# Stored data for newform 810.2.e.e, downloaded from the LMFDB on 25 April 2024.
{"label": "810.2.e.e", "space_label": "810.2.e", "level": 810, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014673420944170, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 581678144017101898, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [4, 2, 1]], [11, [36, -6, 1]], [13, [16, -4, 1]], [17, [-6, 1]], [23, [0, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}-\\zeta_{6}q^{4}+\\zeta_{6}q^{5}+(-2+\\cdots)q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 3240, "analytic_conductor": 6.467882563723711, "hecke_ring_index": 1, "level_radical": 30, "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": "0.020", "prec": 17}, "analytic_rank_proved": true, "char_values": [810, 3, [731, 487], [1, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [271, 541], "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": "1.992", "prec": 17}, {"__RealLiteral__": 0, "data": "0.096", "prec": 17}, {"__RealLiteral__": 0, "data": "11.967", "prec": 20}, {"__RealLiteral__": 0, "data": "3.260", "prec": 17}, {"__RealLiteral__": 0, "data": "109.543", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, 0, 1, -2], "traces": [0, 2, -1, 0, -1, 1, 0, -2, 2, 0, -2, 6, 0, 4, -2, 0, -1, 12, 0, -8, 1, 0, 6, 0, 0, -1, -8, 0, 4, -6, 0, 4, -1, 0, -6, -4, 0, 16, 4, 0, 1, 0, 0, -8, -12, 0, 0, 0, 0, 3, -1, 0, 4, 12, 0, 12, -2, 0, -6, 6, 0, -2, -8, 0, 2, -4, 0, 4, -6, 0, 2, 24, 0, -20, -8, 0, 4, 12, 0, 4, -2, 0, 0, 12, 0, 6, -8, 0, 6, -24, 0, -16, 0, 0, 0, -4, 0, -2, -6, 0, 2, -6, 0, -2, 4, 0, -6, -24, 0, 4, -6, 0, -2, 6, 0, 0, 12, 0, -12, -12, 0, -25, -2, 0, 4, -2, 0, 4, -1, 0, -4, -6, 0, 8, -8, 0, 12, 6, 0, -20, 2, 0, -12, 48, 0, -12, 10, 0, -8, 6, 0, 16, -8, 0, -24, -4, 0, 4, 4, 0, 1, 0, 0, 40, 0, 0, 12, -24, 0, -3, -12, 0, 16, 18, 0, -2, 6, 0, 12, -12, 0, 4, 8, 0, 0, 8, 0, 36, 0, 0, 8, 12, 0, 10, -2, 0, 3, 36, 0, -32, -1, 0, -6, -12, 0, 0, 4, 0, -8, -24, 0, 4, -6, 0, 12, -16, 0, -16, -2, 0, -6, 24, 0, -26, 4, 0, -12, 0, 0, -14, 0, 0, -6, 12, 0, 0, 6, 0, -12, -12, 0, 10, 50, 0, 4, -3, 0, -16, 4, 0, 1, -36, 0, 0, -2, 0, -1, 6, 0, -16, 8, 0, 12, 24, 0, 6, 8, 0, 4, -36, 0, 16, -6, 0, 6, 6, 0, -8, 40, 0, -4, 12, 0, 4, -12, 0, -24, 0, 0, 38, 6, 0, 10, -18, 0, -6, 16, 0, -12, 0, 0, -16, 16, 0, 4, -4, 0, -32, 12, 0, -4, -12, 0, 10, -8, 0, -8, -18, 0, 36, 1, 0, 0, -48, 0, -8, -20, 0, 0, 0, 0, 4, -24, 0, 48, -4, 0, -14, -3, 0, 6, 48, 0, -40, -8, 0, 18, 0, 0, 22, 4, 0, -12, -30, 0, 12, 12, 0, 6, -48, 0, -6, -2, 0, 8, -10, 0, -26, 0, 0, -16, -12, 0, 28, 36, 0, 0, -48, 0, 40, -4, 0, 12, 0, 0, -12, -20, 0, 4, -18, 0, 0, 3, 0, -18, 8, 0, -32, 16, 0, -1, -36, 0, -16, 12, 0, 24, 48, 0, 22, 0, 0, -2, -24, 0, 24, 4, 0, -24, -6, 0, -14, -8, 0, 12, -6, 0, -4, 12, 0, 8, 0, 0, 76, 8, 0, -2, 0, 0, -8, 12, 0, -48, -24, 0, -12, -26, 0, -2, 24, 0, 0, 6, 0, 0, -8, 0, -26, 28, 0, 0, -18, 0, 34, -6, 0, -6, 24, 0, -16, 0, 0, 6, 48, 0, 4, 24, 0, 24, 36, 0, 32, 10, 