# Stored data for newform 990.2.n.i, downloaded from the LMFDB on 19 April 2024.
{"label": "990.2.n.i", "space_label": "990.2.n", "level": 990, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029690405716958, "dim": 8, "is_polredabs": true, "nf_label": "8.0.2769390625.1", "trace_hash": 1064467764780087237, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [13456, 7192, 808, -896, 505, -76, 38, -3, 1]], [13, [14641, 7381, -898, -2097, 1505, -123, 62, -1, 1]], [17, [256, -192, 608, -1104, 1105, 276, 38, 3, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+(-1-\\beta _{2}+\\beta _{3}-\\beta _{5})q^{4}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "n", "char_is_real": false, "Nk2": 3960, "analytic_conductor": 7.905189800106758, "hecke_ring_index": 1, "level_radical": 330, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [990, 5, [551, 397, 541], [5, 5, 4]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 5, 11], "conrey_indexes": [91, 181, 361, 631], "field_disc": 2769390625, "field_disc_factorization": [[5, 6], [421, 2]], "field_poly": [841, -87, -198, 75, 21, 5, -2, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "8.026", "prec": 17}, {"__RealLiteral__": 0, "data": "1.804", "prec": 17}, {"__RealLiteral__": 0, "data": "204.852", "prec": 24}, {"__RealLiteral__": 0, "data": "211.707", "prec": 24}, {"__RealLiteral__": 0, "data": "9031.717", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c5", "trace_display": [-2, 0, -2, 3], "traces": [0, 8, -2, 0, -2, -2, 0, 3, -2, 0, 8, -10, 0, 1, 3, 0, -2, -3, 0, -12, -2, 0, 10, 0, 0, -2, 1, 0, -2, -27, 0, -6, 8, 0, 22, -2, 0, -4, 13, 0, -2, 23, 0, -2, -10, 0, -5, -5, 0, -53, -2, 0, 1, 18, 0, 5, -2, 0, -27, 40, 0, -20, -11, 0, -2, -4, 0, 18, -3, 0, 3, 10, 0, 36, -4, 0, -2, -50, 0, -11, -2, 0, -12, -16, 0, -8, 13, 0, 5, 46, 0, -39, 5, 0, 15, -12, 0, 16, 62, 0, 8, -59, 0, -12, 1, 0, -7, 16, 0, 0, -10, 0, -2, 9, 0, -5, 18, 0, 40, 52, 0, 42, 20, 0, -11, -2, 0, 25, -2, 0, 1, -70, 0, 8, 8, 0, -8, -8, 0, 53, 3, 0, -20, -5, 0, 18, 36, 0, -4, -37, 0, -6, 13, 0, 10, 34, 0, -44, 4, 0, -2, -60, 0, 33, -22, 0, 64, -25, 0, -97, -3, 0, -12, -29, 0, -2, 5, 0, -24, -62, 0, -48, -9, 0, 5, -4, 0, 60, -20, 0, -12, 32, 0, 34, -14, 0, -53, 38, 0, 34, -2, 0, 56, -72, 0, 23, -12, 0, -4, 40, 0, 0, -7, 0, 26, 13, 0, 24, 40, 0, 10, 64, 0, -5, 3, 0, -6, -14, 0, 0, 0, 0, 18, -6, 0, -5, -30, 0, -38, -12, 0, 86, -33, 0, -20, 22, 0, -54, -6, 0, -2, 37, 0, -20, -30, 0, -2, -16, 0, 111, 1, 0, -10, 20, 0, -22, -57, 0, -17, -12, 0, -18, -8, 0, 22, 5, 0, -9, 53, 0, -2, 36, 0, 11, 10, 0, -80, 178, 0, -33, -27, 0, -44, 13, 0, -30, 16, 0, 58, 60, 0, -42, -26, 0, -12, 10, 0, -130, -10, 0, -6, -40, 0, -34, 16, 0, 4, 61, 0, -25, 8, 0, -60, 2, 0, 1, -42, 0, -12, -100, 0, 106, -16, 0, 35, 8, 0, -12, -97, 0, 22, 35, 0, -59, -12, 0, 16, 34, 0, 50, -2, 0, -10, -18, 0, 0, 1, 0, 28, 72, 0, 6, 112, 0, 96, -44, 0, 66, -5, 0, -4, -12, 0, 38, 15, 0, 15, -24, 0, -92, 13, 0, 32, 40, 0, 5, 44, 0, -14, 98, 0, -80, 22, 0, -22, 14, 0, -96, -11, 0, -2, -97, 0, -32, 56, 0, 88, -95, 0, -37, 23, 0, -17, 5, 0, -16, 1, 0, -55, -40, 0, 10, -10, 0, 18, -8, 0, 130, -84, 0, -2, 80, 0, 18, -76, 0, -40, -5, 0, 34, -10, 0, 49, -26, 0, -24, -10, 0, 3, 33, 0, 100, -6, 0, -14, -39, 0, 68, -10, 0, -5, -90, 0, -42, 18, 0, 29, 38, 0, 98, -5, 0, -20, 65, 0, 13, -38, 0, 8, -98, 0, -168, -4, 0, -18, -4, 0, -4, 10, 0, -53, 73, 0, 107, -74, 0, 34, -110, 0, -27, -2, 0, -33, -17, 0, 6, 15, 0, 25, -97, 0, -4, -2, 0, -16, -17, 0, 20, -44, 0, 1, 21, 0, -40, 45, 0, -50, 76, 0, 76, 18, 0, 53, -99, 0, 16, -17, 0, -2, 10, 0, 90, -18, 0, -3, 40, 0, 11, -8, 0, 5, 128, 0, 144, -29, 0, -62, 66, 0, 41, -2, 0, -24, 66, 0, 9, -14, 0, 0, -79, 0, 70, -40, 0, -177, 5, 0, -24, 22, 0, -27, -16, 0, -65, 16, 0, 13, -24, 0, -6, 40, 0, -4, 10, 0, -28, -37, 0, -50, -78, 0, -16, -42, 0, 64, 42, 0, 18, -12, 0, -20, -45, 0, -104, 0, 0, 45, 160, 0, 2, -11, 0, 10, 96, 0, -2, 36, 0, 56, -26, 0, 81, -11, 0, -104, -10, 0, -106, 10, 0, -2, -60, 0, 28, 125, 0, 2, -57, 0, -45, -4, 0, -42, -24, 0, -10, 23, 0, 15, 66, 0, -28, -29, 0, -16, -57, 0, -35, 35, 0, 18, 40, 0, -82, -12, 0, 63, 108, 0, -14, -3, 0, -85, -24, 