# Stored data for newform 165.2.a.c, downloaded from the LMFDB on 25 April 2024.
{"label": "165.2.a.c", "space_label": "165.2.a", "level": 165, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007199288295589, "dim": 3, "is_polredabs": true, "nf_label": "3.3.148.1", "trace_hash": 2131098535040944473, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, -5, 1, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+q^{3}+(1+\\beta _{1}+\\beta _{2})q^{4}+q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 660, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 1.3175316333511264, "hecke_ring_index": 2, "level_radical": 165, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.008", "prec": 17}, "analytic_rank_proved": true, "char_values": [165, 1, [56, 67, 46], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 148, "field_disc_factorization": [[2, 2], [37, 1]], "field_poly": [1, -3, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "2.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "22.245", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "242.497", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1], [11, -1]], "trace_display": [-1, 3, 3, 0], "traces": [0, 3, -1, 3, 5, 3, -1, 0, -9, 3, -1, 3, 5, -2, -12, 3, 13, -2, -1, 8, 5, 0, -1, 0, -9, 3, 10, 3, -8, -10, -1, 8, -29, 3, -30, 0, 5, -6, 0, -2, -9, -14, -12, 4, 5, 3, 24, -8, 13, 11, -1, -2, -30, -6, -1, 3, -4, 8, -18, 12, 5, -6, 16, 0, 13, -2, -1, -4, 42, 0, -12, 8, -9, -14, 2, 3, 48, 0, 10, 12, 13, 3, 26, 0, -8, -2, -8, -10, -9, -10, -1, 8, 16, 8, -16, 8, -29, 22, 39, 3, 5, -26, -30, -8, 42, 0, -22, 8, 5, -6, -1, -6, 48, -18, 0, 0, 2, -2, -28, 16, -9, 3, 26, -14, -40, 3, -12, -32, -17, 4, 10, 4, 5, -40, 20, 3, -70, -2, 24, 40, -8, -8, 16, -2, 13, -10, 38, 11, -10, -18, -1, 4, -56, -2, -12, 8, -30, 2, 36, -6, -29, -64, -1, -4, -42, 3, 28, 4, -4, -11, -30, 8, 68, -14, -18, 0, 13, 12, 46, 4, 5, -14, 16, -6, 8, -6, 16, -2, 40, 0, 0, -8, 13, 2, -26, -2, -19, -6, -1, 16, -9, -4, 54, 24, 42, -14, -40, 0, -46, 8, -12, 8, -26, 8, -12, 4, -9, 16, -46, -14, 5, -44, 2, 0, 4, 3, 6, 40, 48, 34, 24, 0, -10, -26, 10, -8, 4, 12, 24, 16, 13, 22, -1, 3, 6, 11, 26, -40, 48, 0, -1, 68, -8, 0, -20, -2, 61, 6, -8, 0, -30, -10, -20, -36, -9, -6, -72, -10, -60, 26, -1, 4, 114, 8, 38, 3, 16, -10, 8, 8, -4, -14, -16, 68, -40, 8, 10, -24, -29, 57, -18, 22, -34, -22, 39, 12, 18, 3, 46, -16, 5, -48, -84, -26, 24, -6, -30, -60, -8, -8, 16, 32, 42, 6, 66, 0, -52, 50, -22, -10, 13, 8, -64, 24, 5, -2, -4, -6, 82, -16, -1, 20, -80, -6, -40, -4, 48, 58, -39, -18, 42, 8, 0, -48, -80, 0, -26, 8, 2, 42, -12, -2, -29, -2, -28, 8, -54, 16, -92, 32, -9, 39, -38, 3, -40, -14, 26, -32, -96, -14, 2, 64, -40, 22, -30, 3, -48, -12, -12, -60, 48, -32, 8, -16, -17, 0, 38, 4, 90, 10, 10, -32, 47, 4, -66, 12, 5, -38, 0, -40, 13, 6, 20, 48, -46, 3, 64, -6, -70, 6, 26, -2, 24, 64, 24, 0, 82, 40, 0, 20, -8, 50, -48, -8, 10, -2, 16, -64, 40, -2, -8, 24, 13, -10, -16, -10, -42, 80, 38, -44, -9, 11, 100, -12, -10, -10, 24, -18, 24, -18, -1, -14, -30, 4, -4, 8, -56, 10, 26, -2, 16, 6, -12, -32, 42, 8, 2, 36, -30, 16, -16, 2, -44, 4, 36, 8, 112, -6, 8, -48, -29, 4, 6, -64, 5, 22, -1, -88, 26, -4, 39, 76, -42, 68, 56, 3, -40, 16, 28, 4, 5, 4, -4, 4, -4, -26, 24, -11, -8, 10, -30, -56, -5, 8, -26, -8, 68, -8, 24, -14, 42, -34, -18, 60, 60, 0, -8, -96, 13, 