0, -25, -4, 0, 76, -2, 0, -3, -6, 0, -36, 32, 0, -8, -24, 0, 4, 1, 0, 18, 0, 0, -12, 0, 0, -2, 18, 0, 20, 2, 0, -12, 2, 0, 0, -16, 0, -4, -24, 0, -8, -6, 0, 24, 24, 0, 23, -12, 0, -16, 0, 0, -12, 4, 0, 18, 36, 0, -44, -8, 0, -6, 2, 0, 40, -12, 0, -12, 24, 0, 8, -8, 0, -20, -84, 0, -64, 2, 0, 12, -24, 0, -6, -8, 0, 24, 36, 0, -44, -24, 0, 0, 0, 0, -44, -19, 0, 6, 24, 0, 36, -20, 0, 36, -36, 0, -16, -6, 0, -8, 36, 0, -24, 6, 0, 0, -24, 0, 10, 32, 0, -32, 25, 0, -38, 4, 0, 2, 0, 0, 16, 16, 0, 12, -30, 0, -20, 8, 0, 24, 24, 0, -1, 10, 0, 4, 96, 0, 40, 4, 0, -18, 2, 0, -12, -72, 0, -2, 24, 0, 4, 0, 0, 24, 96, 0, 72, 4, 0, -20, -18, 0, 6, 0, 0, 0, -30, 0, -2, 4, 0, 12, 16, 0, 0, -24, 0, -4, 12, 0, -14, 28, 0, 6, 6, 0, -4, 6, 0, -24, -24, 0, 12, 20, 0, -8, 24, 0, -44, -36, 0, 0, 20, 0, 0, 22, 0, -2, -84, 0, -64, 6, 0, -30, -12, 0, 34, -24, 0, -24, 0, 0, 24, 6, 0, 24, 48, 0, 8, 3, 0, -2, -6, 0, 10, -16, 0, 20, -48, 0, -32, -26, 0, 0, 48, 0, 40, 8, 0, -12, 0, 0, -6, -56, 0, -72, 24, 0, -20, 0, 0, 24, 32, 0, -80, -20, 0, -4, 36, 0, -4, -24, 0, 0, -24, 0, -14, -12, 0, 10, -12, 0, -8, -2, 0, -18, 0, 0, 72, 0, 0, -6, -4, 0, 28, -18, 0, -4, -24, 0, -16, 16, 0, 16, 18, 0, 0, 2, 0, 72, -60, 0, 0, -16, 0, -6, 48, 0, -104, -12, 0, 48, 20, 0, 32, -44, 0, 0, -30, 0, -14, -2, 0, 12, -48, 0, 52, -12, 0, 4, 18, 0, 24, 48, 0, 12, 48, 0, -7, -14, 0, 4, -6, 0, 100, -6, 0, -6, 0, 0, -8, 8, 0, -24, 42, 0, -20, 8, 0, 0, -48, 0, 36, -38, 0, 8, -24, 0, -16, 4, 0, 0, 2, 0, 28, -8, 0, -6, 72, 0, -8, 24, 0, -24, 48, 0, -4, 24, 0, 52, 0, 0, -6, -2, 0, -12, -48, 0, 72, 0, 0, 6, 2, 0, 40, 0, 0, 16, 0, 0, -72, -26, 0, -14, 24, 0, -104, 0, 0, -18, 48, 0, -8, -68, 0, 12, 36, 0, -12, -6, 0, -12, 72, 0, -44, 8, 0, 0, -42, 0, 0, -12, 0, -96, 24, 0, -40, 4, 0, -12, -60, 0, 24, -12, 0, 36, 12, 0, 15, -64, 0, -20, -10, 0, -2, -25, 0, 2, 12, 0, 80, -38, 0, -2, -6, 0, -72, 6, 0, 12, -48, 0, 18, -36, 0, -16, 0, 0, 64, 4, 0, -24, -16, 0, -44, -8, 0, -2], "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": "90.2.a.a", "char_is_minimal": false, "conrey_index": 271, "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], [-1, 1], [0, 0], [0, -1], [0, 1], [0, 0], [-2, 2], [1, 0], [0, 0], [-1, 0], [6, -6], [0, 0], [0, 4], [0, -2], [0, 0], [-1, 1], [6, 0], [0, 0], [-4, 0], [1, -1], [0, 0], [0, 6], [0, 0], [0, 0], [-1, 1], [-4, 0], [0, 0], [2, 0], [-6, 6], [0, 0], [0, 4], [0, -1], [0, 0], [-6, 6], [-2, 0], [0, 0], [8, 0], [4, -4], [0, 0], [0, 1], [0, 0], [0, 0], [-8, 8], [-6, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 3], [0, -1], [0, 0], [4, -4], [6, 0], [0, 0], [6, 0], [-2, 2], [0, 0], [0, -6], [0, 6], [0, 0], [-2, 2], [-4, 0], [0, 0], [1, 0], [-4, 4], [0, 0], [0, 4], [0, -6], [0, 0], [2, -2], [12, 0], [0, 0], [-10, 0], [-8, 8], [0, 0], [0, 4], [0, 12], [0, 0], [4, -4], [-1, 0], [0, 0], [0, 0], [12, -12], [0, 0], [0, 6], [0, -8], [0, 0], [6, -6], [-12, 0], [0, 0], [-8, 0], [0, 0], [0, 0], [0, 0], [0, -4], [0, 0], [-2, 2], [-3, 0], [0, 0], [1, 0]]}