# Stored data for newform 819.2.bm.b, downloaded from the LMFDB on 25 April 2024.
{"label": "819.2.bm.b", "space_label": "819.2.bm", "level": 819, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4506211001041715, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 328377217164295218, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [3, 0, 1]], [5, [12, -6, 1]]], "qexp_display": "q+(1-2\\zeta_{6})q^{2}-q^{4}+(4-2\\zeta_{6})q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 91, "char_orbit_label": "bm", "char_is_real": false, "Nk2": 3276, "analytic_conductor": 6.539747925542864, "hecke_ring_index": 1, "level_radical": 273, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.186", "prec": 17}, "analytic_rank_proved": true, "char_values": [819, 6, [92, 703, 379], [6, 2, 5]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 7, 13], "conrey_indexes": [478, 550], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "1.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.035", "prec": 17}, {"__RealLiteral__": 0, "data": "11.198", "prec": 20}, {"__RealLiteral__": 0, "data": "0.079", "prec": 17}, {"__RealLiteral__": 0, "data": "87.529", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 6, 5], "traces": [0, 2, 0, 0, -2, 6, 0, 5, 0, 0, -6, -6, 0, -5, 3, 0, -10, 12, 0, 3, -6, 0, 6, -12, 0, 7, -9, 0, -5, 6, 0, 18, 0, 0, 0, 18, 0, 0, 3, 0, -6, -6, 0, 1, 6, 0, 0, -18, 0, 11, -21, 0, 5, -6, 0, -12, 3, 0, -18, 0, 0, -1, 18, 0, -2, -24, 0, 6, -12, 0, -6, -6, 0, -21, -6, 0, -3, -18, 0, 8, -30, 0, -6, 0, 0, 36, 3, 0, 6, 0, 0, -8, 12, 0, 18, 12, 0, -21, 15, 0, -7, 12, 0, -11, -9, 0, 18, 12, 0, 21, 36, 0, -25, 12, 0, -36, -6, 0, -12, 30, 0, 1, 3, 0, -18, 0, 0, 11, 0, 0, -12, 0, 0, 6, -6, 0, 0, 0, 0, 4, -18, 0, 6, 24, 0, 0, -21, 0, 0, 18, 0, -6, 3, 0, 6, 72, 0, 13, 24, 0, 18, -30, 0, -9, 6, 0, 36, -36, 0, -1, -36, 0, -1, -12, 0, 28, 30, 0, -36, 24, 0, 10, -30, 0, 0, -6, 0, -36, 18, 0, 0, -6, 0, 21, 21, 0, -11, 6, 0, -22, -21, 0, 36, 24, 0, -24, -33, 0, 25, -12, 0, 5, 6, 0, 0, 6, 0, 36, 21, 0, 12, -30, 0, 30, -9, 0, 36, 0, 0, 9, 36, 0, -18, -12, 0, -36, 0, 0, 18, 0, 0, 0, -3, 0, 1, 48, 0, -3, 18, 0, -24, 6, 0, 36, -33, 0, 38, 0, 0, 3, 24, 0, 0, 0, 0, 0, 12, 0, -6, 0, 0, 0, -60, 0, 0, 0, 0, -38, 12, 0, -6, 0, 0, 23, 6, 0, 12, -12, 0, 38, -72, 0, 21, 30, 0, -12, -6, 0, 18, 30, 0, 1, -6, 0, -15, 0, 0, 0, 18, 0, 0, -18, 0, -1, -39, 0, -8, 42, 0, 0, -6, 0, -18, 18, 0, -49, -9, 0, -6, -54, 0, 9, 0, 0, -36, 12, 0, -58, 45, 0, -36, -72, 0, 20, 3, 0, 36, 36, 0, -57, -42, 0, -18, -24, 0, -12, 0, 0, 72, 18, 0, -16, 0, 0, 8, -84, 0, 19, 60, 0, -18, -24, 0, -22, 36, 0, 18, -42, 0, -18, -12, 0, 18, -24, 0, -48, -21, 0, 21, 6, 0, -72, 15, 0, 6, 48, 0, 3, 0, 0, -35, 0, 0, -18, -12, 0, -36, 6, 0, 0, 0, 0, 11, 6, 0, 36, 27, 0, 0, 24, 0, 0, -15, 0, 18, 42, 0, -4, -12, 0, 6, -30, 0, -34, 72, 0, -21, -18, 0, 34, 36, 0, -54, -24, 0, -36, 30, 0, -5, 18, 0, 24, -12, 0, 24, -54, 0, 0, -9, 0, 36, 6, 0, 0, -30, 0, -36, -12, 0, 18, 108, 0, -12, -6, 0, 21, -30, 0, -72, -42, 0, -9, -24, 0, -1, -42, 0, 0, 3, 0, 12, -12, 0, 36, -21, 