# Stored data for newform 845.2.t.b, downloaded from the LMFDB on 10 October 2024.
{"Nk2": 3380, "analytic_conductor": 6.747358970798192, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 65, "char_degree": 4, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 20, "char_orbit_label": "t", "char_order": 12, "char_parity": 1, "char_values": [845, 12, [677, 171], [9, 5]], "cm_discs": [], "conrey_index": 188, "dim": 4, "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 12, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, 0, -1, 0, 1]], [3, [4, 4, 2, 2, 1]], [7, [4, 2, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504905330983757, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 3, 1, 3, 0], [1, 1, 65, 6, 1, 4, 0], [1, 1, 65, 20, 1, 12, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "845.2.t.b", "level": 845, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 13], "level_radical": 65, "minimal_twist": "65.2.f.a", "nf_label": "4.0.144.1", "prim_orbit_index": 20, "qexp_display": "q+(\\zeta_{12}-\\zeta_{12}^{3})q^{2}+(\\zeta_{12}-\\zeta_{12}^{2}-\\zeta_{12}^{3})q^{3}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c12", "self_twist_discs": [], "self_twist_type": 0, "space_label": "845.2.t", "trace_display": [0, -2, 8, -4], "trace_hash": 1410756562721235647, "trace_moments": [{"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "3.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.370", "prec": 17}, {"__RealLiteral__": 0, "data": "62.301", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1551.077", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.252", "prec": 17}, "traces": [0, 4, 0, -2, -2, 8, 2, -4, 0, 0, -2, -2, 4, 0, 0, -6, 2, 2, 4, 10, -4, 8, 2, 6, 6, 12, 0, 16, -4, 0, 2, -20, 0, 0, 4, -8, 0, 0, 20, 0, 12, -14, 4, -2, 4, 2, 6, -24, 2, 6, -8, 0, 0, 20, -8, -6, 0, 0, 0, 14, 12, 28, 10, 0, -28, 0, -8, 0, 2, 12, 8, 2, -6, 0, 0, -14, 10, 8, 0, 0, 4, -10, -14, -24, -4, 6, 4, 0, 6, -10, 8, 0, -12, 20, 0, 30, -20, 0, 0, 4, -6, 0, -4, -28, 0, 24, 10, -14, -8, 36, 2, 0, -8, -10, -20, 6, 0, 0, -28, 4, 6, 0, 0, -28, 10, 8, -4, 18, 0, 8, 0, -80, 0, 20, -8, 16, -6, -32, 0, 0, -8, 12, -4, 0, 0, 0, 20, 6, 0, 6, -2, -28, -30, 2, 4, -20, 0, 52, 4, 0, -10, -24, 0, 0, 28, -4, 0, -36, -24, 0, 4, 10, -2, -22, 0, -12, 2, -56, -10, -40, 2, 0, 0, -56, 18, 0, 0, 0, 12, -16, 20, -16, 14, 0, -8, 0, -12, 