# Stored data for newform 819.2.a.i, downloaded from the LMFDB on 18 April 2024.
{"label": "819.2.a.i", "space_label": "819.2.a", "level": 819, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36028797052519219, "dim": 3, "is_polredabs": true, "nf_label": "3.3.316.1", "trace_hash": 1031476025559212698, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-2, -4, 1, 1]], [5, [-2, -3, 2, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(1+\\beta _{2})q^{4}+(-1+\\beta _{1})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3276, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 6.539747925542864, "hecke_ring_index": 1, "level_radical": 273, "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [819, 1, [92, 703, 379], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 7, 13], "conrey_indexes": [1], "field_disc": 316, "field_disc_factorization": [[2, 2], [79, 1]], "field_poly": [2, -4, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.856", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "20.407", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "215.130", "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], [7, 1], [13, -1]], "trace_display": [-1, 0, -2, -3], "traces": [0, 3, -1, 0, 3, -2, 0, -3, -3, 0, -8, -2, 0, 3, 1, 0, -1, -4, 0, -4, 2, 0, -4, -10, 0, -5, -1, 0, -3, -24, 0, -4, -7, 0, 14, 2, 0, 0, 10, 0, -2, -2, 0, 10, -12, 0, -18, 8, 0, 3, 15, 0, 3, -8, 0, 6, 3, 0, 12, 4, 0, -6, 2, 0, -17, -2, 0, -12, -22, 0, 8, 6, 0, -10, -30, 0, -8, 2, 0, -14, 14, 0, 10, 12, 0, -10, 26, 0, 12, -2, 0, -3, 12, 0, -10, -6, 0, -10, -1, 0, 1, -32, 0, -16, -3, 0, 8, 0, 0, 0, 20, 0, 1, -12, 0, 28, -38, 0, 32, 4, 0, -17, 2, 0, 20, 0, 0, 0, 41, 0, -8, -16, 0, 4, 40, 0, 22, 8, 0, -18, -2, 0, 20, -2, 0, 12, 28, 0, 26, -20, 0, 10, 8, 0, 4, 2, 0, 4, -26, 0, 26, 10, 0, 0, 18, 0, -66, 16, 0, 3, 16, 0, -40, -8, 0, 5, 20, 0, 36, -34, 0, 24, 1, 0, -12, 30, 0, 8, 60, 0, 6, 4, 0, -22, 12, 0, 3, -2, 0, 6, -1, 0, 6, 24, 0, -8, 24, 0, -1, -2, 0, 2, 26, 0, 8, -36, 0, 4, 38, 0, 8, -4, 0, -20, 7, 0, 24, 32, 0, -10, 26, 0, 38, -32, 0, 2, -60, 0, -14, 28, 0, 6, 23, 0, -6, -2, 0, -4, -20, 0, 34, 26, 0, 6, -52, 0, -1, 12, 0, 0, 2, 0, -20, 6, 0, 0, -10, 0, 20, -2, 0, 64, -6, 0, -14, -16, 0, -4, -32, 0, 2, 0, 0, 0, 8, 0, -4, 2, 0, -15, 74, 0, -70, 18, 0, -36, -26, 0, -6, -10, 0, -10, -60, 0, -12, 4, 0, 60, 12, 0, -14, -18, 0, -36, -74, 0, -12, -30, 0, 26, -10, 0, 18, 18, 0, -5, -44, 0, -18, -8, 0, 8, -8, 0, 2, -28, 0, -12, -1, 0, -28, -22, 0, -3, 40, 0, -22, -28, 0, -2, -15, 0, 4, 62, 0, -26, 6, 0, 86, -6, 0, -43, -22, 0, -3, -18, 0, 18, 24, 0, 4, 8, 0, 14, -20, 0, -60, -24, 0, -2, -20, 0, -28, 52, 0, -6, -2, 0, -14, -10, 0, -30, -3, 0, 38, 40, 0, -38, 72, 0, -31, 6, 0, -4, -42, 0, -12, 4, 0, 2, -24, 0, 24, -4, 0, 54, -7, 0, -12, 14, 0, -12, -58, 0, -26, 14, 0, 6, -28, 0, -6, -68, 0, 10, -2, 0, -54, -8, 0, 48, -8, 0, 14, -42, 0, -34, 22, 0, 17, 34, 0, -28, -82, 0, -36, 2, 0, -64, -58, 0, 36, -78, 0, 18, 14, 0, 24, 54, 0, 12, -66, 0, 60, 14, 0, 20, 22, 0, 0, 16, 0, 0, 24, 0, -25, -2, 0, 72, 6, 0, -8, -20, 0, 50, 10, 0, -24, -6, 0, -22, -40, 0, 48, 52, 0, 26, 56, 0, 24, -74, 0, 10, 9, 0, -78, -8, 0, -50, 30, 0, -2, -50, 