# Stored data for newform 546.2.bk.b, downloaded from the LMFDB on 20 April 2024. {"label": "546.2.bk.b", "space_label": "546.2.bk", "level": 546, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4506073562087970, "dim": 12, "is_polredabs": true, "trace_hash": 857810869794966073, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [16, 0, -144, 0, 1248, 0, -424, 0, 108, 0, -12, 0, 1]]], "qexp_display": "q-\\beta _{6}q^{2}-\\beta _{2}q^{3}+\\beta _{2}q^{4}+\\beta _{8}q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 91, "char_orbit_label": "bk", "char_is_real": false, "Nk2": 2184, "analytic_conductor": 4.359831950361909, "hecke_ring_index": 4, "level_radical": 546, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [546, 6, [365, 157, 379], [6, 4, 3]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3, 7, 13], "conrey_indexes": [25, 415], "field_disc": 752609431977984, "field_disc_factorization": [[2, 16], [3, 14], [7, 4]], "field_poly": [49, 0, 21, 0, 270, 0, -247, 0, 90, 0, -15, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.733", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "757.412", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "117269.597", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c6", "trace_display": [0, -6, 0, 0], "traces": [0, 12, 0, -6, 6, 0, 0, 0, 0, -6, 0, 0, 6, 12, -18, 0, -6, 18, 0, 0, 0, 0, 12, 0, 0, -6, 0, 12, 0, 12, 0, 0, 0, 0, 0, 24, -12, 0, -6, -6, 0, 0, 6, 24, 0, 0, 0, 0, 12, -18, 0, 18, 6, -18, 0, 48, -6, 0, 0, 0, 0, 6, -48, 0, -12, -12, -6, 0, -18, 0, 0, 0, 0, 0, 0, -6, 0, -24, 0, 24, 0, -6, -12, 0, 0, 0, 0, -6, 6, 0, 0, -24, 0, 0, 6, 24, 0, 0, 0, 0, 6, -36, 0, -48, 0, -36, 0, -12, 6, 0, 0, 0, 0, -12, -6, 0, 6, -6, -12, 0, 0, -36, 0, 0, 0, 0, 12, -48, 0, -12, 24, 48, 0, 42, 12, 0, 0, 0, 0, 24, 36, 0, 18, 12, -6, 0, -48, 6, 0, 0, 0, 0, 6, -36, 0, 0, 6, -42, 0, -18, 0, 0, 0, 0, 0, -24, 36, 0, -12, -36, -12, 0, 12, -42, 0, 0, 0, 0, -48, 48, 0, -132, 6, -12, 0, 12, 24, 0, 0, 0, 0, 24, 6, 0, 48, 24, -6, 0, -6, 72, 0, 0, 0, 0, 36, 60, 0, 0, -6, 36, 0, 120, 18, 0, 0, 0, 0, 48, -96, 0, 24, 30, 0, 0, 12, 12, 0, 0, 0, 0, 0, -6, 0, 90, 0, -72, 0, -48, -42, 0, 0, 0, 0, -6, 12, 0, 24, -96, -24, 0, -12, 72, 0, 0, 0, 0, -6, -60, 0, 12, -24, -6, 0, 48, 6, 0, 0, 0, 0, 18, 0, 0, -36, 36, 120, 0, 0, -66, 0, 0, 0, 0, 6, -60, 0, 24, 60, -60, 0, 0, 60, 0, 0, 0, 0, -168, 0, 0, 0, 0, -12, 0, 84, -36, 0, 0, 0, 0, 6, 96, 0, 12, 0, 108, 0, 12, 48, 0, 0, 0, 0, 24, 84, 0, 6, 6, -54, 0, -24, -90, 0, 0, 0, 0, -6, 144, 0, -36, -24, 6, 0, -24, 12, 0, 0, 0, 0, -144, 6, 0, 66, 12, -6, 0, 6, 12, 0, 0, 0, 0, 0, 84, 0, 72, -36, -192, 0, 12, 0, 0, 0, 0, 0, -18, 30, 0, -6, 132, -18, 0, -24, 24, 0, 0, 0, 0, 72, -12, 0, 18, 24, 168, 0, -96, -60, 0, 0, 0, 0, 42, 12, 0, -6, 0, 36, 0, 42, 24, 0, 0, 0, 0, -96, 96, 0, 60, 0, -12, 0, -192, -12, 0, 0, 0, 0, 54, -36, 0, -24, 12, -24, 0, -6, -12, 0, 0, 0, 0, 24, -24, 0, 12, -96, -48, 0, 12, -102, 0, 0, 0, 0, -48, -6, 