# Stored data for newform 990.2.a.m, downloaded from the LMFDB on 19 June 2025.
{"Nk2": 3960, "analytic_conductor": 7.905189800106758, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [5, 1], [11, -1]], "atkin_lehner_string": "--+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [990, 1, [551, 397, 541], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 33, "field_disc_factorization": [[3, 1], [11, 1]], "field_poly": [-8, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[7, [-8, -1, 1]], [13, [-2, 1]], [17, [-6, -3, 1]]], "hecke_orbit": 13, "hecke_orbit_code": 54043195562001374, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "990.2.a.m", "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": "110.2.a.d", "nf_label": "2.2.33.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}+q^{4}-q^{5}+\\beta q^{7}+q^{8}-q^{10}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "990.2.a", "trace_display": [2, 0, -2, 1], "trace_hash": 2257275915847242031, "trace_moments": [{"__RealLiteral__": 0, "data": "0.060", "prec": 17}, {"__RealLiteral__": 0, "data": "1.895", "prec": 17}, {"__RealLiteral__": 0, "data": "0.470", "prec": 17}, {"__RealLiteral__": 0, "data": "8.818", "prec": 17}, {"__RealLiteral__": 0, "data": "3.724", "prec": 17}, {"__RealLiteral__": 0, "data": "56.979", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, "traces": [0, 2, 2, 0, 2, -2, 0, 1, 2, 0, -2, 2, 0, 4, 1, 0, 2, 3, 0, 7, -2, 0, 2, 6, 0, 2, 4, 0, 1, 3, 0, 1, 2, 0, 3, -1, 0, 13, 7, 0, -2, 0, 0, -8, 2, 0, 6, 6, 0, 3, 2, 0, 4, -9, 0, -2, 1, 0, 3, -6, 0, -5, 1, 0, 2, -4, 0, 16, 3, 0, -1, -3, 0, -8, 13, 0, 7, 1, 0, -14, -2, 0, 0, -6, 0, -3, -8, 0, 2, -3, 0, 2, 6, 0, 6, -7, 0, -14, 3, 0, 2, -12, 0, 4, 4, 0, -9, 24, 0, -8, -2, 0, 1, -18, 0, -6, 3, 0, -6, -15, 0, 2, -5, 0, 1, -2, 0, 16, 2, 0, -4, -27, 0, -13, 16, 0, 3, -6, 0, -8, -1, 0, -3, 4, 0, -3, -8, 0, 13, -3, 0, 10, 7, 0, 1, -1, 0, 13, -14, 0, -2, -30, 0, -29, 0, 0, -6, 15, 0, -18, -3, 0, -8, 12, 0, 1, 2, 0, -3, 24, 0, -20, 2, 0, 6, -13, 0, 3, 6, 0, -7, -12, 0, 1, -14, 0, 3, 30, 0, 19, 2, 0, -12, -15, 0, 0, 4, 0, 4, 7, 0, -5, -9, 0, 24, 8, 0, 17, -8, 0, -2, 6, 0, -26, 1, 0, -18, -6, 0, -20, -6, 0, 3, 3, 0, -6, -6, 0, -15, 18, 0, -44, 2, 0, -5, -3, 0, 14, 1, 0, -2, 6, 0, 6, 16, 0, 2, -36, 0, 23, -4, 0, -27, 21, 0, 9, -13, 0, 16, 6, 0, -32, 3, 0, -6, 2, 0, -14, -8, 0, -1, -36, 0, 22, -3, 0, 4, 66, 0, -13, -3, 0, -8, -24, 0, 6, 13, 0, -3, 12, 0, -4, 10, 0, 7, 5, 0, 22, 1, 0, -1, -33, 0, -44, 13, 0, -14, -3, 0, 3, -2, 0, -30, 27, 0, 4, -29, 0, 0, -30, 0, 16, -6, 0, 15, -16, 0, 31, -18, 0, -3, 1, 0, 11, -8, 0, 12, 30, 0, 16, 1, 0, 2, 24, 0, 3, -3, 0, 24, 0, 0, 3, -20, 0, 2, 8, 0, -8, 6, 0, -13, 45, 0, 40, 3, 0, 6, 6, 0, 34, -7, 0, -12, -30, 0, -1, 1, 0, -14, -12, 0, 42, 3, 0, 30, 14, 0, 4, 19, 0, 2, -21, 0, 2, -12, 0, -15, 13, 0, -38, 0, 0, 4, 30, 0, 6, 4, 0, 7, 24, 0, -14, -5, 0, -9, 3, 0, -19, 24, 0, 8, 24, 0, -2, 17, 0, -8, 54, 0, -8, -2, 0, 6, -36, 0, 3, -26, 0, 