0, 24, 20, 0, 46, -18, 0, 29, -18, 0, 8, -2, 0, -8, -20, 0, -70, -2, 0, -12, -56, 0, -34, -38, 0, -38, 74, 0, -20, 36, 0, 14, 24, 0, 36, 42, 0, 10, -14, 0, -82, 100, 0, -12, 76, 0, -8, 4, 0, -50, -12, 0, -10, -4, 0, 46, -63, 0, -24, -12, 0, -34, 70, 0, -4, 0, 0, 6, 20, 0, 34, 30, 0, 10, -2, 0, -18, 54, 0, 54, -26, 0, 24, -6, 0, 58, -12, 0, 16, 8, 0, -26, -46, 0, -12, 26, 0, -4, -4, 0, 44, 2, 0, -9, -18, 0, 74, -56, 0, -76, 12, 0, 2, 52, 0, 3, 24, 0, -6, 20, 0, 0, -12, 0, -44, -10, 0, 28, 15, 0, -4, -26, 0, 36, -38, 0, 10, 10, 0, -10, -32, 0, 8, 6, 0, 58, -36, 0, -36, 4, 0, 28, 104, 0, 3, -32, 0, 10, 28, 0, 4, 48, 0, 6, 1, 0, -12, -8, 0, 32, -106, 0, -76, 50, 0, -8, 32, 0, -1, -44, 0, -30, 12, 0, 22, 32, 0, 8, -40, 0, -6, 36, 0, 6, -32, 0, 12, 30, 0, 16, -7, 0, -6, 34, 0, -68, 3, 0, 62, 66, 0, 38, 44, 0, 88, -60, 0, -46, 60, 0, -8, -40, 0, 26, -10, 0, 16, 0, 0, 18, -40, 0, 12, 50, 0, -28, 52, 0, 20, -10, 0, 0, -8, 0, 8, 4, 0, 6, -20, 0, -42, 34, 0, 32, 14, 0, 42, 12, 0, -28, 40, 0, -1, 70, 0, 72, 78, 0, 66, 12, 0, -6, -48, 0, -16, -34, 0, -70, -9, 0, -10, 42, 0, -28, 2, 0, 42, 56, 0, 92, 38, 0, 60, 44, 0, 16, 68, 0, -20, -30, 0, 28, -24, 0, -32, 8, 0, -60, 50, 0, -17, -4, 0, -18, 16, 0, -40, 28, 0, 119, -38, 0, -8, -2, 0, 17, -42, 0, -38, 86, 0, 14, -2, 0, 28, 22, 0, -24, -52, 0, -20, 40, 0, 30, -62, 0, -20, 38, 0, -12, 54, 0, 10, 0, 0, -52, -12, 0, -48, -34, 0, -76, -22, 0, 34, 100, 0, 0, -38, 0, -100, -18, 0, -52, -41, 0, 22, 8, 0, -18, -16, 0, 82, -2, 0, 58, 68, 0, 8, -82, 0, 74, 14, 0, -6, 16, 0, 32, -36, 0, 70, 6, 0, -34, 24, 0, 34, 58, 0, -4, -26, 0, 64, 12, 0, -32, -40, 0, 20, -98, 0, 8, -4, 0, -72, -68, 0, -10, -24, 0, -22, -56, 0, 24, 48, 0, -34, -8, 0, -39, -30, 0, -6, 24, 0, 34, 25, 0, 22, 36, 0, 18, -76, 0, 2, 4, 0, -42, 2, 0, -8, -60, 0, -36, -148, 0, -8, -142, 0, 48, 32, 0, -20, -78, 0, -86, 32, 0, 40], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "91.2.a.d", "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], [0, 0, 0], [1, 0, 1], [-1, 1, 0], [0, 0, 0], [-1, 0, 0], [-1, 0, -1], [0, 0, 0], [-3, 1, -1], [-1, 1, -1], [0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0], [-1, 2, -1], [-1, -1, -1], [0, 0, 0], [-1, -1, 0], [0, 2, 0], [0, 0, 0], [-2, 2, 0], [-4, 2, 1], [0, 0, 0], [-1, -2, 1], [0, -1, 0], [0, 0, 0], [-1, 0, -1], [-8, 0, -1], [0, 0, 0], [-1, -1, 2], [-3, 2, 1], [0, 0, 0], [4, 2, 2], [1, -1, 0], [0, 0, 0], [-1, 3, 1], [3, 1, 1], [0, 0, 0], [0, -2, 0], [0, -2, 2], [0, 0, 0], [4, -2, -3], [-4, 0, 0], [0, 0, 0], [-7, 3, -3], [3, -1, 4], [0, 0, 0], [1, 0, 0], [5, 0, 1], [0, 0, 0], [1, 0, 1], [-2, -2, 3], [0, 0, 0], [3, -3, 1], [1, 0, 1], [0, 0, 0], [1, 9, 1], [2, -2, -4], [0, 0, 0], [-2, 0, 0], [1, -1, -1], [0, 0, 0], [-5, -2, -1], [-1, 1, 0], [0, 0, 0], [-2, -6, 4], [-6, -4, -2], [0, 0, 0], [3, -1, 1], [3, -3, 1], [0, 0, 0], [-3, -1, -4], [-10, 0, -4], [0, 0, 0], [-2, -2, -2], [1, -1, 1], [0, 0, 0], [-6, 4, -1], [6, -4, 2], [0, 0, 0], [4, -2, 0], [1, 9, -4], [0, 0, 0], [-3, -1, -1], [9, -1, 5], [0, 0, 0], [4, 0, 0], [1, -5, 2], [0, 0, 0], [-1, 0, 0], [2, 6, -2], [0, 0, 0], [-1, -7, -3], [-2, 0, -1], [0, 0, 0], [-3, -1, 0], [0, -1, 0], [0, 0, 0], [1, -2, -3]]}