# Stored data for newform 384.5.b.c, downloaded from the LMFDB on 24 April 2024.
{"label": "384.5.b.c", "space_label": "384.5.b", "level": 384, "weight": 5, "hecke_orbit": 3, "hecke_orbit_code": 9007268058104192, "dim": 8, "is_polredabs": true, "nf_label": "8.0.49787136.1", "trace_hash": 1487095714005409646, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [891136, 0, 2144, 0, 1]]], "qexp_display": "q-\\beta _{2}q^{3}+(\\beta _{1}-\\beta _{3})q^{5}-\\beta _{5}q^{7}+3^{3}q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "b", "char_is_real": true, "Nk2": 9600, "analytic_conductor": 39.69406582419622, "hecke_ring_index": 21743271936, "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": [384, 2, [127, 133, 257], [1, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [319], "field_disc": 49787136, "field_disc_factorization": [[2, 8], [3, 4], [7, 4]], "field_poly": [16, 0, 12, 0, 5, 0, 3, 0, 1], "hecke_ring_index_factorization": [[2, 28], [3, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "7.340", "prec": 17}, {"__RealLiteral__": 0, "data": "0.258", "prec": 17}, {"__RealLiteral__": 0, "data": "569.388", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62681.739", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "4.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 1392, 0, 0, 0, 0, 0, 0, 0, -3576, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, -1008, 0, 0, 0, 0, 0, 0, 0, 10376, 0, 0, 0, 0, 0, 0, 0, -9504, 0, 0, 0, 0, 0, 0, 0, 23808, 0, 0, 0, 0, 0, 0, 0, -10256, 0, 0, 0, 0, 0, 0, 0, 5832, 0, 0, 0, 0, 0, 0, 0, -31632, 0, 0, 0, 0, 0, 0, 0, -45200, 0, 0, 0, 0, 0, 0, 0, 33408, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 64504, 0, 0, 0, 0, 0, 0, 0, -33696, 0, 0, 0, 0, 0, 0, 0, 23568, 0, 0, 0, 0, 0, 0, 0, 69760, 0, 0, 0, 0, 0, 0, 0, 37584, 0, 0, 0, 0, 0, 0, 0, -154368, 0, 0, 0, 0, 0, 0, 0, 81032, 0, 0, 0, 0, 0, 0, 0, -54432, 0, 0, 0, 0, 0, 0, 0, -150528, 0, 0, 0, 0, 0, 0, 0, -298000, 0, 0, 0, 0, 0, 0, 0, 94176, 0, 0, 0, 0, 0, 0, 0, 579456, 0, 0, 0, 0, 0, 0, 0, 30336, 0, 0, 0, 0, 0, 0, 0, -96552, 0, 0, 0, 0, 0, 0, 0, -186000, 0, 0, 0, 0, 0, 0, 0, -70928, 0, 0, 0, 0, 0, 0, 0, 89568, 0, 0, 0, 0, 0, 0, 0, 364560, 0, 0, 0, 0, 0, 0, 0, 199040, 0, 0, 0, 0, 0, 0, 0, -186624, 0, 0, 0, 0, 0, 0, 0, -763536, 0, 0, 0, 0, 0, 0, 0, 90136, 0, 0, 0, 0, 0, 0, 0, -38880, 0, 0, 0, 0, 0, 0, 0, 582144, 0, 0, 0, 0, 0, 0, 0, -307568, 0, 0, 0, 0, 0, 0, 0, -502560, 0, 0, 0, 0, 0, 0, 0, -513792, 0, 0, 0, 0, 0, 0, 0, 48272, 0, 0, 0, 0, 0, 0, 0, 836352, 0, 0, 0, 0, 0, 0, 0, 655632, 0, 0, 0, 0, 0, 0, 0, 923896, 0, 0, 0, 0, 0, 0, 0, -27216, 0, 0, 0, 0, 0, 0, 0, -731904, 0, 0, 0, 0, 0, 0, 0, -1426944, 0, 0, 0, 0, 0, 0, 0, 863712, 0, 0, 0, 0, 0, 0, 0, 583536, 0, 0, 0, 0, 0, 0, 0, 1163024, 0, 0, 0, 0, 0, 0, 0, -842400, 0, 0, 0, 0, 0, 0, 0, -1654416, 0, 0, 0, 0, 0, 0, 0, -1251472, 0, 0, 0, 0, 0, 0, 0, 280152, 0, 0, 0, 0, 0, 0, 0, 1608048, 0, 0, 0, 0, 0, 0, 0, 599312, 0, 0, 0, 0, 0, 0, 0, -872064, 0, 0, 0, 0, 0, 0, 0, -1323648, 0, 0, 0, 0, 0, 0, 0, 161280, 0, 0, 0, 0, 0, 0, 0, 228960, 0, 0, 0, 0, 0, 0, 0, 43776, 0, 0, 0, 0, 0, 0, 0, 2523008, 0, 0, 0, 0, 0, 0, 0, -256608, 0, 0, 0, 0, 0, 0, 0, -26352, 0, 0, 0, 0, 0, 0, 0, -1065208, 0, 0, 0, 0, 0, 0, 0, 1353312, 0, 0, 0, 0, 0, 0, 0, 3588864, 0, 0, 0, 0, 0, 0, 0, -2187648, 0, 0, 0, 0, 0, 0, 0, -1798848, 0, 0, 0, 0, 0, 0, 0, -2500080, 0, 0, 0, 0, 0, 0, 0, -512624, 0, 0, 0, 0, 0, 0, 0, 642816, 0, 0, 0, 0, 0, 0, 0, 2910480, 0, 0, 0, 0, 0, 0, 0, -417040, 0, 0, 0, 0, 0, 0, 0, -892800, 0, 0, 0, 0, 0, 0, 0, -2190480, 0, 0, 0, 0, 0, 0, 0, -1697144, 0, 0, 0, 0, 0, 0, 0, 1583712, 0, 0, 0, 0, 0, 0, 0, 2793072, 0, 0, 0, 0, 0, 0, 0, 362880, 0, 0, 0, 0, 0, 0, 0, -276912, 0, 0, 0, 0, 0, 0, 0, -5082624, 0, 0, 0, 0, 0, 0, 0, 1795952, 0, 0, 0, 0, 0, 0, 0, -458784, 0, 0, 0, 0, 0, 0, 0, -364800, 0, 0, 0, 0, 0, 0, 0, 4469472, 0, 0, 0, 0, 0, 0, 0, -76032, 0, 0, 0, 0, 0, 0, 0, 2347776, 0, 0, 0, 0, 0, 0, 0, 466560, 0, 0, 0, 0, 0, 0, 0, 157464, 0, 0, 0, 0, 0, 0, 0, 1436544, 0, 0, 0, 0, 0, 0, 0, 97408, 0, 0, 0, 0, 0, 0, 