# Stored data for newform 966.2.i.l, downloaded from the LMFDB on 25 April 2024. {"label": "966.2.i.l", "space_label": "966.2.i", "level": 966, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49540145690444742, "dim": 8, "is_polredabs": true, "nf_label": "8.0.1768034304.4", "trace_hash": 1499329877594542120, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [49, 14, 11, -2, 1]], [11, [35344, 29328, 20764, 5220, 1485, 198, 55, 6, 1]]], "qexp_display": "q+(-1-\\beta _{2})q^{2}+\\beta _{2}q^{3}+\\beta _{2}q^{4}+(\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 3864, "analytic_conductor": 7.713548835255685, "hecke_ring_index": 4, "level_radical": 966, "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": "0.010", "prec": 17}, "analytic_rank_proved": true, "char_values": [966, 3, [323, 829, 925], [3, 2, 3]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 7, 23], "conrey_indexes": [277, 415], "field_disc": 1768034304, "field_disc_factorization": [[2, 12], [3, 4], [73, 2]], "field_poly": [49, -14, -31, 18, 14, -6, -1, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.077", "prec": 17}, {"__RealLiteral__": 0, "data": "7.745", "prec": 17}, {"__RealLiteral__": 0, "data": "4.256", "prec": 17}, {"__RealLiteral__": 0, "data": "245.558", "prec": 24}, {"__RealLiteral__": 0, "data": "169.287", "prec": 24}, {"__RealLiteral__": 0, "data": "13887.457", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [-4, -4, 4, 0], "traces": [0, 8, -4, -4, -4, 4, 8, 0, 8, -4, 4, -6, -4, 12, -6, -8, -4, 10, -4, 4, -8, 6, 12, -4, -4, -16, -6, 8, 6, 12, 4, -2, -4, -6, -20, -10, 8, 0, 4, -6, 4, 8, 0, 40, -6, 4, -4, -10, 8, 0, 32, 10, -6, 0, -4, 20, 0, -8, -6, -6, 4, 0, 4, -6, 8, 14, -6, -18, 10, 8, 2, 84, -4, -6, 0, -16, -8, -2, 12, 6, 4, -4, -4, -20, -6, 68, -20, -6, -6, 0, -8, 10, 8, -2, -10, 20, -4, -20, -18, 12, -16, -12, 10, 6, 12, 8, 0, 6, -4, -28, -10, 0, -6, 52, 4, 4, -6, -6, 12, -36, -8, -30, 0, -4, -2, -120, 6, 76, -4, -20, 14, -16, 12, -24, 36, 4, 10, -6, -4, -16, 8, 20, -42, -20, -4, -2, 12, 18, 0, 2, -16, -2, 4, -20, -38, 60, -6, 0, 6, 0, -8, -6, 8, 16, -4, -10, 10, -20, 6, -28, -34, 4, -20, -20, 12, 8, 12, -6, 0, 30, 4, -24, 10, 0, -4, -8, -2, -12, 20, 0, -40, 40, -4, -48, 10, -28, 18, 48, -6, -4, -16, -18, 24, -10, -20, -20, 6, -4, -6, -120, -10, -32, 0, -42, 6, -12, 8, 50, 56, -6, -10, -6, 0, -84, 6, 32, -26, 22, 4, 28, -8, 40, 12, 4, -6, 10, -6, -12, 18, 80, 4, -34, -30, -4, 0, 66, 8, -12, -2, 10, 60, 4, 0, 12, -38, -34, -4, 36, 40, 68, -28, -6, -16, -4, -6, -32, -24, 0, -18, 10, 4, 2, -20, -20, 12, 8, -4, -26, 8, 4, -10, 108, -10, -30, -42, 20, 40, -48, 8, -2, -2, 10, -6, -184, 0, -124, 0, -6, 2, -6, 32, 92, 4, -12, 4, 32, 10, 112, 40, -12, -30, -30, -6, 22, 0, 2, -12, 18, 0, 2, 4, -12, 6, 8, -4, -40, 16, -28, 8, -102, 20, -12, 10, 0, 10, -132, 0, -4, 14, -26, -34, -46, -8, 36, 40, 4, -20, -14, -6, 68, -16, 12, -6, -20, -6, 34, 0, 18, -60, -16, 4, 0, 12, 