# Stored data for newform 990.2.n.b, downloaded from the LMFDB on 15 September 2025.
{"Nk2": 3960, "analytic_conductor": 7.905189800106758, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 11, "char_degree": 4, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 14, "char_orbit_label": "n", "char_order": 5, "char_parity": 1, "char_values": [990, 5, [551, 397, 541], [5, 5, 4]], "cm_discs": [], "conrey_index": 91, "dim": 4, "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 10, "has_non_self_twist": 1, "hecke_cutters": [[7, [0, 1]], [13, [25, -25, 10, 0, 1]], [17, [1, -2, 4, -3, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504493014123486, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 3, 1, 5, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "990.2.n.b", "level": 990, "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": false, "level_primes": [2, 3, 5, 11], "level_radical": 330, "minimal_twist": "990.2.n.b", "nf_label": "4.0.125.1", "prim_orbit_index": 3, "qexp_display": "q+(-1+\\zeta_{10}-\\zeta_{10}^{2}+\\zeta_{10}^{3})q^{2}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c5", "self_twist_discs": [], "self_twist_type": 0, "space_label": "990.2.n", "trace_display": [-1, 0, -1, 0], "trace_hash": 1464268970480218175, "trace_moments": [{"__RealLiteral__": 0, "data": "0.005", "prec": 17}, {"__RealLiteral__": 0, "data": "3.949", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "43.855", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "861.958", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, "traces": [0, 4, -1, 0, -1, -1, 0, 0, -1, 0, 4, -1, 0, 0, 0, 0, -1, 3, 0, -2, -1, 0, 9, -6, 0, -1, 5, 0, 0, 3, 0, 0, 4, 0, -2, 0, 0, -4, -2, 0, -1, 18, 0, 2, -1, 0, 9, 17, 0, 7, -1, 0, 5, -22, 0, 4, 0, 0, 3, 12, 0, 16, 15, 0, -1, -10, 0, -46, 3, 0, 0, 22, 0, 0, -4, 0, 8, 0, 0, -19, -1, 0, -12, -2, 0, -2, 7, 0, -11, 0, 0, 0, -6, 0, -8, -2, 0, -12, -28, 0, 4, 15, 0, -12, 0, 0, 18, -26, 0, 4, -1, 0, 0, -13, 0, 9, 8, 0, 12, 0, 0, 19, -4, 0, 15, -1, 0, -26, -1, 0, 0, -6, 0, 0, 14, 0, -2, 2, 0, -16, 0, 0, -8, -25, 0, 8, 0, 0, 11, -11, 0, -20, -2, 0, 0, -30, 0, 43, 6, 0, -1, 0, 0, -29, -12, 0, -12, 32, 0, -7, 3, 0, -8, -12, 0, 0, 4, 0, 10, 17, 0, 48, 0, 0, -6, 11, 0, -12, -18, 0, -2, 16, 0, -18, -2, 0, 7, 8, 0, -58, -1, 0, -20, 0, 0, 18, -12, 0, -10, -22, 0, 18, 18, 0, 14, 7, 0, 0, 14, 0, 9, 0, 0, -10, 0, 0, 22, -20, 0, -16, -6, 0, -22, -2, 0, 17, -3, 0, 0, 4, 0, 72, 19, 0, 16, 7, 0, 0, 0, 0, -1, -17, 0, 39, -16, 0, -1, -14, 0, 0, 5, 0, -6, 10, 0, 8, 0, 0, 9, 44, 0, 26, -2, 0, 2, -11, 0, 13, -16, 0, 0, 32, 0, 15, 22, 0, 5, 0, 0, 18, 3, 0, 0, 16, 0, -3, -14, 0, -26, -15, 0, 0, 0, 0, -2, -14, 0, -38, 0, 0, 0, 2, 0, 44, -32, 0, 6, -22, 0, 3, 4, 0, 0, -4, 0, 0, 36, 0, -12, 0, 0, -72, -2, 0, -23, 14, 0, -4, -7, 0, -2, -75, 0, 0, -8, 0, 18, -12, 0, 66, 0, 0, -1, 66, 0, -18, -10, 0, -18, -44, 0, 15, -12, 0, 0, 0, 0, -42, 9, 0, -4, 0, 0, -8, 13, 0, -8, -20, 0, 0, -2, 0, 16, -28, 0, 0, -48, 0, -2, 40, 0, -12, 7, 0, -52, 26, 0, -62, 27, 0, -1, -12, 0, -60, -20, 0, 0, -4, 0, 54, 18, 0, 18, 0, 0, 8, 0, 0, 8, 18, 0, 60, 18, 0, -22, -2, 0, 0, 24, 0, 2, -60, 0, 34, 0, 0, -16, -12, 0, -22, -1, 0, -5, 54, 0, 10, 20, 0, 0, -52, 0, 48, -18, 0, -20, 0, 0, -14, 24, 0, 9, -18, 0, 24, 8, 0, -7, 18, 0, 0, 17, 0, -18, 37, 0, -2, 0, 0, 14, 18, 0, 5, -18, 0, -1, 28, 0, -26, -14, 0, 7, 49, 0, -19, -20, 0, -30, 0, 0, -32, -1, 0, 8, 53, 0, 10, -6, 0, -26, 59, 0, 0, -1, 0, -14, 18, 0, 62, 0, 