# Stored data for newform 966.2.i.i, downloaded from the LMFDB on 24 April 2024. {"label": "966.2.i.i", "space_label": "966.2.i", "level": 966, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029346808333254, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2601.1", "trace_hash": 852126990271302812, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [16, 4, 5, -1, 1]], [11, [9, 3, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+(-1+\\beta _{2})q^{3}+(-1+\\beta _{2}+\\cdots)q^{4}+\\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": 1, "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": "0.013", "prec": 17}, "analytic_rank_proved": true, "char_values": [966, 3, [323, 829, 925], [3, 2, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7, 23], "conrey_indexes": [277, 415], "field_disc": 2601, "field_disc_factorization": [[3, 2], [17, 2]], "field_poly": [16, 4, 5, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.038", "prec": 17}, {"__RealLiteral__": 0, "data": "3.844", "prec": 17}, {"__RealLiteral__": 0, "data": "1.450", "prec": 17}, {"__RealLiteral__": 0, "data": "55.148", "prec": 20}, {"__RealLiteral__": 0, "data": "49.802", "prec": 20}, {"__RealLiteral__": 0, "data": "1442.537", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [2, -2, 1, 2], "traces": [0, 4, 2, -2, -2, 1, -4, 2, -4, -2, -1, -6, -2, 4, -8, -2, -2, -3, 2, -2, -2, -10, -12, 2, 2, 1, 2, 4, -10, -16, -1, -9, 2, -6, -6, -4, 4, -10, 2, -2, -1, -12, -2, 16, -6, 1, -2, 5, 4, -26, 2, -3, -2, -3, 2, -6, -2, 4, -8, -7, 1, 4, -18, 8, 4, -16, 6, 4, -3, -4, -5, 10, 2, -5, 10, 1, 4, -30, -4, 0, 1, -2, -6, -18, 8, 48, 8, 8, 6, 0, 2, 2, -4, -9, -5, -16, 2, 22, -22, 12, 1, -19, 3, 21, -4, -1, -6, -1, -2, 29, -3, 20, 8, -12, 2, -1, 8, -2, -14, -15, 2, 4, -4, 6, -9, -6, 10, 30, 2, -8, 16, 33, 12, 8, 8, 1, 3, -3, -2, 50, -1, -10, 5, -6, -2, 13, -10, 4, 20, 10, -1, 13, 2, 6, -6, 42, -2, -13, 0, -3, 2, -8, -4, 9, 6, 3, -9, -36, 10, 20, 24, -2, -8, 21, 16, 5, 12, -7, 0, 22, 1, 34, -8, -8, -2, -12, 9, -9, -10, 2, -32, 16, -2, -11, 11, 32, 4, 10, 6, -19, -1, 4, -38, -8, 6, -20, -21, 2, -2, 12, 4, 78, -3, -5, 1, 38, -4, -45, 58, -5, 3, -54, 10, 70, 10, -2, -6, 0, -2, 27, -2, 24, 16, -20, 2, 6, -7, 0, -3, 6, 1, -33, -4, -2, -8, -11, 12, -36, 9, 9, -3, -16, 2, -12, 15, -24, -2, 4, -16, 40, 32, 8, -33, 10, 6, 14, 10, 0, 4, 