 0, -233396, 0, 0, 0, -560388, 0, 0, 0, -39312, 0, 0, 0, -399452, 0, 0, 0, 176256, 0, 0, 0, 183978, 0, 0, 0, 973224, 0, 0, 0, 299988, 0, 0, 0, 291528, 0, 0, 0, 568676, 0, 0, 0, 366804, 0, 0, 0, -644112, 0, 0, 0, 165792, 0, 0, 0, -35424, 0, 0, 0, -249804, 0, 0, 0, -192920, 0, 0, 0, -1101912, 0, 0, 0, -376776, 0, 0, 0, 38376, 0, 0, 0, 278784, 0, 0, 0, 194832, 0, 0, 0, 461160, 0, 0, 0, 78660, 0, 0, 0, 33048, 0, 0, 0, -157248, 0, 0, 0, -929196, 0, 0, 0, -902088, 0, 0, 0, -560062, 0, 0, 0, -334152, 0, 0, 0, 175176, 0, 0, 0, -720884, 0, 0, 0, 1357944, 0, 0, 0, 72684, 0, 0, 0, 670560, 0, 0, 0, 466548, 0, 0, 0, 53136, 0, 0, 0, 154728, 0, 0, 0, 940116, 0, 0, 0, -27648, 0, 0, 0, -682076, 0, 0, 0, 1827936, 0, 0, 0, -412776, 0, 0, 0, -347616, 0, 0, 0, -193692, 0, 0, 0, 239832, 0, 0, 0, -1255484, 0, 0, 0, 1193556, 0, 0, 0, 61776, 0, 0, 0, -494404, 0, 0, 0, -63516, 0, 0, 0, -209952, 0, 0, 0, 389642, 0, 0, 0, 260760, 0, 0, 0, 248328, 0, 0, 0, -1240148, 0, 0, 0, -304428, 0, 0, 0, -371952, 0, 0, 0, -9504, 0, 0, 0, 661428, 0, 0, 0, 50004, 0, 0, 0, 1444316, 0, 0, 0, -753984, 0, 0, 0, -8856, 0, 0, 0, -1105820, 0, 0, 0, -1218060, 0, 0, 0, 791640, 0, 0, 0, -1113336, 0, 0, 0, 1683864, 0, 0, 0, 85536, 0, 0, 0, 451656, 0, 0, 0, -89916, 0, 0, 0, -1651104, 0, 0, 0, -1066004, 0, 0, 0, 2208384, 0, 0, 0, -737856, 0, 0, 0, 869088, 0, 0, 0, -177684, 0, 0, 0, -39366, 0, 0, 0, 1665964, 0, 0, 0, 45216, 0, 0, 0, -222768, 0, 0, 0, -36792, 0, 0, 0, 1536480, 0, 0, 0, -954936, 0, 0, 0, -591572, 0, 0, 0, -2052300, 0, 0, 0, 557928, 0, 0, 0, 724612, 0, 0, 0, -2052156, 0, 0, 0, 419760, 0, 0, 0, 76032, 0, 0, 0, -1625064, 0, 0, 0, -812592, 0, 0, 0, -489944, 0, 0, 0, -1522956, 0, 0, 0, -625644, 0, 0, 0, 4790016, 0, 0, 0, 495348, 0, 0, 0, 1124424, 0, 0, 0, -200736, 0, 0, 0, 500484, 0, 0, 0, -246024, 0, 0, 0, 31372, 0, 0, 0, 1676244, 0, 0, 0, 414072, 0, 0, 0, -1402394, 0, 0, 0, 383292, 0, 0, 0, 1381752, 0, 0, 0, -691876, 0, 0, 0, -535980, 0, 0, 0, 727056, 0, 0, 0, 2890440, 0, 0, 0, 182880, 0, 0, 0, 708372, 0, 0, 0, -2232580, 0, 0, 0, 38340, 0, 0, 0, -99792, 0, 0, 0, 60192, 0, 0, 0, -891072, 0, 0, 0, 1415232, 0, 0, 0, -2275992, 0, 0, 0, -1319304, 0, 0, 0, -296460, 0, 0, 0, 498528, 0, 0, 0, -53856, 0, 0, 0, -56376, 0, 0, 0, -1207340, 0, 0, 0, -2557644, 0, 0, 0, 1466640, 0, 0, 0, -1962524, 0, 0, 0, -568812, 0, 0, 0, 898128, 0, 0, 0, -337064, 0, 0, 0, 1205844, 0, 0, 0, 16848, 0, 0, 0, -2508382, 0, 0, 0, -2249688, 0, 0, 0, 301104, 0, 0, 0, 2013792, 0, 0, 0, -2081484, 0, 0, 0, -872964, 0, 0, 0, 4408488, 0, 0, 0, 1275264, 0, 0, 0, 592632, 0, 0, 0, 1071740, 0, 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, 4, 2, -1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 2, "minimal_twist": "48.5.g.a", "char_is_minimal": false, "conrey_index": 127, "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], [1, 0], [0, 0], [0, -3], [0, 0], [42, 0], [0, 0], [0, -44], [0, 0], [-27, 0], [0, 0], [0, -12], [0, 0], [182, 0], [0, 0], [0, -126], [0, 0], [-246, 0], [0, 0], [0, -68], [0, 0], [-396, 0], [0, 0], [0, 432], [0, 0], [1139, 0], [0, 0], [0, 81], [0, 0], [-78, 0], [0, 0], [0, -852], [0, 0], [-108, 0], [0, 0], [0, -1848], [0, 0], [-530, 0], [0, 0], [0, -546], [0, 0], [-918, 0], [0, 0], [0, -492], [0, 0], [-1134, 0], [0, 0], [0, -2184], [0, 0], [-3407, 0], [0, 0], [0, 738], [0, 0], [4626, 0], [0, 0], [0, -504], [0, 0], [-612, 0], [0, 0], [0, -132], [0, 0], [-1346, 0], [0, 0], [0, 1188], [0, 0], [7644, 0], [0, 0], [0, 628], [0, 0], [3888, 0], [0, 0], [0, 1056], [0, 0], [-926, 0], [0, 0], [0, -3417], [0, 0], [-1584, 0], [0, 0], [0, 2540], [0, 0], [729, 0], [0, 0], [0, 6924], [0, 0], [-10332, 0], [0, 0], [0, 234], [0, 0], [11586, 0], [0, 0], [0, -8008], [0, 0], [-7668, 0], [0, 0], [0, -2856], [0, 0], [-13118, 0], [0, 0], [0, 324], [0, 0]]}