60, -20, 52, 0, 4, -4, -4, 16, 50, 4, -52, -12, 60, -10, -40, -6, -4, 20, -38, 40, 8, 8, 110, 96, -20, 10, -20, 14, -20, 0, 32, -24, 2, -6, -18, 8, 48, 32, 18, -18, 44, -12, -8, -28, 152, 10, 24, -20, -6, -12, 22, 8, -90, -6, 8, 60, -56, 2, 24, 16, -10, 0, 88, 84, 76, -12, -20, -12, -8, -4, 32, -58, 4, -28, 4, -6, 26, 20, -18, 12, -24, 0, -56, 42, -4, 0, 32, -16, -60, -26, -2, -44, -106, -8, 34, 28, 10, 4, -112, -2, 120, -6, -30, 4, 20, 12, 108, -20, 0, -6, 68, 6, 64, 18, 0, -40, 44, 4, -40, 68, 0, 60, 46, -4, 2, 0, -32, -114, -40, -4, 36, -12, -10, 4, -10, -20, 52, 60, 10, -2, -72, -6, 8, -6, 14, -38, 74, 68, 56, 8, 4, 36, 42, -20, -144, -40, 40, 14, -22, -6, 26, 32, 8, 8, 20, -6, -4, 16, 12, 48, -24, 0, -70, -18, 30, -20, -48, -8, 34, 2, 12, 10, -312, 10, -232, -6, 0, 8, 24, 8, 28, 52, -8, 8, 46, -2, -16, 2, 24, -54, 54, -10, 34, 60, 6, 84, 82, 20, 30, -20, -80, 24, 32, -4, -42, -2, -48, 4, -22, -20, 38, -6, 14, 92, 40, -18, -184, 62, -24, 0, 68, 12, 70, -4, -4, -6, -46, -16, 108, -160, 36, -2, 126, -12, -2, -8, 38, -64, 54, 10, 44, -56, 40, -2, -52, 6, -22, -30, -4, 60, -100, 12, -12, 22, 60, 0, 96, 8, -72, 6, 16, 18, 86, 0, 42, -4, -42, 4, -10, 6, 32, 0, 24, -4, -52, -4, 34, 80, 8, -32, 10, -28, 24, -4, 12, 84, -112, -10, -60, -12, -6, -20, -128, 0, -6, 10, 42, 66, 88, -6, -12, 2, -16, 14, -20, 52, -26, 68, 22, -46, -4, 4, 20, -36, -56, -20, 50, 4, -36, 40, -38, 28, 120, -6, 4, -34, -8, 8, 16, -6, 36, -6, 10, 40, 16, 12, -24, 34, 6, 0, 4, -36, -184, 30, -40, -16, -18, -8, 30, 0, -34, 12, -8, -30, 12, 10, 8, -26, 56, 0, -24, -8, 48, 8, 0, -4, 60, -8, 24, -28, -32, -2, -50, -52, 10, 24, -164, -120, 42, -10, -2, 20, 60, 6, 176, 2, -6, 20, 44, 76, -68, -80, -34, 8, 4, -4, -44, -232, -72, -48, -78, -20, 56, -20, -28, 40, 76, 14, -52, 10, 12, -18, -16, -16, -6, -24, -4, -4, -74, 12, -116, -18, 16, -4, -8, -24, -188, -16, 0, 18, -52, 36, 2, -88, 10, -12, -40, 4, 32, 38, -4, -76, 72, 10, -40, -48, 10, 40, 46, -6, -36, 6, -16, -26, -60, -4, -18, -90, -26, 12, -78, -16, 198, 60, -2, 28, 64, 8, -156, -12, -54, 16, -14, 20, 30, 0, -30, 88, 0, -42, 224, -116, -40, 6, 4, -20, -76, 24, 24, 16, -30, -4, 164, -16, 4, 8, 4, -2, 54, -28, 10, -8, 8, 12, -70, 26, 92, -10, 28, 18, 48, -6, 62, -24, -64, 0, -54, 112, -6, 42, -8, 2, 60, -6, 12, -16, -50, -16, 66, 120, 68, 52, 68, -2, 58, 22, 24, -4, -24, 4, -82, 34, 32, -56, 82, -20, 78, 4, -56, 56, 68, -38, -32, -60, 6, -6, 112, 60, -108, -8, -30, 20, 100, -6, -108, -102, -44, 10, -18, 0, -4, 12, -10, -136, 46, 6, 38, -32, -36, -36, -48, 0, -32, -40, 2, -88, 28, -8, -14, -40, 6, -34, -160, -6, 52, -30, -4, 46, -94, 8, -32, -4, -40, 0, -46, 16, -88, 48, 56, 20, 52, -4, -56, -72, 18, 24, -20, -10, 18, -2, 24, -82, -200, 10, -8, 52, 0, -120], "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]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "966.2.i.l", "char_is_minimal": true, "conrey_index": 