24, -1, -25, 6, -10, -6, 3, 2, 20, 25, 18, 4, -30, -5, -22, -5, -16, -12, -6, -4, -47, -13, -11, -5, -46, 26, 10, 10, -6, -10, 2, -2, 8, 26, -19, -2, -2, 3, 6, 24, -42, 21, 3, 2, -29, -26, 5, 0, -27, 3, 24, 1, 2, -10, 108, -2, 18, -9, 29, 12, -20, 6, 8, 9, -10, -18, 4, 2, 38, 10, 6, -24, -27, -4, -40, -16, -1, -21, -18, 8, 120, 1, 4, 6, 30, 7, -6, 0, 12, 44, 2, -1, 2, 17, -8, -10, -124, -4, -41, 2, 6, -24, -15, 18, -25, 9, 3, -5, -84, -8, -16, -16, -15, -16, 24, -4, -3, -22, -8, -11, 42, 16, -6, 26, -66, 5, 51, -6, -10, -38, 2, -2, -11, -4, -60, -19, -2, 32, 60, 3, -4, 20, -3, -42, -35, 4, -13, 2, -25, 6, 42, 5, -22, 39, 5, 3, 27, -10, -16, 2, -6, -38, -18, -2, -72, -9, -26, 29, 2, 5, 49, 6, 22, -108, -39, -10, 34, 35, -20, 2, 80, -1, 18, 6, 13, 0, 64, -4, -15, -27, -3, -1, 0, 30, 64, 8, -21, 20, -25, 4, 20, 12, -13, 7, -24, 0, -36, 12, 6, 3, 40, -1, -44, -66, -2, -8, 31, 2, -23, -4, -18, 2, 14, 6, 63, 36, 3, 18, 5, 18, -1, 3, 18, -8, -68, -8, -36, -6, -10, -15, -44, -48, -25, -4, -2, -4, -36, -8, -30, 50, -42, 16, 0, -8, -30, -66, -4, 20, -90, -6, -2, 7, 14, 2, 56, 0, 9, -4, 22, 48, 12, -2, -34, 25, -17, 3, 12, -2, -46, -3, 4, -3, 42, 4, 0, 40, -12, -25, -21, 9, -120, 5, 18, -15, 8, 5, -20, -44, -10, -10, -18, 16, 6, -6, -32, 24, 2, -2, -64, 47, -11, -26, -9, -22, -9, 5, -16, -23, -86, 22, 120, 5, -5, -10, -42, -12, 24, -20, -19, -2, 59, -1, -86, -32, -8, 13, -2, 19, 25, -4, 40, -4, 22, -3, 17, 3, 40, 30, -54, -21, -42, -21, 2, 6, 0, 4, 36, 29, -6, -13, 132, 1, -56, 0, -39, 27, 33, 6, -26, 48, -5, -1, -85, 1, -20, -2, -76, 54, -3, 2, -21, 36, 36, -18, 30, -29, -25, 6, 10, -25, 90, 3, 43, -8, -54, 18, -80, -20, -8, 18, -35, 2, -24, -8, 20, 19, 1, -10, -37, 12, 11, -48, 0, 27, -9, -2, -156, 34, -54, -8, -20, 1, 47, -42, 6, -36, 38, -8, -42, 60, 40, -4, 30, 2, -44, -6, 6, 60, -95, 14, 59, 6, 0, 0, -18, 15, 96, 22, -3, -2, -30, -2, -84, 4, -33, -17, -21, -4, 112, -2, 4, -62, 90, 4, 11, -82, 13, 4, 12, -6, -53, -12, 72, -3, 28, 9, -22, 25, 9, 18, 4, 6, -37, 5, 8, -42, -38, -10, 56, -8, 6, 16, 44, -30, 145, -32, -24, -24, -24, -2, 102, 12, -8, -11, 86, 8, 30, -22, 10, 84, -28, -16, -15, -3, -16, 22, 72, -33, -22, -5, 10, 102, -6, -12, 4, 10, -7, -19, 42, -8, -66, -1, 0, 11, -15, -8, -5, -120, 24, 19, 6, -1, -34, 40, 50, 30, 72, -3, 60, -8, 8, 40, 30, 3, 10, -21, -6, -7, 56, 2, 46, 13, 20, 4, 6, -50, -26, -6, -9, 