0, 5, 8, 0, -60, 9, 0, -35, 0, 0, -38, -22, 0, 0, 30, 0, -26, 9, 0, 14, -28, 0, 26, 26, 0, 3, 14, 0, 9, 2, 0, 4, -44, 0, 0, -32, 0, -6, -34, 0, -15, 0, 0, -28, 18, 0, -13, -10, 0, -18, 20, 0, -60, 30, 0, 0, -6, 0, 50, 13, 0, 3, 0, 0, -2, 0, 0, 16, -60, 0, 0, 12, 0, 11, 54, 0, 0, -11, 0, 15, -10, 0, -30, 0, 0, 40, -41, 0, 2, -2, 0, 16, 25, 0, 50, 62, 0, 0, 88, 0, 40, 15, 0, 42, 0, 0, -1, -76, 0, -22, -18, 0, -31, -19, 0, -2, 34, 0, 70, 58, 0, -1, -62, 0, 54, 0, 0, -4, -41, 0, 12, -10, 0, 36, 14, 0, -6, 18, 0, 0, 104, 0, -56, -12, 0, 8, 0, 0, 33, -23, 0, -46, -64, 0, 34, -4, 0, 18, -84, 0, 0, 3, 0, 15, 20, 0, -3, 0, 0, 7, -50, 0, -6, -12, 0, -12, -6, 0, 6, -44, 0, 0, 46, 0, -28, 9, 0, 21, 0, 0, 54, 22, 0, -10, -45, 0, -10, 2, 0, -44, -38, 0, 0, 15, 0, 48, -22, 0, 8, 0, 0, 0, -6, 0, 40, -42, 0, -6, 24, 0, 0, -4, 0, 0, 76, 0, 24, 62, 0, -2, 0, 0, 46, 17, 0, -5, -20, 0, -12, -40, 0, 8, -12, 0, 0, -24, 0, -3, -45, 0, -50, 0, 0, -18, -56, 0, 0, -12, 0, 40, -24, 0, -88, 18, 0, 7, 43, 0, -3, 48, 0, -19, 0, 0, -20, 23, 0, 2, -28, 0, 9, -1, 0, -72, 0, 0, 0, -60, 0, 15, -82, 0, 30, 0, 0, 31, -14, 0, -16, -41, 0, -12, -94, 0, -62, -12, 0, 0, 70, 0, 62, -2, 0, 5, 14, 0, -18, -2, 0, 43, 54, 0, -30, -50, 0, 18, 18, 0, 0, 8, 0, -2, 21, 0, 42, 0, 0, 14, 102, 0, -44, 7, 0, 20, -39, 0, -12, 34, 0, 0, 46, 0, -5, -16, 0, 18, 0, 0, -40, 48, 0, -11, -28, 0, -44, 5, 0, -56, -30, 0, 0, 0, 0, -20, -16, 0, 17, 0, 0, 28, -60, 0, -44, 48, 0, 22, -42, 0, 51, -10, 0, 0, 82, 0, 8, -44, 0, 24, 0, 0, 31, -6, 0, 17, -20, 0, -14, 24, 0, 3, 30, 0, 14, -7, 0, 88, 3, 0, 98, 0, 0, -8, 116, 0, 18, -3, 0, 12, 24, 0, 0, -2, 0, 0, -18, 0, -24, -36, 0, 88, 0, 0, -149, -15, 0, -18, 42, 0, 188, 4, 0, -12, -36, 0, 0, 34, 0, -14, -30, 0, 50, -28, 0, 49, -56, 0, -52, 11, 0, 0, 42, 0, -142, 0, 0, 0, 27, 0, 12, -32, 0, 4], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-1, 1, -1, 1], [0, 0, 0, 0], [0, 0, 0, -1], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [1, 0, 0, 0], [-1, -1, -1, 3], [0, 0, 0, 0], [2, -3, 3, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [1, 0, 1, 0], [0, 0, 0, 0], [0, 0, 2, 0], [-1, 1, -1, 1], [0, 0, 0, 0], [2, 0, -2, -1], [-3, 0, -3, 3], [0, 0, 0, 0], [0, 0, 1, 0], [1, -1, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 1, 0, 6], [0, 0, 0, 0], [6, -9, 9, -6], [1, 0, 0, 0], [0, 0, 0, 0], [-1, 0, -1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 3, 0, 5], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 6, -6, 6], [0, 0, 0, 0], [-1, 0, -3, 3], [-2, 4, -1, 2], [0, 0, 0, 0], [3, 0, 0, -3], [0, 5, -7, 5], [0, 0, 0, 0], [0, 7, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [0, 1, -3, 1], [-6, -2, 2, 6], [0, 0, 0, 0], [3, -2, 4, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, -5, -1], [3, -3, 0, 3], [0, 0, 0, 0], [6, -2, 6, 0], [3, -3, 0, 6], [0, 0, 0, 0], [-1, 1, -1, 1], [-2, 0, 1, -1], [0, 0, 0, 0], [-12, 0, -1, 1], [1, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [8, -2, 8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, -2, -3], [0, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-9, 4, -4, 9], [0, 0, 1, 0], [0, 0, 0, 0], [-6, 6, -6, 0], [-2, 4, -2, 0], [0, 0, 0, 0], [0, -1, 0, -1], [1, 2, -2, -1], [0, 0, 0, 0], [-2, -1, 0, -2], [-2, 0, -4, 4], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 3, 0, 3], [0, 0, 0, 0], [-5, 7, -5, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-8, 6, -6, 8], [-7, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0]]}