# Stored data for newform 363.3.b.e, downloaded from the LMFDB on 19 April 2024.
{"label": "363.3.b.e", "space_label": "363.3.b", "level": 363, "weight": 3, "hecke_orbit": 5, "hecke_orbit_code": 18014467279290731, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 1451445878731192800, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]], [5, [0, 1]], [7, [-75, 0, 1]]], "qexp_display": "q+3q^{3}+4q^{4}-5\\beta q^{7}+9q^{9}+12q^{12}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 3267, "analytic_conductor": 9.891033596278778, "hecke_ring_index": 1, "level_radical": 33, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, "analytic_rank_proved": true, "char_values": [363, 2, [122, 244], [1, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [3, 11], "conrey_indexes": [122], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.918", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.610", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "296.589", "prec": 24}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 6, 0, 0], "traces": [0, 2, 0, 6, 8, 0, 0, 0, 0, 18, 0, 0, 24, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 54, 0, 0, 0, -118, 0, 0, 0, 0, 72, -94, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 150, 0, 0, 0, 0, 0, 162, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, -354, 0, 0, 0, -338, 0, 0, 200, 0, 0, -314, 0, 0, 0, 0, 216, 0, 0, -282, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -472, 0, 0, 0, 0, 0, 0, 0, 0, -630, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 156, -376, 0, 0, 0, 0, 0, 0, 0, 0, 386, 0, 0, 0, 0, 0, -74, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384, 0, 0, 0, 208, 0, 0, 554, 0, 78, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 166, 0, 450, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 486, 0, 0, 0, 1008, 0, 0, 0, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, -1062, 0, 0, 0, 0, 0, 0, 0, 0, 0, 578, 0, -1014, 0, 0, 0, 0, 0, 0, 0, 0, 600, 1440, 0, 0, 0, 0, 0, 0, 0, -942, 0, 0, 0, 284, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 648, 0, 0, 0, 0, 0, 0, 598, 0, -846, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1924, 0, 0, -960, 0, 0, -1436, 0, 0, 0, 0, -1416, 0, 0, 0, 0, 0, 0, -1388, 0, 0, 0, 0, 0, 0, 0, 0, -1352, 0, 0, 0, 0, 0, 0, 0, 0, 862, 0, -1890, 800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1256, 0, 0, 0, 0, 0, 0, 0, 0, 716, 0, 0, 0, 0, 0, 270, 0, 0, 0, 0, 864, 1006, 0, 0, 0, 0, 0, 0, 0, 468, 0, 0, -1128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1052, 0, 0, 0, 0, 0, 0, 0, 1158, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1924, 0, -222, 0, 0, 0, 0, 0, 0, -1888, 0, 0, 1754, 0, 0, 0, 0, 0, 0, 0, 138, 0, 0, 0, -510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1058, 0, 0, -2520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2730, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1152, 2066, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, -1504, 0, 0, 0, 0, 1662, 0, 0, 0, 0, 0, 234, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -428, 0, 0, 0, 0, 0, 1250, 0, 0, 1544, 0, 0, -1348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1846, 0, 0, 0, 0, 0, 0, 0, 0, -296, 0, 0, 0, 0, 0, 0, 0, 0, 2402, 0, 0, 0, 0, 0, 0, 0, 498, 0, 0, 0, 0, 0, 1350, 184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, 2038, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1868, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -964, 0, 1458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2762, 0, 0, 0, 0, 0, -3022, 0, 0, 0, 0, 0, -2850, 0, 0, 0, 0, 1536, 0, 0, 0, 0, 0, 0, -2950, 0, 0, 0, 0, 0, 0, 0, 0, 832, 0, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 2216, 0, 0, 0, 0, 0, 0, 0, 312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6048, 0, -2160, 0, 0, 0, -3242, 0, 0, 0, 0, 0, -3218, 0, 0, 0, 0, 0, 0, 0, -3186, 0, 0, 0, 1682, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3098, 0, 0, 0, 0, 0, 0, 0, 1734, 0, 0, 0, 0, 0, -3042, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2518, 0, 0, 0, 0, 0, -390, 0, 0, 664, 0, 0, 0, 0, 0, 0, 0, 1800, 0, 0, 4320, 0, 0, 0, -2906, 0, 0, 0, 0, 0, 0, 0, 0, -208, 0, 0, 0, 0, 0, 0, 0, 0, -2350, 0, -2826, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 852, 0, 0, 0, 0, 0, 0, 0, 0, 0, 816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1944, -4800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4032, 0, 0, 92, 0, 1794, 0, 0, 0, 0, 0, -2538, 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, -3], [1, 1, 11, 2, -1, 2, 0], [1, 1, 33, 4, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "363.3.b.e", "char_is_minimal": true, "conrey_index": 122, "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], [3, 0], [4, 0], [0, 0], [0, 0], [0, -5], [0, 0], [9, 0], [0, 0], [0, 0], [12, 0], [0, 8], [0, 0], [0, 0], [16, 0], [0, 0], [0, 0], [0, 21], [0, 0], [0, -15], [0, 0], [0, 0], [0, 0], [25, 0], [0, 0], [27, 0], [0, -20], [0, 0], [0, 0], [-59, 0], [0, 0], [0, 0], [0, 0], [0, 0], [36, 0], [-47, 0], [0, 0], [0, 24], [0, 0], [0, 0], [0, 0], [0, -48], [0, 0], [0, 0], [0, 0], [0, 0], [48, 0], [26, 0], [0, 0], [0, 0], [0, 32], [0, 0], [0, 0], [0, 0], [0, 0], [0, 63], [0, 0], [0, 0], [0, 0], [0, -9], [0, 0], [0, -45], [64, 0], [0, 0], [0, 0], [13, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 17], [0, 0], [75, 0], [0, 84], [0, 0], [0, 0], [0, -91], [0, 0], [81, 0], [0, 0], [0, 0], [0, -60], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-120, 0], [0, 0], [-177, 0], [0, 0], [0, 0], [0, 0], [-169, 0], [0, 0], [0, 0], [100, 0]]}