# Stored data for newform 18.3.b.a, downloaded from the LMFDB on 25 April 2024.
{"label": "18.3.b.a", "space_label": "18.3.b", "level": 18, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 68769808402, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 305516784036938827, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta q^{2}-2q^{4}-3\\beta q^{5}-4q^{7}-2\\beta q^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 162, "analytic_conductor": 0.4904644758485344, "hecke_ring_index": 1, "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": [18, 2, [11], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [17], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "1.858", "prec": 17}, {"__RealLiteral__": 0, "data": "0.056", "prec": 17}, {"__RealLiteral__": 0, "data": "14.244", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "137.199", "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, -8], "traces": [0, 2, 0, 0, -4, 0, 0, -8, 0, 0, 12, 0, 0, 16, 0, 0, 8, 0, 0, -32, 0, 0, -48, 0, 0, 14, 0, 0, 16, 0, 0, 88, 0, 0, 36, 0, 0, -68, 0, 0, -24, 0, 0, -80, 0, 0, 48, 0, 0, -66, 0, 0, -32, 0, 0, 144, 0, 0, -12, 0, 0, 100, 0, 0, -16, 0, 0, 16, 0, 0, -48, 0, 0, -32, 0, 0, 64, 0, 0, -152, 0, 0, -132, 0, 0, -108, 0, 0, 96, 0, 0, -64, 0, 0, 240, 0, 0, 352, 0, 0, -28, 0, 0, -56, 0, 0, -108, 0, 0, 112, 0, 0, -32, 0, 0, -144, 0, 0, -96, 0, 0, -334, 0, 0, -176, 0, 0, 184, 0, 0, 96, 0, 0, 128, 0, 0, -72, 0, 0, 304, 0, 0, 144, 0, 0, 36, 0, 0, 136, 0, 0, -296, 0, 0, 192, 0, 0, -164, 0, 0, 48, 0, 0, 112, 0, 0, -336, 0, 0, -210, 0, 0, 160, 0, 0, -56, 0, 0, -36, 0, 0, -464, 0, 0, -96, 0, 0, 432, 0, 0, -192, 0, 0, 412, 0, 0, 132, 0, 0, 40, 0, 0, -84, 0, 0, 396, 0, 0, 64, 0, 0, 592, 0, 0, 0, 0, 0, -352, 0, 0, -288, 0, 0, -872, 0, 0, 444, 0, 0, 16, 0, 0, 24, 0, 0, -720, 0, 0, -144, 0, 0, 64, 0, 0, -200, 0, 0, -256, 0, 0, 384, 0, 0, 576, 0, 0, 32, 0, 0, 272, 0, 0, 480, 0, 0, 324, 0, 0, -32, 0, 0, 760, 0, 0, -444, 0, 0, -656, 0, 0, 96, 0, 0, -416, 0, 0, -384, 0, 0, 254, 0, 0, 64, 0, 0, 288, 0, 0, -780, 0, 0, 320, 0, 0, -128, 0, 0, -1040, 0, 0, 528, 0, 0, -188, 0, 0, 304, 0, 0, -144, 0, 0, -192, 0, 0, 112, 0, 0, 264, 0, 0, 1072, 0, 0, -96, 0, 0, -416, 0, 0, 216, 0, 0, 656, 0, 0, 492, 0, 0, -476, 0, 0, -192, 0, 0, -432, 0, 0, 576, 0, 0, -210, 0, 0, 128, 0, 0, 568, 0, 0, -408, 0, 0, -380, 0, 0, -480, 0, 0, -320, 0, 0, 96, 0, 0, -576, 0, 0, -704, 0, 0, -432, 0, 0, -468, 0, 0, 292, 0, 0, 56, 0, 0, 704, 0, 0, 48, 0, 0, 736, 0, 0, 112, 0, 0, 1008, 0, 0, 768, 0, 0, -80, 0, 0, 216, 0, 0, -400, 0, 0, -480, 0, 0, 1084, 0, 0, -224, 0, 0, -8, 0, 0, 288, 0, 0, 108, 0, 0, 64, 0, 0, -1584, 0, 0, -48, 0, 0, -800, 0, 0, 288, 0, 0, -1208, 0, 0, 36, 0, 0, -64, 0, 0, 192, 0, 0, -224, 0, 0, -384, 0, 0, -544, 0, 0, 668, 0, 0, 1192, 0, 0, -396, 0, 0, 108, 0, 0, 352, 0, 0, 448, 0, 0, -144, 0, 0, 252, 0, 0, -368, 0, 0, 128, 0, 0, 516, 0, 0, 2880, 0, 0, -192, 0, 0, -1472, 0, 0, -1056, 0, 0, 482, 0, 