0, -3, 31, 0, 13, 41, 0, 92, 26, 0, -36, -62, 0, 102, -10, 0, 3, -42, 0, -194, 10, 0, 17, -74, 0, 4, 10, 0, 1, 105, 0, 90, 68, 0, 72, 120, 0, -187, -9, 0, -48, 18, 0, -114, -9, 0, 36, 22, 0, 4, 66, 0, 0, -120, 0, -26, -4, 0, 73, 132, 0, 8, -47, 0, 20, -24, 0, 70, -5, 0, -19, -6, 0, 91, 18, 0, -2, 16, 0, 20, -8, 0, -20, -20, 0, 36, -50, 0, 34, -1, 0, -6, 16, 0, 98, -87, 0, -110, 110, 0, 22, -44, 0, 73, 3, 0, -11, 124, 0, -200, 89, 0, -6, -105, 0, 75, -2, 0, 18, -100, 0, 125, -32, 0, -59, -3, 0, -7, -72, 0, -85, 18, 0, 28, 33, 0, -12, -44, 0, 15, 58, 0, 40, -126, 0, -46, -16, 0, 1, 88, 0, -20, -10, 0, 0, -72, 0, 31, -30, 0, -10, 63, 0, 42, -22, 0, -8, 30, 0, -8, -20, 0, 26, -126, 0, 38, 13, 0, -10, -42, 0, -29, 18, 0, 104, 40, 0, -89, -40, 0, 75, -2, 0, 36, -16, 0, 5, 122, 0, 58, -81, 0, 44, 15, 0, 45, 46, 0, 30, 0, 0, -62, -2, 0, -42, -116, 0, -28, -110, 0, -6, -8, 0, 97, 36, 0, -39, -66, 0, 40, 108, 0, -10, -30, 0, 57, 5, 0, 15, -140, 0, 16, 73, 0, -27, 8, 0, -93, 29, 0, 28, -35, 0, -22, 98, 0, 15, -44, 0, -100, -30, 0, -40, 72, 0, -18, -12, 0, 52, 62, 0, -8, 8, 0, 72, 42, 0, 14, 97, 0, -39, -56, 0, -222, -33, 0, 16, -27, 0, 63, 56, 0, 10, -64, 0, -205, 62, 0, 73, -63, 0, -22, -133, 0, -54, 90, 0, 62, -6, 0, 90, -11, 0, 128, -27, 0, 8], "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, 11, 3, 1, 5, 0]], "char_orbit_index": 14, "prim_orbit_index": 3, "minimal_twist": "330.2.m.f", "char_is_minimal": true, "conrey_index": 91, "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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 1, 2, 1], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 0, -2, -1, 0, -2], [1, -1, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 3, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, -3, 2, -1, -1, -1, -2], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, -1, -2, 0, -1], [0, 2, 0, -1, -2, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, -2, 0, -1, 0, 1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 1], [-5, -1, 0, 0, 1, -4, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 4, 0, -2, -1, -1, -1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 2, 1, 0, -1, 0, -1, -1], [0, 1, 0, -1, -2, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, -3, 1, -2, -2, 0, 0], [2, 0, 0, -3, -1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 1, 0, -1, 0, 0], [3, 1, 2, 2, -2, -2, -3, -4], [0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 3, 0, -1, 2, -1, -1], [0, -1, 2, -2, 0, 2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 0, 2, 1, 2, 0], [-3, 2, -2, 4, -1, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 7, -1, 4, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 0, 0, 1, 1, 0, 2], [0, -1, -4, 3, 2, -2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 2, -2, 0, 0, -1, 0], [-1, 0, -1, 1, 1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, -5, 0, 0, 0, -1, 0], [6, 0, -1, 1, 0, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -2, -2, 4, 0, 0, 0, -2], [-5, -1, -4, 4, 1, -4, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [-1, 2, 0, 1, 0, -1, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 2, -1, 1, 4, 2, 3], [-1, 0, 2, 1, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 1, 2, 1], [0, 0, 0, -2, -2, -2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -6, 6, 0, 2, 0, 0], [1, -2, 1, -3, 2, 2, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 2, 0, 1, 3, 1, 1], [-8, 3, -3, 4, -4, -4, -4, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 4, -3, 0, 3, -3, 3], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, 1, 2, -2, -4, 2, 1], [0, 0, 0, 0, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -3, 1, 1, 1, 2], [-1, 0, -2, 3, 0, -3, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -2, 2, 1, 0, 0, 1], [5, -4, -3, -1, 1, -1, 2, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, -3, -10, -1, -1, 0, -2], [1, 0, -1, 0, -2, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, -2, -1, -2, 1, -1], [-1, 1, 2, -1, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -2, 4, 4, -2, 2, 2], [4, -2, -8, 0, 1, -7, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0]]}