0, -334368, 0, 0, 0, 0, 0, 0, 0, -2388720, 0, 0, 0, 0, 0, 0, 0, -3067408, 0, 0, 0, 0, 0, 0, 0, 290304, 0, 0, 0, 0, 0, 0, 0, -2300928, 0, 0, 0, 0, 0, 0, 0, 493056, 0, 0, 0, 0, 0, 0, 0, -854064, 0, 0, 0, 0, 0, 0, 0, -1607664, 0, 0, 0, 0, 0, 0, 0, -3162240, 0, 0, 0, 0, 0, 0, 0, 3740256, 0, 0, 0, 0, 0, 0, 0, -258960, 0, 0, 0, 0, 0, 0, 0, 1530120, 0, 0, 0, 0, 0, 0, 0, 1787616, 0, 0, 0, 0, 0, 0, 0, 2650128, 0, 0, 0, 0, 0, 0, 0, -1826944, 0, 0, 0, 0, 0, 0, 0, -1220400, 0, 0, 0, 0, 0, 0, 0, -1940976, 0, 0, 0, 0, 0, 0, 0, -1216128, 0, 0, 0, 0, 0, 0, 0, -3110400, 0, 0, 0, 0, 0, 0, 0, 6158592, 0, 0, 0, 0, 0, 0, 0, 5424000, 0, 0, 0, 0, 0, 0, 0, 1317600, 0, 0, 0, 0, 0, 0, 0, 3673968, 0, 0, 0, 0, 0, 0, 0, -2815888, 0, 0, 0, 0, 0, 0, 0, 902016, 0, 0, 0, 0, 0, 0, 0, -2181360, 0, 0, 0, 0, 0, 0, 0, 1831304, 0, 0, 0, 0, 0, 0, 0, -6298560, 0, 0, 0, 0, 0, 0, 0, -2502288, 0, 0, 0, 0, 0, 0, 0, 434048, 0, 0, 0, 0, 0, 0, 0, -921888, 0, 0, 0, 0, 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, 8, 2, 1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 4, "minimal_twist": "384.5.b.c", "char_is_minimal": true, "conrey_index": 319, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [27, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 15, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [174, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 45, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 18, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -12, -18, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-447, 0, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -27, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 89, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 36, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-180, 0, 0, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -157, 0, 0, 0, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 20, 0, 21, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, -21, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-126, 0, 0, 0, 0, 0, 0, 9], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 153, 0, 0, 0, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 27, 0, -27, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 96, -54, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1297, 0, 0, 0, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -177, 0, 0, 0, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -25, 0, -5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 36, -160, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1188, 0, 0, 0, 0, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 252, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -88, 0, -249, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -27, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2976, 0, 0, 0, 0, 0, 0, 17], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -432, 0, 0, 0, 12, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -90, 0, 216, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 300, 18, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1282, 0, 0, 0, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 453, 0, 0, 0, 18, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 148, 0, -456, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 108, -243, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [729, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -403, 0, 0, 0, 35, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 238, 0, -1182, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 71, -98, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3954, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 873, 0, 0, 0, 27, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 123, 0, 234, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -12, -576, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5650, 0, 0, 0, 0, 0, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 189, 0, 0, 0, 27, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}