0, -2, -16, 48, -8, 24, 0, 0, -14, 14, 12, 0, 0, 4, -8, -10, -8, -14, -2, 48, 20, 18, 20, 12, 0, 0, 4, 0, 8, -20, 0, 0, -12, 18, 0, 0, -4, 0, -48, 14, 4, -4, 12, 6, 34, 36, 14, 28, 12, 0, 0, -60, 12, -22, 0, 0, 12, -18, -8, 34, -22, 0, 0, 0, 0, 0, -2, 12, 60, -20, -20, 0, 0, -24, -18, 4, 0, 0, -14, 12, -30, -56, -10, -12, -4, -12, -18, 2, -40, 0, 56, -10, 0, 0, -8, 0, 0, 12, 14, 0, -16, 12, 0, 28, -4, -14, 24, 20, 56, 2, -72, -4, 28, 30, 0, 0, 36, -26, 4, 0, 0, 20, 0, -56, -28, 12, 0, 20, 0, 16, 0, -42, 24, -16, -6, 12, 0, 0, 8, 4, -52, 0, 0, 6, 20, 10, -80, -6, 24, 44, -6, 0, -18, 32, 0, -20, -24, 0, 2, 20, 0, 0, 4, -12, 0, -16, 36, 0, 40, -28, 2, -6, -28, 0, -20, -40, 30, -4, -26, 0, 0, 32, 2, 30, 0, 0, -60, 6, 24, -36, 2, 0, 72, 0, 24, 0, 40, 12, 8, -2, 32, 0, 0, 6, -22, 16, 0, 0, -20, 0, 0, 24, 14, -42, 64, 14, 28, 6, -48, 0, -56, -20, 0, -12, 44, 0, 0, -60, 14, 0, 56, 28, 0, 12, 26, 8, 34, -40, 0, -18, 120, 20, 0, 6, 0, 0, 100, 0, -10, 0, 0, 28, 6, 12, -28, -10, 0, 48, 0, 120, 0, 6, 16, -12, 34, 8, 0, 0, 40, 2, -36, 0, 0, 12, -52, 42, 8, 4, 70, -8, -10, 6, 14, -20, 0, 68, 24, 0, -4, 28, 0, 0, 16, 6, 0, -28, 0, 0, 4, -10, 4, -12, 12, -4, -36, -8, 6, -12, -24, 0, 0, -36, -26, -8, 0, 0, 80, 22, -28, -4, 12, 0, 88, 0, -40, 0, -18, 40, 56, 2, -20, 0, 0, 10, -14, -40, 0, 0, -14, -24, -40, 48, 6, -8, -36, 18, -16, -10, 108, 0, -36, -32, 0, -2, 0, 0, 0, -60, 0, 0, 48, -20, 0, -16, -4, -2, 30, -24, -30, -18, 40, 6, 12, -40, 0, 0, 32, -28, -6, 0, 0, -30, -36, 0, 24, 4, 0, -120, 0, -24, 0, 6, -100, -84, 12, 0, 0, 0, 12, 6, 32, 0, 0, -6, 76, -4, -16, 14, 18, -48, 26, -50, 0, -56, 0, -4, -40, 0, -56, -24, 0, 0, 100, 10, 0, 12, 40, 0, -28, 18, -20, -26, 0, -8, 22, -24, -8, -28, 54, 0, 0, 0, -2, -6, 0, 0, -68, 12, 16, 20, 2, 0, -56, 0, -80, 0, -26, 36, -160, 14, -20, 0, 0, -4, 34, 12, 0, 0, 60, 0, 0, 72, 4, -16, -56, 20, -30, -26, -16, 0, -92, 20, 0, -6, 48, 0, 0, -20, -64, 0, 12, -4, 0, -24, -6, -22, -4, 12, -28, 0, -56, -18, 4, -12, 0, 0, 0, 14, 36, 0, 0, 28, -58, -12, -4, -30, 0, 16, 0, 80, 0, -2, -16, 4, 28, 62, 0, 0, 0, -18, 140, 0, 0, 40, 4, 28, 16, 2, 18, -60, -8, -14, 6, 0, 0, -40, 68, 0, 18, 60, 0, 0, 56, -18, 0, -12, -8, 0, -84, -16, 70, -2, -24, -30, -14, 72, -36, -16, 2, 0, 0, -68, 30, 4, 0, 0, -64, -2, 20, 12, 0, 0, -280, 0, -8, 0, 0, -6, 52, -40, -44, 0, 0, 8, -20, 12, 0, 0, -20, -16, 34, 80, -12, -40, -20, 22, 