# Stored data for newform 966.2.g.e, downloaded from the LMFDB on 25 April 2024.
{"label": "966.2.g.e", "space_label": "966.2.g", "level": 966, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014810859897798, "dim": 16, "is_polredabs": true, "trace_hash": 1998310151688914720, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [256, 0, -464, 0, 226, 0, -29, 0, 1]], [11, [25600, 0, 27200, 0, 2680, 0, 90, 0, 1]]], "qexp_display": "q+q^{2}+\\beta _{2}q^{3}+q^{4}-\\beta _{8}q^{5}+\\beta _{2}q^{6}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 161, "char_orbit_label": "g", "char_is_real": true, "Nk2": 3864, "analytic_conductor": 7.713548835255685, "hecke_ring_index": 128, "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": "0.766", "prec": 17}, "analytic_rank_proved": true, "char_values": [966, 2, [323, 829, 925], [2, 1, 1]], "hecke_ring_generator_nbound": 23, "inner_twist_count": 4, "level_primes": [2, 3, 7, 23], "conrey_indexes": [643], "field_disc": 95428956661682176000000000000, "field_disc_factorization": [[2, 24], [5, 12], [13, 12]], "field_poly": [65536, 0, 0, 0, 96196, 0, 0, 0, 27081, 0, 0, 0, 326, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 7]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.046", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1872.227", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "383687.592", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "1.2.3.c2", "trace_display": [16, 0, 0, 0], "traces": [0, 16, 16, 0, 16, 0, 0, 0, 16, -16, 0, 0, 0, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, -8, 0, 36, 0, 0, 0, 20, 0, 0, 16, 0, 0, -16, -16, 0, 0, -4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -16, -48, -16, 0, 0, 0, 0, 20, -4, 0, 0, 16, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, -8, 0, 0, 80, 0, 0, 0, 0, 36, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 112, 0, -184, 0, 60, 0, 0, 0, -52, 16, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, -16, -12, -48, 0, -16, 0, 0, -8, 0, 0, 0, -68, 0, 0, 20, 0, -4, 0, 0, 0, 0, -52, 16, 24, 0, -80, 0, 0, 0, 12, -32, 0, 0, 0, 0, 0, 0, -16, 0, -20, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 80, 0, 0, -156, 0, 0, 0, 28, 0, 0, 36, 0, 0, 0, 0, 0, 0, 8, 0, 0, -36, -8, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 20, 20, 144, 0, 0, 0, 0, 112, 0, 0, 0, -184, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, -52, 0, 16, 0, 0, 28, 0, -20, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, -16, 0, -12, 0, -48, 0, 0, 0, -16, -48, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -84, -68, 40, 0, -48, 0, 0, 20, 0, 0, 0, -4, 0, 0, 16, 0, 148, 0, 0, 0, 0, -52, -40, 16, 0, 24, 0, 0, 0, -80, 72, 0, 0, 0, 0, 0, 0, 12, 0, -32, 0, 0, 0, 0, -52, 0, 28, 0, 0, 0, 4, 0, 0, -16, 0, 0, -8, -20, 0, 0, 56, 0, 0, 0, 0, 0, 0, -8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -156, 0, 0, 0, 0, 0, 0, 40, 28, 0, 0, 0, 0, 20, 36, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 8, 184, 0, 44, 0, 0, -36, 0, -8, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 44, 0, 40, 0, 0, 0, 40, -36, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 20, -36, 20, 0, 144, 0, 0, 68, 0, 0, 0, 160, 0, 0, 112, 0, 0, 0, 0, 0, 0, 52, -184, -212, 0, -92, 0, 0, 0, 32, 60, 0, 0, 0, 0, 0, 0, -160, 0, 88, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 16, 0, 0, -236, 0, 0, 28, 96, 0, 0, -20, 0, 0, 0, 0, 0, 0, 160, 0, 0, -20, -180, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 24, 48, 148, 0, 0, 0, 0, -16, 40, 0, 0, -12, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 112, -16, 0, -48, 0, 0, -124, 0, -240, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, -84, 0, -68, 0, 40, 0, 0, 0, -48, -68, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 120, -4, 216, 0, 160, 0, 0, 16, 0, 0, 0, 148, 0, 0, 128, 0, 48, 0, 0, 0, 0, -52, 76, -40, 0, 16, 0, 0, 0, 24, -76, 0, 0, 0, 0, 0, 0, -80, 0, 72, 0, 0, 0, 0, 120, 0, 16, 0, 0, 0, 204, 0, 0, 12, 0, 0, 92, -32, 0, 0, -56, 0, 0, 0, 0, 0, 0, -52, 0, 0, -20, 28, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -8, 240, -20, 0, 0, 0, 0, -84, 56, 0, 0, -280, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -8, -80, 0, 280, 0, 0, -4, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 44, 0, 32, 0, -264, 0, 0, 0, 8, -156, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -512, 40, 0, 28, 0, 0, 96, 0, 0, 0, 16, 0, 0, 20, 0, 36, 0, 0, 0, 0, -252, 0, -256, 0, -40, 0, 0, 0, -120, 120, 0, 0, 0, 0, 0, 0, -368, 0, -436, 0, 0, 0, 0, 8, 0, 184, 0, 0, 0, 44, 0, 0, 0, 0, 0, -36, 276, 0, 0, -8, 0, 0, 0, 0, 0, 0, 156, 0, 0, -92, -80, 0, 0, 0, 0, 0, 0, 0, 424, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -476, 56, -352, 0, 0, 0, 0, 0, 224, 0, 0, 44, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, -128, 40, 0, -36, 0, 0, -136, 0, 232, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 20, 0, -36, 0, 20, 0, 0, 0, 144, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 36, 160, -12, 0, 144, 0, 0, 112, 0, 0, 0, 0, 0, 0, 208, 0, 496, 0, 0, 0, 0, 52, -352, -184, 0, -212, 0, 0, 0, -92, 56, 0, 0, 0, 0, 0, 0, 32, 0, 60, 0, 0, 0, 0, 52, 0, 112, 0, 0, 0, -20, 0, 0, -160, 0, 0], "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, 2, -1, 2, 0], [1, 1, 23, 2, -1, 2, 0], [1, 1, 161, 3, 1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "966.2.g.e", "char_is_minimal": true, "conrey_index": 643, "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, 0, 0, 0, 0], [1, 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, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 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, 0, 0, -1, 0, 0, 0, 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, 1, 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, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, -1, 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, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, -1, 1, 1, 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, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 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, 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, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, -1, 3, 0, 0, 0, 1, 0, 0, 2, -2, 2, -2, -2, -1, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 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, -4, 0, 0, 0, -1, 0, 0, 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, -1, 0, -1, -1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0], [-1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 1, -1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, -1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 2, 1, -2, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0], [1, -1, 2, 0, 1, 0, 0, 0, 0, 2, -2, 2, -2, -1, -1, -2], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [1, 0, 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, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 3, 0, 1, 1, -2, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 3, 0, 0, 0, 1, 0, 0, 2, -2, 2, -2, -2, -1, -1], [-3, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -4, 0, -1, 0, 0, 0, 0, -1, 1, -1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0], [1, -1, 3, 0, 1, 0, 1, 0, 0, 1, -1, 1, -1, -1, -1, 0], [0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0], [0, 2, -2, 0, -1, 0, 0, 0, 0, -1, 1, -1, 1, 0, 2, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 1, -2, -1, 2, 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, 0, 0, 0, 0], [0, 0, -4, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [-1, -1, 0, 0, -1, 0, 0, 0, 0, 2, -2, 2, -2, -3, -1, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 1, 1, 0, 0, 0], [-1, 1, 0, 0, -1, 0, -1, 0, 0, -2, 2, -2, 2, 1, 1, 2], [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, -2, 1, -1, 0, -3, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 1, -1, 1, 1, 1, 0], [5, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 4, 0, 3, 0, 0, 0], [0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, -1, 1, 1, 1, 0]]}