# Stored data for newform 85.2.a.a, downloaded from the LMFDB on 21 January 2025.
{"Nk2": 340, "analytic_conductor": 0.6787284171808833, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, 1], [17, -1]], "atkin_lehner_string": "+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [85, 1, [52, 71], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-1, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 33554517, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "85.2.a.a", "level": 85, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [5, 17], "level_radical": 85, "minimal_twist": "85.2.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}+2q^{3}-q^{4}-q^{5}+2q^{6}-2q^{7}+\\cdots", "related_objects": ["EllipticCurve/Q/85/a"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "85.2.a", "trace_display": [1, 2, -1, -2], "trace_hash": 1357271102347283934, "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "0.999", "prec": 17}, {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "1.986", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.005", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.005", "prec": 17}, "traces": [0, 1, 1, 2, -1, -1, 2, -2, -3, 1, -1, 2, -2, 2, -2, -2, -1, 1, 1, 0, 1, -4, 2, 6, -6, 1, 2, -4, 2, -6, -2, -10, 5, 4, 1, 2, -1, 2, 0, 4, 3, 10, -4, 4, -2, -1, 6, 12, -2, -3, 1, 2, -2, -10, -4, -2, 6, 0, -6, 8, 2, -14, -10, -2, 7, -2, 4, 8, -1, 12, 2, -2, -3, -14, 2, 2, 0, -4, 4, -14, 1, -11, 10, 4, 4, -1, 4, -12, -6, 6, -1, -4, -6, -20, 12, 0, 10, 2, -3, 2, -1, -6, 2, 12, -6, 4, -10, 2, 4, 2, -2, 4, 2, -6, 0, -6, 6, 2, 8, -2, 6, -7, -14, 20, 10, -1, -2, 8, -3, 8, -2, 6, -4, 0, 8, 4, -3, -2, 12, 14, -2, 24, -2, 4, -1, 6, -14, -6, -2, 6, 2, -12, 0, 1, -4, 10, -4, 6, -14, -20, -5, -12, -11, -2, -10, -4, 4, 2, 12, -9, -1, 0, -4, -6, -12, -2, -2, 16, 6, -24, 1, 26, -4, -28, -18, -2, -20, 2, -12, 8, 0, 8, 14, 18, 2, -4, 3, 2, 2, 6, -3, 16, -6, 12, -2, -10, 12, 6, -2, 0, 4, 2, 10, -4, 2, -4, 12, 20, 2, -28, 2, 2, 4, 16, -10, 1, -6, -2, 0, 10, -6, -8, 18, -14, 2, -12, -8, -28, -2, -8, 2, -6, -7, -10, 14, 3, 20, 0, 30, 8, -1, 28, 2, 12, 8, -2, -17, -2, 8, -4, 2, -6, 6, -8, -12, 10, 0, 12, -8, 10, 4, -16, -1, -8, -2, 2, -12, -30, 14, -10, -6, -6, 24, 6, 2, 0, 4, -20, 5, 1, 6, 4, 14, 30, -6, -8, -6, -8, 