20, -8, -24, 0, 48, 72, 0, -10, 108, 0, 0, 0, 8, 0, 20, 28, 0, 28, 18, 32, -18, -84, -16, 28, 184, -6, 68, 12, 0, 0, 12, 28, -72, 0, 0, 76, 70, -24, -58, -22, 0, 16, 0, -24, 0, 10, -36, -4, 0, 4, 0, 0, 10, -42, 12, 0, 0, -2, -56, 26, 120, -40, -22, -68, -30, 20, 4, 0, 0, -108, -4, 0, -8, -40, 0, 0, -24, 6, 0, 6, -156, 0, -112, 50, 2, 0, -72, -30, -10, -8, -60, -12, -80, 0, 0, -12, 0, 8, 0, 0, -8, 30, -32, -28, -78, 0, 48, 0, 96, 0, 12, 4, -168, 6, 80, 0, 0, 54, 36, -68, 0, 0, 0, 48, -14, 0, 38, 20, 60, 2, 12, -18, -8, 0, -28, -16, 0, 24, -84, 0, 0, 28, -16, 0, 36, -8, 0, -20, -28, -12, 26, 20, -32, -6, 0, 14, -64, 42, 0, 0, -28, 34, 36, 0, 0, -54, 20, -16, 120, 14, 0, -64, 0, 56, 0, -8, -20, -24, -18, -44, 0, 0, -12, 0, -48, 0, 0, -6, 0, 50, 24, 4, -32, -24, -18, 6, 0, 132], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, -1], [0, 1, -1, -1], [-1, 0, 1, 0], [2, 0, 0, -1], [1, -1, -1, 0], [-2, 0, 2, 0], [0, 0, 0, 3], [0, 1, 0, 0], [0, 2, -1, -2], [0, 1, -1, -1], [1, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 2], [0, 1, -3, -1], [0, 0, 1, 0], [1, 1, -1, 0], [1, 0, 0, 0], [5, 5, -5, 0], [-2, 1, 2, 0], [2, 0, 0, 2], [1, -1, -1, 0], [0, 3, 3, -3], [0, 3, 3, -3], [3, 0, 0, -4], [0, 0, 0, 0], [4, 0, 0, -4], [0, 0, -2, 0], [0, 0, 0, 0], [1, -3, -1, 0], [-5, 0, 0, 5], [0, -5, 0, 0], [0, -2, 0, 0], [1, 0, 0, -1], [-4, 2, 4, 0], [0, -1, 0, 1], [0, 0, 0, 0], [5, 0, 0, -5], [0, 0, 0, 0], [3, 0, 0, 6], [0, -7, -7, 7], [0, 2, 2, -2], [-1, 1, 1, 0], [1, 0, 0, 1], [1, 2, -1, 0], [3, 3, -3, 0], [-6, 0, 0, 0], [1, 1, -1, 0], [0, 0, 3, 0], [0, 3, -4, -3], [0, 0, 0, -2], [0, 0, 0, 0], [5, 0, 0, 5], [0, 4, -4, -4], [0, 1, -3, -1], [0, -6, 0, 0], [0, 0, 0, -10], [0, 0, 0, 0], [7, -7, -7, 0], [3, 0, 0, 1], [14, 0, -14, 0], [0, -5, 5, 5], [0, -2, 0, 2], [-7, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, -4, 0, 4], [0, -1, 1, 1], [6, 0, -6, 0], [2, 0, 0, 4], [1, -1, -1, 0], [-3, 0, 3, 0], [0, 0, 0, 10], [0, 0, 0, 0], [0, -1, -7, 1], [0, -5, 5, 5], [2, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 2], [0, 1, 2, -1], [0, 0, -5, 0], [-7, -7, 7, 0], [-6, 0, 0, 0], [-2, -2, 2, 0], [3, 1, -3, 0], [1, 0, 0, 1], [0, 0, 0, 0], [0, 3, 3, -3], [0, -5, -5, 5], [2, 0, 0, -1], [0, 0, 0, 0], [-3, 0, 0, 3], [0, 0, 10, 0], [0, -6, 0, 6], [15, 5, -15, 0], [-5, 0, 0, 5], [0, -2, 0, 0], [0, 3, 0, 0], [1, 0, 0, -1], [-3, 4, 3, 0]]}