# Stored data for newform 405.2.e.a, downloaded from the LMFDB on 23 April 2024.
{"label": "405.2.e.a", "space_label": "405.2.e", "level": 405, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 274911461781, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 680418885227671273, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [4, 2, 1]], [7, [0, 1]], [11, [25, 5, 1]]], "qexp_display": "q+(-2+2\\zeta_{6})q^{2}-2\\zeta_{6}q^{4}-\\zeta_{6}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1620, "analytic_conductor": 3.2339412818618554, "hecke_ring_index": 1, "level_radical": 15, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [405, 3, [326, 82], [2, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [3, 5], "conrey_indexes": [136, 271], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.079", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.156", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "126.821", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 0, -1, 0], "traces": [0, 2, -2, 0, -2, -1, 0, 0, 0, 0, 4, -5, 0, -4, 0, 0, 4, -8, 0, -10, -2, 0, -10, -6, 0, -1, 16, 0, 0, 5, 0, 9, 8, 0, 8, 0, 0, -20, 10, 0, 0, -7, 0, 2, 20, 0, 24, -2, 0, 7, -2, 0, -8, 16, 0, 10, 0, 0, 10, 1, 0, 2, -36, 0, -16, -4, 0, -6, 8, 0, 0, 2, 0, -16, 20, 0, 10, 0, 0, -12, -8, 0, 28, -6, 0, 4, 4, 0, 0, -18, 0, 0, -12, 0, -4, 5, 0, -14, -28, 0, 4, 3, 0, -2, 0, 0, -16, -12, 0, -2, -10, 0, 0, 16, 0, -6, -20, 0, -4, 0, 0, -14, 4, 0, 18, 2, 0, 32, 0, 0, -8, -15, 0, 0, 24, 0, 0, -12, 0, 19, 0, 0, -2, 40, 0, -10, 16, 0, 20, 2, 0, 5, 0, 0, 0, 9, 0, -2, -24, 0, 8, 0, 0, 16, -14, 0, -12, -12, 0, -3, -16, 0, -8, 6, 0, 0, 20, 0, 18, 46, 0, -50, 0, 0, 0, 10, 0, 20, 8, 0, -20, -1, 0, -26, -28, 0, 14, 24, 0, 32, 0, 0, 6, 0, 0, -7, 8, 0, -32, 25, 0, -11, -16, 0, 12, -4, 0, 0, 2, 0, -10, 16, 0, -8, 0, 0, -64, -4, 0, -6, -12, 0, 0, 12, 0, 4, 2, 0, 0, 16, 0, 11, 56, 0, -8, 7, 0, 20, 0, 0, -2, -24, 0, 60, -32, 0, -16, 6, 0, 0, 16, 0, 60, -10, 0, -8, 0, 0, -12, -62, 0, -16, -16, 0, -24, -5, 0, 18, -76, 0, 0, -6, 0, -6, -2, 0, -40, 0, 0, -2, 10, 0, 16, -18, 0, 1, 0, 0, -8, -24, 0, 0, 10, 0, -20, -4, 0, 20, 0, 0, 18, 9, 0, 4, 8, 0, 48, 2, 0, 25, 8, 0, 0, 40, 0, 8, -16, 0, 0, 0, 0, 21, 24, 0, 48, -6, 0, 8, -6, 0, 8, -90, 0, 0, 0, 0, 12, -20, 0, -13, 0, 0, -80, 18, 0, -1, 18, 0, -46, -54, 0, 12, 50, 0, 0, 8, 0, -18, -48, 0, -40, 0, 0, -16, 40, 0, 0, -40, 0, 8, 10, 0, -2, 36, 0, 0, 104, 0, 56, -6, 0, 24, 0, 0, -24, 24, 0, -76, -32, 0, 4, -30, 0, 36, -12, 0, 0, 50, 0, -14, -14, 0, -4, 0, 0, 12, 32, 0, 50, -16, 0, -13, 44, 0, 0, 4, 0, 0, 12, 0, 4, 6, 0, -52, 0, 0, 2, 30, 0, 29, 0, 0, -64, -6, 0, 9, -16, 0, 0, 34, 0, 70, 32, 0, -8, 0, 0, 38, 24, 0, 24, 15, 0, 6, -20, 0, -12, 8, 0, 0, -4, 0, 0, 10, 0, 5, 0, 0, -64, 15, 0, 40, 22, 0, -28, 28, 0, 16, 0, 0, 14, -43, 0, -20, -80, 0, 72, 0, 0, -7, -2, 0, 24, -40, 0, -6, -60, 0, -32, -2, 0, 0, 64, 