6, 12, -2, -8, -12, -12, 0, 14, 1, -16, 4, 24, 10, 6, -12, 2, 6, 2, 14, 10, -20, -12, -7, 4, -12, 0, 11, 2, -2, 4, -30, -24, -4, 16, -4, 2, 2, -8, 4, -6, -9, -12, 1, -20, 0, 20, -12, -12, -6, -26, 12, 22, -2, -8, 10, -14, 16, 2, -6, -4, -24, 20, 3, -19, 26, -14, 4, 14, -28, -34, -6, 10, -2, 20, 20, 10, 2, -2, -36, -12, 8, -2, 0, 16, 8, 0, -6, 4, 18, 4, -2, 26, -4, 6, 9, 12, 2, 14, -2, -14, 6, 0, -1, 18, 16, -20, 6, 11, 12, 4, -6, -38, -10, -4, -12, -16, 6, -4, 10, 28, 0, 18, -4, 26, 2, 12, 30, 1, -4, 28, -2, 8, -4, -38, 4, -34, 20, 12, -2, 0, -28, 6, 6, -3, 2, 24, -4, -6, 16, 12, -14, 18, 1, 20, 6, -24, -2, 4, 0, 6, 10, -4, 6, -26, -8, -36, 6, 20, -14, 28, -2, -16, -12, 12, -24, 8, -28, 0, 2, -10, -8, -18, -10, 4, -6, -24, 7, -2, -10, 22, 42, -4, 3, -16, -20, -6, 0, -2, 10, 4, 8, -14, 1, 4, 28, 6, 6, 6, 12, -18, -8, -34, -2, 28, -11, 0, -2, -12, -8, 24, -4, -12, 6, -30, -6, 32, -6, -4, -8, -10, -4, 13, 10, 8, 0, 20, 12, -2, -24, -48, 10, -6, -4, -14, -16, 52, 5, -2, -8, -22, 2, -14, 2, 0, -36, 28, -30, -4, -14, 2, -10, 8, -2, 4, -6, 4, -24, 6, 6, 22, 6, -38, 0, 18, -4, 16, -20, 6, 7, 6, 1, 36, -6, -8, 4, -20, 42, -2, 30, -12, 6, 0, -8, 4, -2, -30, -8, 2, -6, 12, 12, 16, -6, 10, -8, 8, 12, 7, -12, 18, 0, 24, 14, 24, -1, 46, -16, -20, 12, 42, 24, -14, -10, -24, 6, -12, -4, 1, 2, 0, -6, 2, 2, -4, 42, 4, 10, -8, 20, -6, -12, -2, 3, -30, 4, -14, 12, -8, 0, 28, 33, 16, 2, 40, 2, -14, 4, -6, -10, -14, -24, -44, 4, 46, 16, 4, -12, 0, 2, -36, -2, 32, -8, -28, -20, 10, -6, -4, 9, -30, -12, -4, 3, -4, -20, 18, 0, 2, 20, 20, -4, -20, -12, 2, 6, -4, -26, -14, 36, 10, 22, -28, 2, -30, -8, 0, 14, -24, -14, 12, -16, -6, 2, -14, -18, -60, -4, -4, 24, -16, 20, 14, 1, -24, -19, -12, -26, -6, -14, -12, 12, 13, 14, 4, 28, -2, -34, 6, 30, 16, 10, -8, 2, 0, 20, -6, 60, -6, 10, 4, -2, -4, -2, -2, -12, 56, -12, 12, -8, -22, -2, 24, 0, 6, 16, -4, -8, -1, 0, 16, -34, -18, 4, -4, -18, -6, 4, -10, -6, -8, 26, 0, 4, -4, 6, 24, 3, -6, 12, -6, -2, -16, 14, 12, -6, -28, -14, 20, -6, -2, 0, 12, 5, 6, 18, -28, -16, 12, -20, 20, 18, 26, 11, -2, -12, -32, 4, 2, -2, 0, -38, -4, 10, 2, -4, -34, -36, 4, -16, -42, -6, -2, -4, -60, 14, -3, 28, -2, 0, 40, 18, 26, -12, 7, 26, -12, -2, 9, 12, 14, 10, 12, 1, 12, 4, 34, 28, 0, -6, 34, 8, -24, 4, -40, -38, -4, -20, 