# Stored data for newform 96.3.e.a, downloaded from the LMFDB on 23 April 2024.
{"label": "96.3.e.a", "space_label": "96.3.e", "level": 96, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 274928238688, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2304.1", "trace_hash": 1925896500023726821, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [8, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+\\beta _{2}q^{5}+(2\\beta _{1}-\\beta _{3})q^{7}+(-3+\\cdots)q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 864, "analytic_conductor": 2.61581053785885, "hecke_ring_index": 24, "level_radical": 6, "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": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [96, 2, [31, 37, 65], [2, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [65], "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [1, 0, 4, 0, 1], "hecke_ring_index_factorization": [[2, 3], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "3.606", "prec": 17}, {"__RealLiteral__": 0, "data": "0.951", "prec": 17}, {"__RealLiteral__": 0, "data": "106.631", "prec": 24}, {"__RealLiteral__": 0, "data": "63.603", "prec": 20}, {"__RealLiteral__": 0, "data": "3948.777", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, -152, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 236, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, -252, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 360, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 552, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, -380, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, -352, 0, 0, 0, 0, 0, 0, 0, 768, 0, 0, 0, 616, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, -532, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 936, 0, 0, 0, 0, 0, 0, 0, -1080, 0, 0, 0, 328, 0, 0, 0, 0, 0, 0, 0, 792, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, 0, -204, 0, 0, 0, -984, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 840, 0, 0, 0, 0, 0, 0, 0, 720, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 1056, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, -792, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, -892, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, -504, 0, 0, 0, 1064, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, -408, 0, 0, 0, 0, 0, 0, 0, 456, 0, 0, 0, 2088, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, -664, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, -1012, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, -472, 0, 0, 0, 0, 0, 0, 0, 360, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, -856, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 456, 0, 0, 0, 0, 0, 0, 0, -936, 0, 0, 0, -2136, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, -2456, 0, 0, 0, 0, 0, 0, 0, -708, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 1224, 0, 0, 0, 3144, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, 4752, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 912, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, 0, -2816, 0, 0, 0, 0, 0, 0, 0, -2592, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 1080, 0, 0, 0, -3456, 0, 0, 0, 0, 0, 0, 0, 1224, 0, 0, 0, -1340, 0, 0, 0, 0, 0, 0, 0, -1008, 0, 0, 0, 1320, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 2176, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 0, -2008, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, -2232, 0, 0, 0, 520, 0, 0, 0, 0, 0, 0, 0, 3168, 0, 0, 0, 3176, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 356, 0, 0, 0, 0, 0, 0, 0, -936, 0, 0, 0, -1416, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, 360, 0, 0, 0, 1768, 0, 0, 0, 0, 0, 0, 0, -2520, 0, 0, 0, -2968, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, -448, 0, 0, 0, 0, 0, 0, 0, -5184, 0, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, -408, 0, 0, 0, 0, 0, 0, 0, 4032, 0, 0, 0, -3024, 0, 0, 0, 0, 0, 0, 0, 2484, 0, 0, 0, 1512, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 2144, 0, 0, 0, 0, 0, 0, 0, 3888, 0, 0, 0, 4392, 0, 0, 0, 0, 0, 0, 0, 768, 0, 0, 0, -1336, 0, 0, 0, 0, 0, 0, 0, -2736, 0, 0, 0, -1728, 0, 0, 0, 0, 0, 0, 0, -4896, 0, 0, 0, 528, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, -3456, 0, 0, 0, 0, 0, 0, 0, 936, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, -2448, 0, 0, 0, -1944, 0, 0, 0, 0, 0, 0, 0, 3240, 0, 0, 0, -508, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, 0, 6568, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, -2528, 0, 0, 0, 0, 0, 0, 0, -1080, 0, 0, 0, -2200, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, -1728, 0, 0, 0, -1280, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 4320, 0, 0, 0, 0, 0, 0, 0, 1368, 0, 0, 0, -2584, 0, 0, 0, 0, 0, 0, 0, 2592, 0, 0, 0, 5608, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, 3168, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, -2304, 0, 0, 0, -5616, 0, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, -2336, 0, 0, 0, 0, 0, 0, 0, 1368, 0, 0, 0, -6424, 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, 3, 2, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0], [1, 1, 12, 2, 1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "96.3.e.a", "char_is_minimal": true, "conrey_index": 65, "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, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 2, 0, -1], [0, 0, 0, 0], [-3, 0, -3, 0], [0, 0, 0, 0], [0, 4, 0, 1], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, 8, 0], [0, 0, 0, 0], [0, -2, 0, 1], [0, 0, 0, 0], [18, 0, -9, 0], [0, 0, 0, 0], [0, -8, 0, -2], [0, 0, 0, 0], [17, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, 3], [0, 0, 0, 0], [0, 0, 11, 0], [0, 0, 0, 0], [0, -6, 0, 3], [0, 0, 0, 0], [-36, 0, -9, 0], [0, 0, 0, 0], [0, -8, 0, -2], [0, 0, 0, 0], [-38, 0, 0, 0], [0, 0, 0, 0], [0, -6, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [0, -2, 0, 1], [0, 0, 0, 0], [24, 0, -3, 0], [0, 0, 0, 0], [0, 16, 0, 4], [0, 0, 0, 0], [59, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -8], [0, 0, 0, 0], [0, 0, 5, 0], [0, 0, 0, 0], [0, 8, 0, -4], [0, 0, 0, 0], [-18, 0, 9, 0], [0, 0, 0, 0], [0, 4, 0, 1], [0, 0, 0, 0], [-22, 0, 0, 0], [0, 0, 0, 0], [0, 18, 0, 9], [0, 0, 0, 0], [0, 0, -6, 0], [0, 0, 0, 0], [0, 22, 0, -11], [0, 0, 0, 0], [72, 0, 18, 0], [0, 0, 0, 0], [0, 8, 0, 2], [0, 0, 0, 0], [-30, 0, 0, 0], [0, 0, 0, 0], [0, 17, 0, 0], [0, 0, 0, 0], [0, 0, -54, 0], [0, 0, 0, 0], [0, -6, 0, 3], [0, 0, 0, 0], [-63, 0, 18, 0], [0, 0, 0, 0], [0, -20, 0, -5], [0, 0, 0, 0], [-64, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -11], [0, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [0, -12, 0, 6], [0, 0, 0, 0], [-54, 0, 27, 0], [0, 0, 0, 0], [0, 8, 0, 2], [0, 0, 0, 0], [90, 0, 0, 0], [0, 0, 0, 0], [0, -36, 0, 9], [0, 0, 0, 0]]}