# Stored data for newform 65.2.a.b, downloaded from the LMFDB on 16 April 2024.
{"label": "65.2.a.b", "space_label": "65.2.a", "level": 65, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660924993, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 1916806337191425823, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, 2, 1]]], "qexp_display": "q+(-1+\\beta )q^{2}+\\beta q^{3}+(1-2\\beta )q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 260, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 0.5190276131383225, "hecke_ring_index": 1, "level_radical": 65, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "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": "0.026", "prec": 17}, "analytic_rank_proved": true, "char_values": [65, 1, [27, 41], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 13], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "1.905", "prec": 17}, {"__RealLiteral__": 0, "data": "0.020", "prec": 17}, {"__RealLiteral__": 0, "data": "9.086", "prec": 17}, {"__RealLiteral__": 0, "data": "0.142", "prec": 17}, {"__RealLiteral__": 0, "data": "60.780", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [13, 1]], "trace_display": [-2, 0, 2, 4], "traces": [0, 2, -2, 0, 2, 2, 4, 4, -6, -2, -2, 4, -8, -2, -12, 0, 6, -4, 2, 4, 2, -8, -8, 0, 4, 2, 2, 0, 20, 0, 4, 12, 6, -4, -4, 4, -2, 0, 0, 0, -6, -12, 16, -8, 12, -2, -4, -4, 0, 10, -2, -8, -2, -12, -16, 4, -20, 4, 16, 12, -8, -16, 0, -4, -14, -2, 12, -4, 12, -4, -12, 4, 6, 0, 24, 0, -4, 16, -4, 0, 6, -10, 4, -12, -24, -4, 28, 16, -16, 12, 2, -4, 8, 12, 12, 4, 4, -4, -42, -4, 2, 4, 0, 32, 6, -8, -12, -16, 32, -4, -8, 24, 12, -12, 4, 0, -32, 2, 0, 8, 4, -10, 16, -8, -12, 2, 12, -16, 10, 20, 2, 0, -20, 0, 4, 0, 4, -12, 4, -8, 20, 8, -32, -4, -6, 0, -24, -32, -48, -12, 4, 28, -8, 4, -40, 12, 8, 36, 24, -24, 6, 8, 10, 4, 4, -4, 4, -12, 32, 2, -4, -4, -48, 28, -16, 4, 12, 12, -12, 0, -2, 0, 12, 0, -4, 0, 12, 0, -20, 32, 0, 16, 8, 20, 20, 0, 74, -12, 8, 8, -6, 0, 12, -32, 8, -12, -28, 0, -6, 4, 16, -16, 36, -28, 20, -8, -16, 0, 4, -24, 12, 4, -24, 36, 4, -2, 20, -44, -12, -4, -4, -24, 16, 4, -2, -4, -12, 24, -8, -4, 0, -12, -6, 0, -16, 10, -16, -4, -24, -8, -2, 0, -20, 4, 12, -8, -26, 44, -36, -48, -2, 0, 48, -24, 20, -12, -8, 0, -4, -28, -16, 28, -12, 8, 44, 4, -4, -20, -16, -12, -20, 4, -16, -8, 60, 4, 8, -8, -6, -10, 16, 16, 48, 24, 52, 12, 24, 16, 28, 0, -8, -56, -16, 16, 12, -16, 4, 44, 64, 4, 0, 0, -4, -4, -36, -4, -48, 24, 0, -16, -14, 4, -16, -16, -10, -2, -52, 0, 28, -24, 12, -4, 4, 0, 4, -4, -24, 20, -2, 8, 12, 12, 0, 56, 44, -4, -36, 0, 16, 20, -12, 0, 8, 24, 12, 4, 12, 0, -16, -36, 6, -26, 0, -16, -20, 0, -32, 40, 0, 12, 24, 24, -36, -28, -8, 0, 20, 0, -64, 44, -4, -4, 0, 4, -44, 16, -4, 8, -36, 12, -4, 8, -62, 48, -36, 0, -12, -16, -8, -8, 6, 12, -8, -12, -28, -10, 64, -24, 16, 20, 4, 32, 24, 0, 4, -12, -6, -24, -4, 16, -24, -36, -16, 4, 12, -4, 36, -32, -24, 4, 28, 44, 0, 4, -24, 16, -4, -4, 24, -32, -16, -10, 4, -16, 24, 12, -12, 16, -44, -4, 2, -16, -28, 12, 28, -4, -4, -36, 12, 32, 8, 36, 56, -20, 0, 12, 60, -24, 2, -8, 12, 0, -24, -36, -24, 4, 8, 12, 8, -36, 4, 0, 36, -8, 22, -4, 28, 12, 48, -48, -42, 16, 