6, -34, 2, -20, -28, 12, 16, -6, 2, 0, 2, 28, -14, 6, 60, 2, 42, -3, 16, -2, -16, 24, -22, -12, -16, -6, -22, -16, 0, 12, 24, 6, 24, 18, 60, -1, -10, 20, -16, 18, -26, -24, 30, 2, -6, 4, -38, 0, 8, 6, 28, -10, -12, -4, 16, 18, -32, -26, -4, 8, 2, -36, 12, -30, 58, 20, 0, 14, 12, 28, -2, -6, -38, -16, 4, 12, 34, 12, 60, -8, -8, 8, 26, 28, -28, 0, 20, 6, -18, -10, -8, 8, -24, -18, 4, -14, 69, 4, 2, 6, -18, -24, 32, 21, 0, -2, -8, 10, -28, 22, 4, 14, 34, -4, 12, -3, 2, -16, -6, -60, -2, -6, -48, 0, 24, -2, -58, -50, 32, 4, -6, -8, -62, -14, -8, 3], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 1, 2, -1, -1, 2, -2, -3, 1, -1, 2, -2, 2, -2, -2, -1, 1, 1, 0, 1, -4, 2, 6, -6, 1, 2, -4, 2, -6, -2, -10, 5, 4, 1, 2, -1, 2, 0, 4, 3, 10, -4, 4, -2, -1, 6, 12, -2, -3, 1, 2, -2, -10, -4, -2, 6, 0, -6, 8, 2, -14, -10, -2, 7, -2, 4, 8, -1, 12, 2, -2, -3, -14, 2, 2, 0, -4, 4, -14, 1, -11, 10, 4, 4, -1, 4, -12, -6, 6, -1, -4, -6, -20, 12, 0, 10, 2, -3, 2, -1, -6, 2, 12, -6, 4, -10, 2, 4, 2, -2, 4, 2, -6, 0, -6, 6, 2, 8, -2, 6, -7, -14, 20, 10, -1, -2, 8, -3, 8, -2, 6, -4, 0, 8, 4, -3, -2, 12, 14, -2, 24, -2, 4, -1, 6, -14, -6, -2, 6, 2, -12, 0, 1, -4, 10, -4, 6, -14, -20, -5, -12, -11, -2, -10, -4, 4, 2, 12, -9, -1, 0, -4, -6, -12, -2, -2, 16, 6, -24, 1, 26, -4, -28, -18, -2, -20, 2, -12, 8, 0, 8, 14, 18, 2, -4, 3, 2, 2, 6, -3, 16, -6, 12, -2, -10, 12, 6, -2, 0, 4, 2, 10, -4, 2, -4, 12, 20, 2, -28, 2, 2, 4, 16, -10, 1, -6, -2, 0, 10, -6, -8, 18, -14, 2, -12, -8, -28, -2, -8, 2, -6, -7, -10, 14, 3, 20, 0, 30, 8, -1, 28, 2, 12, 8, -2, -17, -2, 8, -4, 2, -6, 6, -8, -12, 10, 0, 12, -8, 10, 4, -16, -1, -8, -2, 2, -12, -30, 14, -10, -6, -6, 24, 6, 2, 0, 4, -20, 5, 1, 6, 4, 14, 30, -6, -8, -6, -8, 6, 12, -2, -8, -12, -12, 0, 14, 1, -16, 4, 24, 10, 6, -12, 2, 6, 2, 14, 10, -20, -12, -7, 4, -12, 0, 11, 2, -2, 4, -30, -24, -4, 16, -4, 2, 2, -8, 4, -6, -9, -12, 1, -20, 0, 20, -12, -12, -6, -26, 12, 22, -2, -8, 10, -14, 16, 2, -6, -4, -24, 20, 3, -19, 26, -14, 4, 14, -28, -34, -6, 10, -2, 20, 20, 10, 2, -2, -36, -12, 8, -2, 0, 16, 8, 0, -6, 4, 18, 4, -2, 26, -4, 6, 9, 12, 2, 14, -2, -14, 6, 0, -1, 18, 16, -20, 6, 11, 12, 4, -6, -38, -10, -4, -12, -16, 6, -4, 10, 28, 0, 18, -4, 26, 2, 12, 30, 1, -4, 28, -2, 8, -4, -38, 4, -34, 20, 12, -2, 