# Stored data for newform 1386.2.bk.d, downloaded from the LMFDB on 18 April 2024.
{"label": "1386.2.bk.d", "space_label": "1386.2.bk", "level": 1386, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13513272816829802, "dim": 32, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [256, 0, -5264, 0, 104833, 0, -69149, 0, 35812, 0, -5519, 0, 628, 0, -29, 0, 1]], [13, [4096, 0, -4496, 0, 948, 0, -56, 0, 1]]], "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 77, "char_orbit_label": "bk", "char_is_real": false, "Nk2": 5544, "analytic_conductor": 11.06726572014946, "level_radical": 462, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [1386, 6, [155, 199, 1135], [6, 1, 3]], "inner_twist_count": 8, "level_primes": [2, 3, 7, 11], "conrey_indexes": [703, 901], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [32, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 20, 0, 0, 36, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 48, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 10, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 18, 0, 0, 12, 0, 0, 0, 0, 0, -80, 0, 0, 36, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 94, 0, 0, -36, 0, 0, 0, 0, 0, -40, 0, 0, -36, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 16, 0, 0, 0, 0, 0, -52, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 64, 0, 0, -16, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 232, 0, 0, -28, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 78, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, -10, 0, 0, -408, 0, 0, 0, 0, 0, -196, 0, 0, 24, 0, 0, 468, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 126, 0, 0, -120, 0, 0, 0, 0, 0, -52, 0, 0, -84, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 168, 0, 0, 0, 0, 0, -120, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, -512, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 36, 0, 0, 108, 0, 0, 0, 0, 0, 348, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 320, 0, 0, 196, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 48, 0, 0, 416, 0, 0, 0, 0, 0, 0, 0, 0, -116, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 588, 0, 0, 0, 0, 0, -10, 0, 0, 48, 0, 0, 0, 0, 0, -20, 0, 0, 152, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 62, 0, 0, -360, 0, 0, 0, 0, 0, -320, 0, 0, -36, 0, 0, 248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -102, 0, 0, -80, 0, 0, 0, 0, 0, -252, 0, 0, -444, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, 112, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -268, 0, 0, 0, 0, 0, 56, 0, 0, 248, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -116, 0, 0, 0, 0, 0, 0, 0, 0, -124, 0, 0, 0, 0, 0, 616, 0, 0, 8, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 116, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -116, 0, 0, -444, 0, 0, 0, 0, 0, -368, 0, 0, 156, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 196, 0, 0, -684, 0, 0, 0, 0, 0, -20, 0, 0, 336, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -54, 0, 0, -112, 0, 0, 0, 0, 0, -524, 0, 0, 156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -438, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 104, 0, 0, 288, 0, 0, 0, 0, 0, 936, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 0, 0, 0, 0, 0, 324, 0, 0, 0, 0, 0, -64, 0, 0, 164, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, 32, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 212, 0, 0, 132, 0, 0, 0, 0, 0, -200, 0, 0, 280, 0, 0, 276, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 310, 0, 0, -348, 0, 0, 0, 0, 0, 116, 0, 0, -768, 0, 0, -504, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, -272, 0, 0, 0, 0, 0, -36, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, -168, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -236, 0, 0, 116, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -236, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, -224, 0, 0, 56, 0, 0, -828, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 0, 168, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 188, 0, 0, -228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, -78, 0, 0, -840, 0, 0, 0, 0, 0, -552, 0, 0, 172, 0, 0, 408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 516, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 348, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, -40, 0, 0, 0, 0, 0, -788, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -810, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, -96, 0, 0, -296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, -20, 0, 0, 472, 0, 0, 0, 0, 0, 552, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 196, 0, 0, 0, 0, 0, -216, 0, 0, 228, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 468, 0, 0, 0, 0, 0, 108, 0, 0, 672, 0, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, 648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 444, 0, 0, 636, 0, 0, 0, 0, 0, -112, 0, 0, -384, 0, 0, 552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 126, 0, 0, -132, 0, 0, 0, 0, 0, -212, 0, 0, -120, 0, 0, 272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 156, 0, 0, -104, 0, 0, 0, 0, 0, -336, 0, 0, -396, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 192, 0, 0, -392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, -344, 0, 0, 196, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, -420, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 0, 0, -240, 0, 0, 84, 0, 0, -588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -504, 0, 0, 0, 0, 0, 598, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 540, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -324, 0, 0, 0, 0, 0, -118, 0, 0, -444, 0, 0, 0, 0, 0, -576, 0, 0, 984, 0, 0, 468, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 220, 0, 0, -984, 0, 0, 0, 0, 0, 72, 0, 0, 648, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 160, 0, 0, 0, 0, 0, -724, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -564, 0, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 72, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -88, 0, 0, 412, 0, 0, 0, 0, 0, 804, 0, 0, 0, 0, 0, 408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 176, 0, 0, 176, 0, 0, -216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 444, 0, 0, 0, 0, 0, 18, 0, 0, 992, 0, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 8, 0, 0, 348, 0, 0, 0, 0, 0, -44, 0, 0, -96, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 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, 3, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 11, 2, -1, 2, 0], [1, 1, 21, 7, 1, 6, 0], [1, 1, 33, 4, 1, 2, 0], [1, 1, 77, 9, 1, 6, 0], [1, 1, 231, 11, -1, 6, 0]], "char_orbit_index": 37, "prim_orbit_index": 9, "minimal_twist": "1386.2.bk.d", "char_is_minimal": true, "conrey_index": 703, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}