0, -24, -2, 0, -10, 0, 0, 0, 20, 0, 32, -30, 0, -20, -36, 0, -13, 32, 0, 0, -28, 0, 6, 0, 0, 62, -70, 0, 6, 16, 0, -32, 1, 0, -28, 48, 0, 20, -25, 0, 0, 36, 0, 38, -48, 0, -16, 0, 0, -12, 18, 0, 16, 24, 0, 0, 3, 0, -5, -40, 0, 0, 12, 0, -32, 2, 0, 10, 0, 0, -40, 0, 0, 72, -18, 0, -45, 2, 0, -40, -28, 0, 0, 4, 0, -48, 17, 0, 19, 0, 0, -20, -14, 0, -34, -40, 0, 4, 16, 0, 8, -20, 0, 0, 24, 0, 28, -36, 0, -36, 0, 0, -1, 8, 0, -4, 80, 0, -34, 0, 0, 4, -16, 0, 28, -100, 0, 0, -3, 0, -6, 0, 0, -40, -20, 0, -10, -8, 0, -16, 8, 0, -15, -56, 0, 0, -44, 0, -25, 42, 0, 0, 0, 0, -60, -24, 0, -12, 10, 0, -42, -32, 0, 12, -6, 0, 0, 0, 0, 90, 96, 0, 24, 0, 0, -8, -32, 0, -4, -24, 0, 80, 19, 0, 28, -26, 0, 0, 38, 0, 100, 40, 0, 36, 0, 0, -22, 4, 0, 0, 54, 0, -20, -46, 0, 54, 54, 0, 0, -12, 0, 50, 5, 0, -44, 0, 0, -32, -8, 0, 46, -36, 0, 48, 60, 0, -70, 20, 0, 0, 4, 0, 2, 64, 0, -80, 0, 0, 32, 8, 0, 40, -10, 0, 56, -8, 0, 0, 27, 0, 0, 4, 0, -144, 4, 0, -5, 0, 0, -52, 36, 0, -18, 0, 0, -12, 35, 0, -5, -96, 0, 56, -2, 0, -4, -24, 0, -24, 0, 0, -16, 76, 0, -32, -4, 0, 8, -16, 0, 120, 40, 0, 0, 72, 0, 0, 14, 0, -42, 0, 0, 100, -8, 0, -10, 56, 0, 28, -3, 0, 46, 0, 0, 0, 88, 0, 54, -12, 0, 32, -28, 0, -12, -100, 0, 64, -13, 0, 4, -26, 0, -22, 6, 0, 0, 32, 0, 8, 60, 0, 0, 0, 0, 0, -32, 0, -55, 4, 0, -6, -88, 0, -12, 52, 0, 0, -60, 0, -24, 0, 0, -120, 0, 0, 24, 58, 0, 20, -50, 0, -104, 32, 0, -12, -6, 0, 0, -36, 0, 32, 10, 0, -23, 0, 0, -34, 90, 0, -64, -70, 0, 0, 25, 0, 18, 16, 0, 0, 49, 0, -30, 76, 0, -12, 0, 0, -22, 0, 0, 30, -4, 0, 10, -24, 0, 80, -1, 0, -35, -12, 0, -8, -40, 0, 84, 0, 0, -4, -46, 0, -42, 8, 0, -40, -18, 0, 32, 10, 0, 0, -32, 0, 2, 32, 0, 30, 0, 0, -50, -160, 0, -44, -26, 0, 40, 0, 0, -28, -54, 0, 0, -16, 0, -8, 28, 0, 45, -28, 0, 172, -48, 0, -12, -40, 0, 40, -24, 0, -2, -72, 0, 0, -16, 0, -48, 28, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "405.2.a.a", "char_is_minimal": false, "conrey_index": 136, "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], [1, 0], [-2, 2], [0, 0], [0, -2], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0], [2, 0], [-5, 5], [0, 0], [0, -4], [0, 0], [0, 0], [4, -4], [-4, 0], [0, 0], [-5, 0], [-2, 2], [0, 0], [0, -10], [0, -6], [0, 0], [-1, 1], [8, 0], [0, 0], [0, 0], [5, -5], [0, 0], [0, 9], [0, 8], [0, 0], [8, -8], [0, 0], [0, 0], [-10, 0], [10, -10], [0, 0], [0, 0], [0, -7], [0, 0], [2, -2], [10, 0], [0, 0], [12, 0], [-2, 2], [0, 0], [0, 7], [0, -2], [0, 0], [-8, 8], [8, 0], [0, 0], [5, 0], [0, 0], [0, 0], [0, 10], [0, 1], [0, 0], [2, -2], [-18, 0], [0, 0], [-8, 0], [-4, 4], [0, 0], [0, -6], [0, 8], [0, 0], [0, 0], [1, 0], [0, 0], [-8, 0], [20, -20], [0, 0], [0, 10], [0, 0], [0, 0], [-12, 12], [-4, 0], [0, 0], [14, 0], [-6, 6], [0, 0], [0, 4], [0, 4], [0, 0], [0, 0], [-9, 0], [0, 0], [0, 0], [-12, 12], [0, 0], [0, -4], [0, 5], [0, 0], [-14, 14], [-14, 0], [0, 0], [2, 0]]}