0, -96, -36, -12, 0, 48, 18, 0, 0, 0, 0, -6, 0, 0, 24, -12, -132, 0, -42, -6, 0, 0, 0, 0, 36, 6, 0, 0, -48, -48, 0, -72, -48, 0, 0, 0, 0, -132, -48, 0, 6, 18, -24, 0, -42, -72, 0, 0, 0, 0, 96, 18, 0, 0, 18, -24, 0, 24, 12, 0, 0, 0, 0, 12, -132, 0, 84, -24, 60, 0, 60, 96, 0, 0, 0, 0, -30, 0, 0, -42, 144, -48, 0, 6, 48, 0, 0, 0, 0, -66, 66, 0, -144, -30, 72, 0, 6, 6, 0, 0, 0, 0, 12, 12, 0, 24, -24, 12, 0, 96, 0, 0, 0, 0, 0, 36, 90, 0, 12, -12, -48, 0, -168, 6, 0, 0, 0, 0, 72, -96, 0, -24, -12, 108, 0, -12, 48, 0, 0, 0, 0, 12, 84, 0, 72, 84, -36, 0, 108, -60, 0, 0, 0, 0, -60, 12, 0, -120, -48, -18, 0, -42, -120, 0, 0, 0, 0, 0, 0, 0, 156, 12, 66, 0, -18, 42, 0, 0, 0, 0, -60, 60, 0, -36, -78, 132, 0, 0, -144, 0, 0, 0, 0, -78, -180, 0, -90, 72, -72, 0, -36, 48, 0, 0, 0, 0, -216, 24, 0, 24, 30, 72, 0, 0, -84, 0, 0, 0, 0, -18, 120, 0, -6, -18, -18, 0, 204, -24, 0, 0, 0, 0, -72, 78, 0, -12, -18, 0, 0, -84, 30, 0, 0, 0, 0, -36, -180, 0, 24, 0, 96, 0, -72, -72, 0, 0, 0, 0, 24, 48, 0, 0, 120, -48, 0, 0, 84, 0, 0, 0, 0, -66, 66, 0, -96, 30, 12, 0, -60, -6, 0, 0, 0, 0, 78, -12, 0, -12, 192, 18, 0, -24, 48, 0, 0, 0, 0, 24, 156, 0, -36, 12, 240, 0, 84, 48, 0, 0, 0, 0, 48, 48, 0, -24, 0, -6, 0, -36, 120, 0, 0, 0, 0, 96, 24, 0, 156, 12, -30, 0, 12, 12, 0, 0, 0, 0, 48, -144, 0, -12, -54, 60, 0, -72, 216, 0, 0, 0, 0, 36, -120, 0, 0, -48, 18, 0, 114, 0, 0, 0, 0, 0, 60, 18, 0, -72, -12, 120, 0, -60, 156, 0, 0, 0, 0, 0, 54, 0, -66, -12, -126, 0, 132, 18, 0, 0, 0, 0, 48, 24, 0, 60, 48, -12, 0, 36, -60, 0, 0, 0, 0, -24, -48, 0, 30, -30, -108, 0, -36, -144, 0, 0, 0, 0, 0, 72, 0, 60, -48, -48, 0, 336, -156, 0, 0, 0, 0, -24, -264, 0, -240, -30, 84, 0, -12, 0, 0, 0, 0, 0, 90, 0, 0, 18, 0, -84, 0, 6, 54, 0, 0, 0, 0, -42, 24, 0, 72, 48, -168, 0, -96, -24, 0, 0, 0, 0, -156, 0, 0, -24, -72, -30, 0, 144, -48, 0, 0, 0, 0, 180, 12, 0, 48, 0, 420, 0, -216, 72, 0, 0, 0, 0, 24, -24, 0, -24, -132, 66, 0, 0, 372, 0, 0, 0, 0, -12, -60, 0, -90, 12, -12, 0, -240, 0, 0, 0, 0, 0, 120, -12, 0, 276, 6, 6, 0, -54, -72, 0, 0, 0, 0, 12, -72, 0, 198, -192, -168, 0, -120, 24, 0, 0, 0, 0, 186, -72, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0], [1, 1, 13, 2, 1, 2, 0], [1, 1, 91, 18, 1, 6, 0]], "char_orbit_index": 37, "prim_orbit_index": 18, "minimal_twist": "546.2.bk.b", "char_is_minimal": true, "conrey_index": 25, "id": null, "nf_label": 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, 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, -1, 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, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0], [0, 1, 0, 0, 0, 1, -2, 0, 1, 0, 2, 1], [1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, -2, 1, -1, 0, 0, -1, 0], [-2, 0, -1, 1, 1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 1, -1, 0, 0, 0, 1, 1], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0], [0, -4, 0, 0, 0, -2, 1, 0, 0, 0, -2, 0], [0, -1, 0, 0, 0, -1, 1, 0, 0, 0, -1, -1], [0, -1, 0, 0, 0, 0, -1, 