0, -256, 0, 0, 0, 0, 0, 972, 0, 0, -1616, 0, 0, 144, 0, 0, 1072, 0, 0, -336, 0, 0, 608, 0, 0, -608, 0, 0, -640, 0, 0, -804, 0, 0, -1332, 0, 0, -288, 0, 0, 736, 0, 0, 528, 0, 0, -284, 0, 0, -72, 0, 0, -1296, 0, 0, 1236, 0, 0, -1408, 0, 0, -272, 0, 0, 432, 0, 0, 384, 0, 0, 316, 0, 0, 592, 0, 0, 664, 0, 0, 600, 0, 0, 1156, 0, 0, -384, 0, 0, 1792, 0, 0, 1056, 0, 0, -802, 0, 0, 328, 0, 0, 40, 0, 0, -948, 0, 0, -528, 0, 0, -96, 0, 0, 1456, 0, 0, -576, 0, 0, -1152, 0, 0, -224, 0, 0, -1440, 0, 0, -960, 0, 0, 124, 0, 0, 672, 0, 0, 144, 0, 0, 96, 0, 0, -1340, 0, 0, 420, 0, 0, -1408, 0, 0, -2112, 0, 0, 1332, 0, 0, -320, 0, 0, -80, 0, 0, -816, 0, 0, 1188, 0, 0, 112, 0, 0, 1088, 0, 0, 636, 0, 0, 1936, 0, 0, 72, 0, 0, 1152, 0, 0, 1584, 0, 0, 224, 0, 0, 928, 0, 0, -1016, 0, 0, -192, 0, 0, -2288, 0, 0, 192, 0, 0, -608, 0, 0, 432, 0, 0, 2340, 0, 0, -864, 0, 0, 376, 0, 0, -96, 0, 0, -2480, 0, 0, 384, 0, 0, -448, 0, 0, 768, 0, 0, -1820, 0, 0, -824, 0, 0, 616, 0, 0, 1140, 0, 0, 1728, 0, 0, -264, 0, 0, -2720, 0, 0, -912, 0, 0, 800, 0, 0, -80, 0, 0, -2160, 0, 0, -924, 0, 0, 576, 0, 0, 168, 0, 0, -320, 0, 0, 1632, 0, 0, 1280, 0, 0, -792, 0, 0, 664, 0, 0, 384, 0, 0, 1264, 0, 0, -128, 0, 0, 288, 0, 0, -1104, 0, 0, 1646, 0, 0, -1184, 0, 0, 1336, 0, 0, 252, 0, 0, 892, 0, 0, 0, 0, 0, 1456, 0, 0, 432, 0, 0, -1476, 0, 0, 704, 0, 0, 128, 0, 0, -768, 0, 0, -1820, 0, 0, 576, 0, 0, 2128, 0, 0, -912, 0, 0, -736, 0, 0, 1744, 0, 0, -1728, 0, 0, -612, 0, 0, 972, 0, 0, -888, 0, 0, -3536, 0, 0, -384, 0, 0, -4032, 0, 0, -32, 0, 0, 760, 0, 0, 852, 0, 0, -476, 0, 0, -48, 0, 0, 1056, 0, 0, -1008, 0, 0, -356, 0, 0, 1440, 0, 0, 1584, 0, 0, 1920, 0, 0, -256, 0, 0, 288, 0, 0, -288, 0, 0, -1488, 0, 0, 1950, 0, 0, -128, 0, 0, 3400, 0, 0, 2112, 0, 0, -1216, 0, 0, 400, 0, 0, -432, 0, 0, 768, 0, 0, 1404, 0, 0, 512, 0, 0, -1544, 0, 0, -576, 0, 0, 388, 0, 0, -768], "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": 2, "prim_orbit_index": 2, "minimal_twist": "18.3.b.a", "char_is_minimal": true, "conrey_index": 17, "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, 1], [0, 0], [-2, 0], [0, -3], [0, 0], [-4, 0], [0, -2], [0, 0], [6, 0], [0, 12], [0, 0], [8, 0], [0, -4], [0, 0], [4, 0], [0, -9], [0, 0], [-16, 0], [0, 6], [0, 0], [-24, 0], [0, -12], [0, 0], [7, 0], [0, 8], [0, 0], [8, 0], [0, 3], [0, 0], [44, 0], [0, 4], [0, 0], [18, 0], [0, 12], [0, 0], [-34, 0], [0, -16], [0, 0], [-12, 0], [0, 33], [0, 0], [-40, 0], [0, -24], [0, 0], [24, 0], [0, -60], [0, 0], [-33, 0], [0, 7], [0, 0], [-16, 0], [0, 27], [0, 0], [72, 0], [0, 8], [0, 0], [-6, 0], [0, 24], [0, 0], [50, 0], [0, 44], [0, 0], [-8, 0], [0, -24], [0, 0], [8, 0], [0, 18], [0, 0], [-24, 0], [0, -36], [0, 0], [-16, 0], [0, -34], [0, 0], [32, 0], [0, -48], [0, 0], [-76, 0], [0, -12], [0, 0], [-66, 0], [0, 84], [0, 0], [-54, 0], [0, -40], [0, 0], [48, 0], [0, 9], [0, 0], [-32, 0], [0, 24], [0, 0], [120, 0], [0, 48], [0, 0], [176, 0], [0, -33], [0, 0], [-14, 0]]}