59, -22, 12, 8, 28, 46, 8, 84, 4, -46, 11, 5, -54, 44, -14, -102, -6, 16, 4, -110, -6, -1, -32, 8, -8, 98, -6, 48, -22, 16, -64, 48, -2, 26, 32, 40, -18, 8, 0, 48, -62, 0, 16, -30, -8, 32, 0, 13, 14, -99, 2, 2, 24, -26, -6, 86, -2, 38, 76, -19, -48, -28, -6, -26, 70, -1, 16, -102, 16, -32, -40, -9, -26, -64, -4, 116, 3, 54, -32, -144, 24, 26, -48, 42, 102, 8, -14, -4, -10, -40, -28, -40, 0, 88, -48, -46, 3, -50, 8, -18, 4, -12, -32, 76, 8, -54, -32, -26, 30, -18, 8, -17, -2, -12, 28, -32, 4, -184, -8, -9, 12, 10, 16, -76, 10, -46, 4, -146, -14, 16, -84, 5, -30, -20, -44, 108, -40, 2, -48, -52, 0, 20, -6, 4, -30, 14, 3, 19, 50, 6, -16, -70, 40, 16, -4, 48, -2, -8, 34, 44, 20, 24, -4, 22, 0, -12, 40, -10, -52, -38, -26, -8, -50, 10, -16, 13, -8, 14, -88, 4, 34, 16, 12, 110, -32, 24, -2, 12, 16, 8, -8, 13, 48, 35, 22, 14, -10, -1, 8, 48, 3, 38, 72, 6, -90, 168, 11, -8, -4, 26, -56, -10, -40, 88, -12, 48, -18, 74, 0, 42, -8, -1, 8, 40, 68, 28, 4, -8, 26, 20, 0, -56, -30, -20, 128, 56, -2, -112, 8, 61, -34, -12, 6, 62, 114, -8, 8, -138, 0, -46, -32, -30, 8, -48, -10, -123, 2, -20, 60, 142, -36, 36, 0, -9, -12, -6, -6, 96, 18, -72, 96, -29, -10, -2, -14, -60, -64, -64, 26, 126, -70, -1, 8, 88, 4, 2, -4, 114, 120, -82, 8, -42, -82, 38, -8, -56, 3, 16, 40, 16, -6, 28, -10, -126, -130, 8, 4, 48, 8, 36, -16, -4, -11, -22, -14, 16, -11, -16, 0, 70, 68, -30, 0, -40, 54, -40, 8, -60, 22, 10, 52, 68, -24, 8, -16, -29, -14, 70, 57, -112, 12, -18, 56, 2, 22, 144, 0, -34, 14, -44, -22, 13, -18, 39, -36, -148, 12, -76, 92, 18, 16, 46, 3, 16, 48, 46, 4, -36, -16, -10, -64, 5, 36, 26, -48, 54, -14, -84, -28, 40, -26, 16, 24, 24, 0, -122, -6, -50, -16, -30, 20, 8, -60, -58, 48, -8, -6, 24, -8, 38, -34, 16, 40, 18, 32, -36, -2, 42, -30, 32, 6, 40, 46, 66, 48, 148, 0, -8, -28, -52, 20, 0, 50, -104, -66, -22, -8, -96, -10, -8, 32, 13, 35, -20, 8, -86, 2, -64, 40, -9, 24, -26, -12, 5, -24, 96, -2, -122, 6, -4, -10, -19, -6, -68, -24, 82, -6, 44, -16, -104, 96, -1, -56, 48, 20, -16, 16, -80, -26, -92, -6, -9], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "165.2.a.c", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [0, -1, 0], [1, 0, 0], [1, 1, 1], [1, 0, 0], [0, -1, 0], [0, 1, -1], [-2, -2, -1], [1, 0, 0], [0, -1, 0], [1, 0, 0], [1, 1, 1], [0, -1, -1], [-4, 1, -1], [1, 0, 0], [3, 4, 0], [-2, 3, 1], [0, -1, 0], [2, 0, 2], [1, 1, 1], [0, 1, -1], [0, -1, 0], [0, -2, 2], [-2, -2, -1], [1, 0, 0], [2, 3, 1], [1, 0, 0], [-4, 3, 1], [-4, 2, 0], [0, -1, 0], [4, -2, -2], [-8, -3, -2], [1, 0, 0], [-8, -3, -3], [0, 1, -1], [1, 1, 1], [-2, 0, 0], [2, -6, 0], [0, -1, -1], [-2, -2, -1], [-4, -2, 0], [-4, 1, -1], [0, 1, 3], [1, 1, 1], [1, 0, 0], [8, -2, 2], [-4, 2, 2], [3, 4, 0], [5, -4, 0], [0, -1, 0], [-2, 3, 1], [-8, -5, -1], [-2, 2, -2], [0, -1, 0], [1, 0, 0], [0, -3, -1], [2, 0, 2], [-6, 2, -2], [4, 2, -2], [1, 1, 1], [-2, -2, 2], [4, 2, 2], [0, 1, -1], [1, 7, 3], [0, -1, -1], [0, -1, 0], [0, -2, -2], [10, 11, 1], [0, -2, 2], [-4, 1, -1], [4, -2, -2], [-2, -2, -1], [-4, -3, 1], [0, 2, 0], [1, 0, 0], [14, 4, 2], [0, 1, -1], [2, 3, 1], [6, -4, -2], [3, 4, 0], [1, 0, 0], [6, 6, 2], [2, -3, -3], [-4, 3, 1], [-2, 3, 1], [0, -7, -1], [-4, 2, 0], [-2, -2, -1], [-2, -4, 0], [0, -1, 0], [4, -2, -2], [8, -6, -2], [4, -2, -2], [-4, -2, -2], [2, 0, 2], [-8, -3, -2], [6, 2, 2], [12, -1, 4], [1, 0, 0], [1, 1, 1]]}