21, 128, 1, 16, -11, 15, -39, -29, 10, -16, 6, -22, -27, 10, -5, 24, -20, 32, 1, 68, 6, 59, -76, 30, -36, -49, 2, -2, -36, 94, 36, 0, -13, 4, -29, -11, 4, -3, 10, 40, -49, 23, 3, 138, -4, 128, -54, -5, 39, 9, -20, 15, 68, -6, -35, 22, -10, 56, -8, -4, 40, 87, 1, -30, 36, -40, 12, 68, -13, -56, 0, 38, 80, 60, -2, 27, 15, -2, -54, -132, -6, 5, 1, -3, 0, 44, 6, -44, 32, 21, -8, 52, -42, 22, 40, 3, 25, -72, 2, -22, 4, 58, 6, 3, 13, -6, 14, -4, -48, 42, 0, 114, -18, 54, 15, -38, 3, -76, -3, 24, 80, -15, -2, -55, 44, -1, -33, 142, 8, -6, -4, -54, -31, -12, 4, 25, -46, 18, 4, -96, -9, 0, 13, -58, 7, -14, -6, -6, 126, -5, 72, 8, -3, 41, 9, -16, -20, 32, 9, -14, 1, -10, 6], "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.i", "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], [1, 0, 0, 0], [0, 0, 1, 0], [-1, 0, 1, 0], [-1, 0, 1, 0], [0, 1, 0, 0], [-1, 0, 0, 0], [-1, 0, 3, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [0, 1, 0, 1], [-3, 0, 3, 0], [0, 0, -1, 0], [2, 0, 0, 2], [-3, 0, 2, 0], [0, 0, 0, 1], [0, 0, -1, 0], [-3, -3, 3, -3], [1, 0, -1, 0], [0, 2, -2, 0], [0, 0, 0, 1], [-2, 0, -1, 0], [-3, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [1, 1, -1, 1], [0, -2, 2, 0], [1, 0, 0, 0], [-2, 0, -1, 0], [-5, 0, 0, -2], [0, -1, 0, 0], [-6, -3, 6, -3], [1, 0, -1, 0], [0, 0, -3, 0], [-3, 0, 0, -3], [0, 2, 0, 3], [1, 0, 0, 0], [0, 2, -6, 0], [2, 2, -2, 2], [-2, -2, 2, -2], [0, -1, 0, 0], [-2, 0, 0, 2], [1, 0, -3, 0], [2, 0, 0, -4], [0, 0, -3, 0], [0, -1, 0, -1], [-1, 0, 1, 0], [0, -1, 3, 0], [1, 0, 0, 0], [-8, 0, 3, 0], [1, 0, 0, 1], [0, 3, -3, 0], [-2, -2, 2, -2], [-2, -1, 2, -1], [0, 0, 1, 0], [0, 0, 0, 3], [1, 0, -3, 0], [2, 0, 0, 2], [0, 2, -5, 0], [-4, -1, 4, -1], [0, -1, 0, -1], [0, 0, 2, 0], [-6, 0, 0, -3], [3, 0, -2, 0], [1, 0, 0, 0], [0, 0, -8, 0], [3, 0, -3, 0], [2, 0, -2, 0], [0, 3, -3, 0], [-1, 0, 0, 0], [0, -1, 0, 2], [3, 0, 0, 1], [0, 0, 1, 0], [1, 7, -1, 7], [6, 2, -6, 2], [0, -1, 1, 0], [2, 0, 0, 2], [-6, 0, -3, 0], [-2, 0, 0, -2], [0, -6, 3, 0], [0, -1, 0, -1], [-1, 0, 1, 0], [0, -2, -2, 0], [-4, 0, 0, 1], [3, 0, -2, 0], [12, 0, 0, 0], [0, 4, 2, 0], [5, 2, -5, 2], [3, 0, -3, 0], [0, -4, 2, 0], [0, 0, 0, -1], [-2, -6, 6, -2], [-1, 0, 0, 0], [0, 3, -6, 0], [-3, -1, 3, -1], [-8, 0, 8, 0], [0, 0, 1, 0], [4, 0, 0, -3], [-3, 0, -5, 0], [3, 0, 0, 0], [0, -1, 1, 0]]}