277, "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], [-1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, -1, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, -1, -1, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 0, 0], [1, 1, -1, 1, 1, 0, 2, 0], [0, 0, 2, -1, 0, 1, 2, 2], [-1, 0, -1, 0, 0, 0, 0, 0], [1, 1, -1, 0, -1, 0, 0, 0], [-1, 0, 0, 0, 0, 1, 0, 0], [-1, -1, 0, 0, -1, 0, -1, 0], [-1, 0, -1, 0, 0, 0, 0, 0], [1, 0, -2, 0, 1, 0, 2, 0], [0, 0, 1, 0, 0, 0, 0, 0], [1, -1, 1, 0, 0, 2, 1, 1], [-1, -1, 0, 0, -1, 0, -1, 0], [2, 0, 1, 1, 1, -1, 0, -1], [1, -1, -1, 0, -1, 1, -1, -1], [-1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [-2, -2, 4, -2, -2, 0, -4, 0], [-1, 0, -1, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 1, 1, -1, 0, -1], [2, -1, 1, 0, 1, 0, 0, 0], [0, 0, 1, -1, 0, 0, -1, 0], [0, 2, 0, 1, 0, 1, 2, 2], [0, 0, 1, 0, 0, 0, 0, 0], [-1, 1, -1, 1, 1, -2, -1, -1], [-3, 0, -1, 0, -2, 0, -1, 0], [0, 1, 2, 1, 3, -1, 2, 2], [1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 2, 2, -2, -1, -1], [0, -1, -1, 0, 0, -1, -2, -2], [0, -1, 2, -1, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, -1, 0], [1, -2, 0, 0, 0, 1, -1, -1], [-1, 0, -1, -1, -1, 0, 0, 1], [6, 0, 2, 0, 0, -2, 0, 2], [-1, 1, -1, 1, 1, -2, -1, -1], [1, 1, -1, 1, 1, 0, 2, 0], [0, 0, 1, 0, 0, 0, 0, 0], [-4, -1, -4, -3, -3, 2, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -4, 2, -1, 1, 1, 1], [4, 2, 0, 0, 2, 0, 2, 0], [2, 0, 3, 0, 1, 0, -1, 0], [0, -1, 2, -1, 0, 0, 0, 0], [-1, 1, -1, 1, -1, 0, -2, 0], [-1, 0, -1, 0, 0, 0, 0, 0], [5, -1, 5, 0, 3, -3, 1, 3], [-1, 0, -1, -1, -1, 0, 0, 1], [-1, 2, 0, 0, 0, -1, 1, 1], [-2, 0, -2, -1, -1, 0, 0, 0], [-2, -1, 1, -1, -2, 0, -4, 0], [1, 1, -1, 1, 1, 0, 2, 0], [2, 0, 2, 4, 4, 0, 0, 0], [1, -3, 1, 0, 1, 1, -1, -1], [-1, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -2, 3, -4, -1, 4, -1, 2], [0, 0, 2, -1, 0, 1, 2, 2], [-3, 1, 3, 0, -3, 1, -4, 2], [2, 0, 3, 0, 1, 0, -1, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -3, 1, -3, -2, 3, 1, 1], [11, -1, 1, 0, 1, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 0, 0], [0, 2, 1, 1, 0, 1, 2, 2], [0, -1, 1, -2, 0, 1, 2, 2], [-2, 0, -4, 2, 0, 0, 2, 0], [-1, 2, 0, 0, 0, -1, 1, 1], [0, -2, -6, 3, 1, 0, 2, -2], [1, 1, -1, 0, -1, 0, 0, 0], [2, 0, 2, 1, 1, 0, 0, 0], [1, 1, -1, 1, 1, 0, 2, 0], [0, 0, 1, 0, 0, 0, 0, 0], [-1, 1, -1, 0, 0, -2, -1, -1], [-3, -3, -1, 0, -3, 1, -3, -1], [-1, 0, 0, 0, 0, 1, 0, 0], [9, 5, 1, 0, 3, -2, 4, 2], [-8, -2, -6, -4, -2, 4, 0, 2], [0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 2, -1, 0, 1, 2, 2], [-3, -1, -1, -4, -2, 2, -1, 1], [-1, -1, 0, 0, -1, 0, -1, 0], [1, -2, 3, -2, -3, 1, -2, 3], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, -1, -1, -2, -1, -1], [0, 2, 1, 3, 0, -1, -2, -2], [0, -3, -3, -4, 0, 1, 2, 2], [-1, 0, -1, 0, 0, 0, 0, 0], [-2, 1, 1, 0, 3, 0, 2, 0], [-2, -3, 3, -1, 1, 0, -3, -1], [1, -1, -1, 0, -1, 1, -1, -1], [-2, 0, -4, 2, 0, 0, 2, 0]]}