0, -90, -18, 0, 39, 0, 0, 18, 0, 0, 72, -36, 0, -11, 0, 0, -42, 0, 0, 0, -66, 0, 36, -15, 0, -12, -30, 0, -26, 0, 0, 0, 108, 0, 26, 72, 0, -6, 6, 0, 36, -6, 0, 0, -48, 0, -33, -42, 0, 0, 84, 0, -50, 0, 0, 84, 18, 0, 8, 0, 0, -4, 42, 0, 2, -90, 0, 72, 48, 0, 72, 69, 0, 6, -60, 0, 5, -24, 0, -24, -42, 0, -45, 0, 0, 0, -18, 0, 0, -21, 0, -30, -54, 0, 18, -36, 0, 0, 12, 0, 108, -18, 0, 54, -18, 0, -13, 9, 0, 6, 0, 0, 37, -9, 0, 12, 72, 0, 45, 60, 0, 6, 48, 0, -3, -72, 0, 54, 18, 0, 11, -3, 0, -13, 0, 0, -39, 24, 0, -42, 0, 0, -5, 72, 0, 42, 60, 0, 63, 30, 0, 18, -36, 0, 12, 21, 0, 9, -72, 0, 0, 30, 0, 18, -18, 0, 0, 9, 0, 36, 30, 0, -36, 36, 0, -36, 0, 0, -47, 0, 0, 1, 24, 0, -63, -36, 0, 0, 0, 0, 0, 54, 0, -5, 42, 0, 0, 12, 0, 0, 24, 0, -36, -57, 0, -28, 72, 0, 3, 6, 0, 24, 12, 0, -51, 36, 0, -36, -108, 0, 84, -24, 0, -18, -30, 0, -11, -48, 0, -10, -42, 0, -16, -30, 0, 0, 6, 0, 0, 57, 0, 0, -12, 0, -57, 6, 0, 36, -66, 0, 72, 66, 0, 36, 30, 0, 34, 90, 0, 18, -24, 0, 38, -18, 0, 0, -66, 0, 42, 6, 0, -24, -18, 0, -57, 72, 0, -21, 0, 0, 126, 21, 0, -18, -6, 0, 12, 0, 0, -55, 0, 0, 0, -6, 0, 48, 12, 0, 7, 3, 0, 22, -18, 0, -108, 63, 0, -96, 84, 0, -108, -126, 0, 36, -6, 0, 0, -24, 0, 18, -36, 0, 0, 114, 0, 24, 0, 0, 64, -33, 0, -30, 0, 0, 29, 108, 0, 5, 66, 0, -144, 12, 0, -72, -42, 0, -7, -24, 0, -5, 42, 0, 4, 30, 0, -126, 0, 0, 0, 6, 0, 0, -12, 0, -19, -6, 0, 30, 60, 0, 0, -102, 0, -36, -48, 0, -24, 21, 0, -18, 12, 0, 24, 0, 0, 60, -12, 0, -82, 30, 0, -72, 84, 0, 44, -108, 0, -30, -36, 0, 144, -21, 0, -18, 108, 0, -36, 0, 0, 36, 30, 0, -13, 0, 0, -66, 72, 0, -36, -24, 0, -9, 0, 0, -1, 36, 0, -6, 24, 0, -21, -18, 0, 54, -18, 0, 9, 12, 0, -36, -72, 0, -70, -6, 0, 36, -54, 0, 36, 0, 0, -6, 0, 0, 21, -21, 0, 18, 42, 0, 0, 0, 0, 42, 0, 0, 77, 15, 0, 0, 42, 0, 0, -3, 0, 126, -12, 0, 4, -102, 0, 5, 18, 0, 36, -48, 0, 36, -90, 0, 24, -108, 0, 3, -6, 0, 7, -54, 0, 6, -66, 0, -74, -39, 0, -24], "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, 91, 11, 1, 6, 0]], "char_orbit_index": 39, "prim_orbit_index": 11, "minimal_twist": "273.2.t.a", "char_is_minimal": true, "conrey_index": 478, "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], [1, -2], [0, 0], [-1, 0], [4, -2], [0, 0], [2, 1], [1, -2], [0, 0], [0, -6], [-4, 2], [0, 0], [-1, -3], [4, -5], [0, 0], [-5, 0], [6, 0], [0, 0], [1, 1], [-4, 2], [0, 0], [0, 6], [-6, 0], [0, 0], [7, -7], [-7, 5], [0, 0], [-2, -1], [6, -6], [0, 0], [6, 6], [-3, 6], [0, 0], [6, -12], [10, -2], [0, 0], [1, -2], [3, -3], [0, 0], [0, -6], [-2, -2], [0, 0], [0, 1], [4, -2], [0, 0], [-6, 12], [-12, 6], [0, 0], [3, 5], [-7, -7], [0, 0], [1, 3], [-6, 6], [0, 0], [-12, 12], [4, -5], [0, 0], [-6, -6], [2, -4], [0, 0], [-1, 1], [18, -18], [0, 0], [-1, 0], [-10, -4], [0, 0], [4, -2], [-6, 0], [0, 0], [6, -18], [-4, 2], [0, 0], [-7, -7], [-3, 0], [0, 0], [-1, -1], [-10, 2], [0, 0], [0, 8], [-20, 10], [0, 0], [-6, 6], [-6, 12], [0, 0], [24, -12], [2, -1], [0, 0], [0, 6], [6, -12], [0, 0], [1, -10], [6, 0], [0, 0], [0, 18], [6, 0], [0, 0], [-14, 7], [13, -11], [0, 0], [-7, 7]]}