# Stored data for newform 216.3.e.b, downloaded from the LMFDB on 25 April 2024. {"label": "216.3.e.b", "space_label": "216.3.e", "level": 216, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4503874555609304, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 172880863714334058, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [32, 0, 1]]], "qexp_display": "q+\\beta q^{5}+3q^{7}+\\beta q^{11}-17q^{13}+5\\beta q^{17}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 1944, "analytic_conductor": 5.885573710182413, "hecke_ring_index": 4, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [216, 2, [55, 109, 137], [2, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [161], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.899", "prec": 17}, {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "14.944", "prec": 20}, {"__RealLiteral__": 0, "data": "0.475", "prec": 17}, {"__RealLiteral__": 0, "data": "148.009", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 6], "traces": [0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -82, 0, 0, 0, 0, 0, 166, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, -102, 0, 0, 0, 0, 0, 334, 0, 0, 0, 0, 0, -106, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, 178, 0, 0, 0, 0, 0, -220, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 438, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -172, 0, 0, 0, 0, 0, -426, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 0, 94, 0, 0, 0, 0, 0, -202, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, 300, 0, 0, 0, 0, 0, 740, 0, 0, 0, 0, 0, -460, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 318, 0, 0, 0, 0, 0, -374, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, -198, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 118, 0, 0, 0, 0, 0, -460, 0, 0, 0, 0, 0, 340, 0, 0, 0, 0, 0, -1022, 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 372, 0, 0, 0, 0, 0, -786, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 238, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 366, 0, 0, 0, 0, 0, -534, 0, 0, 0, 0, 0, 222, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, 1334, 0, 0, 0, 0, 0, 1246, 0, 0, 0, 0, 0, 742, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, -2240, 0, 0, 0, 0, 0, -620, 0, 0, 0, 0, 0, -1700, 0, 0, 0, 0, 0, -738, 0, 0, 0, 0, 0, 1408, 0, 0, 0, 0, 0, -98, 0, 0, 0, 0, 0, -246, 0, 0, 0, 0, 0, 260, 0, 0, 0, 0, 0, 900, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, -1274, 0, 0, 0, 0, 0, 498, 0, 0, 0, 0, 0, -154, 0, 0, 0, 0, 0, 1122, 0, 0, 0, 0, 0, -1114, 0, 0, 0, 0, 0, 1920, 0, 0, 0, 0, 0, -204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 762, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 326, 0, 0, 0, 0, 0, -2078, 0, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, 702, 0, 0, 0, 0, 0, -1994, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, -340, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 2262, 0, 0, 0, 0, 0, -1874, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 1100, 0, 0, 0, 0, 0, -960, 0, 0, 0, 0, 0, -220, 0, 0, 0, 0, 0, 934, 0, 0, 0, 0, 0, 1486, 0, 0, 0, 0, 0, 278, 0, 0, 0, 0, 0, -1502, 0, 0, 0, 0, 0, -202, 0, 0, 0, 0, 0, 1360, 0, 0, 0, 0, 0, -1740, 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 640, 0, 0, 0, 0, 0, -242, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 1454, 0, 0, 0, 0, 0, 1002, 0, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, -1920, 0, 0, 0, 0, 0, -726, 0, 0, 0, 0, 0, -1922, 0, 0, 0, 0, 0, 1088, 0, 0, 0, 0, 0, -318, 0, 0, 0, 0, 0, -1020, 0, 0, 0, 0, 0, -1580, 0, 0, 0, 0, 0, 820, 0, 0, 0, 0, 0, -1280, 0, 0, 0, 0, 0, 198, 0, 0, 0, 0, 0, 2014, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -962, 0, 0, 0, 0, 0, -700, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 1334, 0, 0, 0, 0, 0, 1394, 0, 0, 0, 0, 0, 4800, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, -1900, 0, 0, 0, 0, 0, 220, 0, 0, 0, 0, 0, 1846, 0, 0, 0, 0, 0, -562, 0, 0, 0, 0, 0, -960, 0, 0, 0, 0, 0, -622, 0, 0, 0, 0, 0, 534, 0, 0, 0, 0, 0, -674, 0, 0, 0, 0, 0, 2598, 0, 0, 0, 0, 0, -1920, 0, 0, 0, 0, 0, -2822, 0, 0, 0, 0, 0, 606, 0, 0, 0, 0, 0, -1226, 0, 0, 0, 0, 0, -660, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 640, 0, 0, 0, 0, 0, -346, 0, 0, 0, 0, 0, 1408, 0, 0, 0, 0, 0, -1660, 0, 0, 0, 0, 0, 462, 0, 0, 0, 0, 0, -880, 0, 0, 0, 0, 0, 1326, 0, 0, 0, 0, 0, -2688, 0, 0, 0, 0, 0, -4318, 0, 0, 0, 0, 0, -960, 0, 0, 0, 0, 0, 3078, 0, 0, 0, 0, 0, -2714, 0, 0, 0, 0, 0, 1314, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 3062, 0, 0, 0, 0, 0, 2420, 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]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "216.3.e.b", "char_is_minimal": true, "conrey_index": 161, "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, 0], [0, 0], [0, 1], [0, 0], [3, 0], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [-17, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [11, 0], [0, 0], [0, 0], [0, 0], [0, 7], [0, 0], [-7, 0], [0, 0], [0, 0], [0, 0], [0, -6], [0, 0], [50, 0], [0, 0], [0, 0], [0, 0], [0, 3], [0, 0], [-33, 0], [0, 0], [0, 0], [0, 0], [0, 6], [0, 0], [10, 0], [0, 0], [0, 0], [0, 0], [0, -15], [0, 0], [-40, 0], [0, 0], [0, 0], [0, 0], [0, -2], [0, 0], [-32, 0], [0, 0], [0, 0], [0, 0], [0, -5], [0, 0], [-41, 0], [0, 0], [0, 0], [0, 0], [0, -17], [0, 0], [83, 0], [0, 0], [0, 0], [0, 0], [0, -4], [0, 0], [127, 0], [0, 0], [0, 0], [0, 0], [0, 3], [0, 0], [19, 0], [0, 0], [0, 0], [0, 0], [0, -22], [0, 0], [-160, 0], [0, 0], [0, 0], [0, 0], [0, -15], [0, 0], [-51, 0], [0, 0], [0, 0], [0, 0], [0, 11], [0, 0], [167, 0], [0, 0], [0, 0], [0, 0]]}