0, -28, 6, 6, -3, 2, 24, -4, -6, 16, 12, -14, 18, 1, 20, 6, -24, -2, 4, 0, 6, 10, -4, 6, -26, -8, -36, 6, 20, -14, 28, -2, -16, -12, 12, -24, 8, -28, 0, 2, -10, -8, -18, -10, 4, -6, -24, 7, -2, -10, 22, 42, -4, 3, -16, -20, -6, 0, -2, 10, 4, 8, -14, 1, 4, 28, 6, 6, 6, 12, -18, -8, -34, -2, 28, -11, 0, -2, -12, -8, 24, -4, -12, 6, -30, -6, 32, -6, -4, -8, -10, -4, 13, 10, 8, 0, 20, 12, -2, -24, -48, 10, -6, -4, -14, -16, 52, 5, -2, -8, -22, 2, -14, 2, 0, -36, 28, -30, -4, -14, 2, -10, 8, -2, 4, -6, 4, -24, 6, 6, 22, 6, -38, 0, 18, -4, 16, -20, 6, 7, 6, 1, 36, -6, -8, 4, -20, 42, -2, 30, -12, 6, 0, -8, 4, -2, -30, -8, 2, -6, 12, 12, 16, -6, 10, -8, 8, 12, 7, -12, 18, 0, 24, 14, 24, -1, 46, -16, -20, 12, 42, 24, -14, -10, -24, 6, -12, -4, 1, 2, 0, -6, 2, 2, -4, 42, 4, 10, -8, 20, -6, -12, -2, 3, -30, 4, -14, 12, -8, 0, 28, 33, 16, 2, 40, 2, -14, 4, -6, -10, -14, -24, -44, 4, 46, 16, 4, -12, 0, 2, -36, -2, 32, -8, -28, -20, 10, -6, -4, 9, -30, -12, -4, 3, -4, -20, 18, 0, 2, 20, 20, -4, -20, -12, 2, 6, -4, -26, -14, 36, 10, 22, -28, 2, -30, -8, 0, 14, -24, -14, 12, -16, -6, 2, -14, -18, -60, -4, -4, 24, -16, 20, 14, 1, -24, -19, -12, -26, -6, -14, -12, 12, 13, 14, 4, 28, -2, -34, 6, 30, 16, 10, -8, 2, 0, 20, -6, 60, -6, 10, 4, -2, -4, -2, -2, -12, 56, -12, 12, -8, -22, -2, 24, 0, 6, 16, -4, -8, -1, 0, 16, -34, -18, 4, -4, -18, -6, 4, -10, -6, -8, 26, 0, 4, -4, 6, 24, 3, -6, 12, -6, -2, -16, 14, 12, -6, -28, -14, 20, -6, -2, 0, 12, 5, 6, 18, -28, -16, 12, -20, 20, 18, 26, 11, -2, -12, -32, 4, 2, -2, 0, -38, -4, 10, 2, -4, -34, -36, 4, -16, -42, -6, -2, -4, -60, 14, -3, 28, -2, 0, 40, 18, 26, -12, 7, 26, -12, -2, 9, 12, 14, 10, 12, 1, 12, 4, 34, 28, 0, -6, 34, 8, -24, 4, -40, -38, -4, -20, 6, -34, 2, -20, -28, 12, 16, -6, 2, 0, 2, 28, -14, 6, 60, 2, 42, -3, 16, -2, -16, 24, -22, -12, -16, -6, -22, -16, 0, 12, 24, 6, 24, 18, 60, -1, -10, 20, -16, 18, -26, -24, 30, 2, -6, 4, -38, 0, 8, 6, 28, -10, -12, -4, 16, 18, -32, -26, -4, 8, 2, -36, 12, -30, 58, 20, 0, 14, 12, 28, -2, -6, -38, -16, 4, 12, 34, 12, 60, -8, -8, 8, 26, 28, -28, 0, 20, 6, -18, -10, -8, 8, -24, -18, 4, -14, 69, 4, 2, 6, -18, -24, 32, 21, 0, -2, -8, 10, -28, 22, 4, 14, 34, -4, 12, -3, 2, -16, -6, -60, -2, -6, -48, 0, 24, -2, -58, -50, 32, 4, -6, -8, -62, -14, -8, 3]}