40, -32, 0, -4, 36, 64, -16, 52, 2, -8, -56, 56, 20, 4, -12, 0, -8, 20, 0, 48, 54, -16, -60, 32, 52, -16, 96, -8, 6, -24, -16, -48, -96, -8, 20, -48, -12, -42, -12, -12, 16, 12, 24, -16, 12, -16, 60, 52, 32, -20, -64, 0, -20, -4, -16, -16, -76, 16, -8, 16, 12, -48, 28, 24, 40, -32, 0, 8, 12, -8, -60, -24, 24, -12, 44, -20, -40, -32, 4, -40, -12, 16, 40, 0, 14, -64, 42, 16, -32, -8, -24, 0, -24, 2, -64, 52, -72, 36, 0, -48, 0, -4, -48, 8, -44, 0, 4, 0, 4, -44, 128, 4, 4, -10, -8, 72, 16, 32, 16, 4, -12, -52, -52, -8, -72, -12, 60, 12, -12, 16, -24, 24, 0, 2, 12, 0, 36, -48, 12, -28, 24, -32, 16, -16, 24, -10, 48, -4, 10, 84, -36, 36, 24, 20, -8, 16, 30, 12, 2, -24, 100, 60, -8, 0, -36, 0, 56, 64, -20, -20, 72, 8, 28, 0, -24, -16, 4, 24, 4, -32, -16, -4, -28, 0, 2, -12, -32, -40, 4, -16, -12, 44, 4, -12, -104, 8, -24, 12, 4, 28, 44, -16, 12, -8, -48, 40, -44, 64, 20, 52, 16, 24, -36, 8, -32, -24, -36, 28, -32, 0, -36, -12, 16, -4, 32, 4, 8, 24, -6, 56, 42, 24, 0, 0, -4, -32, 20, 58, -24, -24, 64, 20, -84, -32, -4, -8, -4, 36, -48, -4, -24, -60, -12, -12, -4, 12, 16, -40, 4, -72, -12, -56, -16, 28, 96, -20, -64, -8, -8, -28, -28, -8, -16, 4, 84, -12, 48, -12, -40, -16, -12, -16, -28, 12, 28, 48, -76, -32, 8, 36, 0, -64, 30, 36, -48, 28, 84, -4, 24, -40, 16, 16, -40, -24, 8, -12, 8, -8, 6, -12, 20, 24, 16, 8, 0, 32, 4, 0, 10, -20, -96, -36, 72, 4, -24, 4, -12, 4, 4, -12, -56, 32, -92, -4, -24, 84, -8, 48, 4, 8, 14, 44, 8, -12, 4, -48, -24, -12, 32, 6, 84, -56, 48, 2, -12, 12, -36, 36, -4, -24, -44, 24, 96, -4, 52, 12, -12, -16, -48, 32, -96, -12, -16, 28, -20, 32, 48, -24, -16, 4, 12, 4, -4, 4, -24, 28, -16, -40, 12, 72, 42, -56, -12, 12, 20, -8, -72, -24, -12, -20, -12, 0, -40, 0, 108, 4, 92, 48, -2, 72, 24, 72, 44, 0, 44, -24, -12, -4, 12, -24, 12, -16, 36, 0, -20, -96, 0, -16, -4, -8, -12, -4, -88, 0, 4, -32, 16, 28, 12, -12, -124, -24, 28, 0, -6, -12, 24, 8, -20, -36, 72, 8, 36, 32, 92, -28, 24, 0, 0, 40, -24, -20, 12, 16, -12, 32, 72, -88, 8, 46, -24, 16, -60, 20, 24, 28, 14, -24, 20, 32, -56, 32, 36, 0, -48, -96, 56, 24, 74, 4, -8, -36, 0, -12, 0, 32, 4, -20, 8, 64, 48, 68, -136, 8, 40, 52, -96, -96, -6], "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": "65.2.a.b", "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], [1, 0], [-1, 1], [0, 1], [1, -2], [1, 0], [2, -1], [2, -2], [-3, 1], [-1, 0], [-1, 1], [2, -1], [-4, 1], [-1, 0], [-6, 4], [0, 1], [3, 0], [-2, -2], [1, -1], [2, 1], [1, -2], [-4, 2], [-4, 3], [0, -1], [2, -3], [1, 0], [1, -1], [0, -4], [10, -6], [0, 4], [2, -1], [6, 3], [3, 1], [-2, 2], [-2, 0], [2, -2], [-1, 2], [0, 6], [0, 1], [0, -1], [-3, 1], [-6, -2], [8, -6], [-4, 5], [6, -5], [-1, 0], [-2, 1], [-2, 2], [0, 3], [5, -8], [-1, 1], [-4, -2], [-1, 2], [-6, -6], [-8, 4], [2, -1], [-10, 8], [2, 2], [8, -4], [6, 3], [-4, 1], [-8, 0], [0, 3], [-2, 2], [-7, 2], [-1, 0], [6, -4], [-2, 0], [6, 2], [-2, 0], [-6, 4], [2, -7], [3, -1], [0, -6], [12, -6], [0, 1], [-2, -3], [8, -6], [-2, 1], [0, 6], [3, 0], [-5, 0], [2, -4], [-6, -2], [-12, 10], [-2, -2], [14, -9], [8, 0], [-8, 5], [6, 0], [1, -1], [-2, 2], [4, -1], [6, 6], [6, -4], [2, 1], [2, 3], [-2, 4], [-21, 13], [-2, 1], [1, -2]]}