0, -1, 0, -1, -1], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [2, 0, 2, -2, -4, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0], [1, 0, 0, -2, -1, 0, 0, -1, 0, -1, 0, 0], [-1, 0, -1, 1, 2, 0, -1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1], [1, 0, 0, -1, 1, 0, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, -2, 1, 0, 0, 0, -4, 0], [3, 0, -3, 0, 1, 0, 0, 2, 0, 2, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0], [-2, 0, -3, 4, 2, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 0, 1, -1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 3, 0, 0, 0, 4, -3, 0, 0, 0, 1, 2], [0, 0, 2, 0, -1, 0, 0, 1, 0, 0, 0, 0], [2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0], [0, -1, 0, 0, 0, -1, 1, 0, -1, 0, -1, -1], [0, -3, 0, 0, 0, 1, -1, 0, -1, 0, -1, -1], [0, -4, 0, 0, 0, -2, -1, 0, -4, 0, -2, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -2, 1, 0, 0, -1, 0, -3, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -1], [4, 0, -2, -1, -2, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, -1, 1, -1, 0, -1, 0, 0], [0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [4, 0, 0, -1, 1, 0, 0, -2, 0, 0, 0, 0], [0, 0, -2, 0, 1, 0, 0, -1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 4, -2, 0, 0, 0, 1, 0], [0, 2, 0, 0, 0, 1, -1, 0, 3, 0, 1, 0], [0, -5, 0, 0, 0, -3, 4, 0, -4, 0, -5, -4], [0, 1, 0, 0, 0, 1, -1, 0, 1, 0, 1, 1], [0, 0, -2, 1, 2, 0, 0, 0, 0, -2, 0, 0], [-4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 3, -1, -2, 1, -4, 0, 2, 1, 1, 0], [0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0], [0, 6, 0, 0, 0, 2, -3, 0, 4, 0, 5, 4], [-4, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 2, 0, 0, -1, 0, 0, 0, 0], [0, 3, 0, 0, 0, 2, -5, 0, 0, 0, 5, 2], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -5, 9, 0, -3, 0, -7, -3], [-1, 0, -1, 2, 1, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0], [0, -2, 0, 0, 0, -4, 2, 0, 0, 0, -1, 0], [-2, 0, -3, 2, 1, 0, 0, 3, 0, 1, 0, 0], [0, 1, 0, 1, -1, 1, -1, 0, 0, 0, 2, 1], [6, 0, -2, -2, -4, 0, 0, 0, 0, -4, 0, 0], [0, -1, 0, 0, 0, -1, 1, 0, -1, 0, -1, -1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 3, -1, -2, 0, 0, 0, 0, 2, 0, 0], [0, 4, 0, 0, 0, 7, -4, 0, 0, 0, 10, 1], [0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0], [0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -3, -2], [0, 4, 0, 0, 0, 2, -2, 0, 0, 0, 2, 0], [-1, 0, -2, 2, 1, 0, 0, 3, 0, 3, 0, 0], [0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0], [0, -2, 0, 0, 0, -1, 8, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-2, 0, 4, -4, 0, -1, 1, 0, -2, 1, 2, 1], [0, 0, 0, 2, -2, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0], [-2, 0, -1, 4, 2, 0, 0, 4, 0, 4, 0, 0], [2, 0, 6, -4, -2, 0, 0, 3, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 7, -3], [0, 0, 0, 0, 0, -1, 4, 0, -2, 0, -1, -3], [0, -1, 0, 0, 0, -1, 1, 0, 0, 0, -2, -1], [2, 0, 0, -1, -2, 0, 0, 0, 0, -1, 0, 0]]}