1, -12, 0, 0, -18, 0, -6, -2, 0, 19, -20, 0, -6, -15, 0, 34, 3, 0, 3, 33, 0, 8, -6, 0, -6, -8, 0, 7, -15, 0, 18, 12, 0, 26, -44, 0, 2, 14, 0, 40, -5, 0, -3, 9, 0, 21, 14, 0, 1, -51, 0, -44, -2, 0, 6, 24, 0, 12, 6, 0, 16, -54, 0, -70, 2, 0, -36, -4, 0, 6, 23, 0, -4, -48, 0, 16, -27, 0, 21, -15, 0, 38, 9, 0, -13, 0, 0, -24, 16, 0, 6, 3, 0, -23, -32, 0, 3, 8, 0, 40, -6, 0, 2, 27, 0, 26, -14, 0, -8, 36, 0, -16, -1, 0, -36, -18, 0, 18, 22, 0, -3, 42, 0, 25, 4, 0, 66, 6, 0, 28, -13, 0, -3, 30, 0, -9, -8, 0, -24, -21, 0, -13, 6, 0, 13, 48, 0, 15, -3, 0, 12, 39, 0, -56, -4, 0, 10, -2, 0, -29, 7, 0, 5, 12, 0, 64, 22, 0, 1, -30, 0, -20, -1, 0, -33, 15, 0, 2, -44, 0, 13, 3, 0, 67, -14, 0, -3, -16, 0, 6, 3, 0, -2, -9, 0, -29, -30, 0, 27, 18, 0, -6, 4, 0, -29, -27, 0, 27, 0, 0, -30, 3, 0, 40, 16, 0, -6, 13, 0, 42, 15, 0, -16, -5, 0, 1, 31, 0, -18, -18, 0, -40, -3, 0, 1, 63, 0, 6, 11, 0, -8, -18, 0, 46, 12, 0, 30, 8, 0, -66, 16, 0, 1, 69, 0, 29, 2, 0, 24, -6, 0, -20, 3, 0, -3, -30, 0, -4, 24, 0, 0, -45, 0, -64, 3, 0, -20, 3, 0, -14, 2, 0, 8, -12, 0, 58, -8, 0, 6, 16, 0, 28, -13, 0, 45, 15, 0, 3, 40, 0, 3, 12, 0, -11, 6, 0, 6, -10, 0, 4, 34, 0, -7, 36, 0, -70, -12, 0, -30, -12, 0, -44, -1, 0, 1, 27, 0, 1, -14, 0, -12, -66, 0, -3, 42, 0, 3, -13, 0, -20, 30, 0, 14, 24, 0, -10, 4, 0, 19, 0, 0, 42, 2, 0, -21, -8, 0, 30, 2, 0, -12, -36, 0, 61, -15, 0, 13, 29, 0, -28, -38, 0, 0, 0, 0, -56, 4, 0, 30, -48, 0, -38, 6, 0, 4, -12, 0, -15, 7, 0, 24, -24, 0, -37, -14, 0, -5, 18, 0, 1, -9, 0, 3, 6, 0, -8, -19, 0, 24, -21, 0, -74, 8, 0, 24, -54, 0, -12, -2, 0, 17, -14, 0, 32, -8, 0, 54, -1, 0, 28, -8, 0, -2, -36, 0, 1, 6, 0, -36, -24, 0, 8, 3, 0, -26, 54, 0, -24, 1, 0, -12, -15, 0, -63, 0, 0, -18, 20, 0, -41, -6, 0, -2, 57, 0, -6, 19, 0, -20, -63, 0, -8, -6, 0, -15, -6, 0, 13, 34, 0, 3, 3, 0, -6, 3, 0, 33, -3, 0, -80, 8, 0, -6, -33, 0, -132, -6, 0, -8, -69, 0, -16, 7, 0, -15, -63, 0, 12, 18, 0, 12, -36, 0, -45, 26, 0, -44, -1, 0, 55, 2, 0, 14, 48, 0, -4, 40, 0, -5, 6, 0, -3, -3, 0, 9, -30, 0, -30, 21, 0, 14, -24, 0, 16, 1, 0, -51, -19, 0, 10, -44, 0, -2], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [1, 0], [0, 0], [1, 0], [-1, 0], [0, 0], [0, 1], [1, 0], [0, 0], [-1, 0], [1, 0], [0, 0], [2, 0], [0, 1], [0, 0], [1, 0], [2, -1], [0, 0], [4, -1], [-1, 0], [0, 0], [1, 0], [4, -2], [0, 0], [1, 0], [2, 0], [0, 0], [0, 1], [2, -1], [0, 0], [0, 1], [1, 0], [0, 0], [2, -1], [0, -1], [0, 0], [6, 1], [4, -1], [0, 0], [-1, 0], [-2, 4], [0, 0], [-4, 0], [1, 0], [0, 0], [4, -2], [4, -2], [0, 0], [1, 1], [1, 0], [0, 0], [2, 0], [-6, 3], [0, 0], [-1, 0], [0, 1], [0, 0], [2, -1], [-4, 2], [0, 0], [-2, -1], [0, 1], [0, 0], [1, 0], [-2, 0], [0, 0], [8, 0], [2, -1], [0, 0], [0, -1], [0, -3], [0, 0], [-2, -4], [6, 1], [0, 0], [4, -1], [0, 1], [0, 0], [-8, 2], [-1, 0], [0, 0], [-2, 4], [-4, 2], [0, 0], [-2, 1], [-4, 0], [0, 0], [1, 0], [-2, 1], [0, 0], [0, 2], [4, -2], [0, 0], [4, -2], [-4, 1], [0, 0], [-6, -2], [1, 1], [0, 0], [1, 0]]}