# Stored data for newform 290.2.a.b, downloaded from the LMFDB on 18 August 2026.
{"Nk2": 1160, "analytic_conductor": 2.315661658617131, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [5, 1], [29, -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": [290, 1, [117, 31], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 13, "field_disc_factorization": [[13, 1]], "field_poly": [-3, -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": [[3, [-3, -1, 1]], [7, [3, -5, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599660925218, "hecke_ring_generator_nbound": 3, "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": true, "label": "290.2.a.b", "level": 290, "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": true, "level_primes": [2, 5, 29], "level_radical": 290, "minimal_twist": "290.2.a.b", "nf_label": "2.2.13.1", "prim_orbit_index": 1, "qexp_display": "q-q^{2}+(1-\\beta )q^{3}+q^{4}-q^{5}+(-1+\\cdots)q^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "290.2.a", "trace_display": [-2, 1, -2, 5], "trace_hash": 1446945493747000738, "trace_moments": [{"__RealLiteral__": 0, "data": "0.037", "prec": 7}, {"__RealLiteral__": 0, "data": "1.929", "prec": 14}, {"__RealLiteral__": 0, "data": "0.167", "prec": 10}, {"__RealLiteral__": 0, "data": "9.436", "prec": 14}, {"__RealLiteral__": 0, "data": "1.325", "prec": 14}, {"__RealLiteral__": 0, "data": "63.971", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.011", "prec": 7}, "traces": [0, 2, -2, 1, 2, -2, -1, 5, -2, 1, 2, -2, 1, 9, -5, -1, 2, 3, -1, 6, -2, -4, 2, 7, -1, 2, -9, 4, 5, 2, 1, -5, -2, 12, -3, -5, 1, -2, -6, 11, 2, -10, 4, 3, -2, -1, -7, 0, 1, 5, -2, -18, 9, 3, -4, 2, -5, -10, -2, 9, -1, -17, 5, -4, 2, -9, -12, -4, 3, -3, 5, 0, -1, -13, 2, 1, 6, -18, -11, 1, -2, -14, 10, -10, -4, -3, -3, 1, 2, -22, 1, 16, 7, -22, 0, -6, -1, 13, -5, 12, 2, -15, 18, 8, -9, 4, -3, 10, 4, -22, -2, 38, 5, 17, 10, -7, 2, 11, -9, 27, 1, 6, 17, -18, -5, -2, 4, 40, -2, 8, 9, 0, 12, 28, 4, -4, -3, -27, 3, 17, -5, 0, 0, 4, 1, -2, 13, -30, -2, 18, -1, 2, -6, -18, 18, 5, 11, 12, -1, -18, 2, 24, 14, -28, -10, -12, 10, -11, 4, 21, 3, -10, 3, 27, -1, 5, -2, -15, 22, -9, -1, -18, -16, 11, -7, 2, 22, -42, 0, 23, 6, 21, 1, -17, -13, -11, 5, 3, -12, -14, -2, -28, 15, 5, -18, 10, -8, -3, 9, -32, -4, 34, 3, 0, -10, -3, -4, 7, 22, 26, 2, -6, -38, 3, -5, 1, -17, 16, -10, 1, 7, 30, -2, 32, -11, 0, 9, -19, -27, 12, -1, -3, -6, -32, -17, -5, 18, 14, 5, -18, 2, -10, -4, -20, -40, 18, 2, -22, -8, -44, -9, 1, 0, -4, -12, -3, -28, -24, -4, -7, 4, 12, 3, -5, 27, -2, -3, 28, -17, -22, 5, 5, 0, -6, 0, 10, -4, -12, -1, 29, 2, -13, -13, 30, 30, -9, 2, -30, -18, 25, 1, 1, -2, -27, 6, 17, 18, -12, -18, 56, -5, 39, -11, -28, -12, 4, 1, -14, 18, -2, -2, 18, -24, 48, -14, 9, 28, 2, 10, 0, 12, 38, -10, 38, 11, 4, -4, -7, -21, 15, -3, -34, 10, 10, -3, 3, -27, 6, 1, 16, -5, 5, 2, 20, 15, 0, -22, -45, 9, -49, 1, 6, 18, -23, 16, 13, -11, -42, 7, -18, -2, 27, -22, -53, 42, -1, 0, 9, -23, -54, -6, 20, -21, 13, -1, 18, 17, 8, 13, -36, 11, 30, -5, 78, -3, -1, 12, 13, 14, -38, 2, 53, 28, -42, -15, 14, -5, 80, 18, -4, -10, -33, 8, 42, 3, 10, -9, 2, 32, 7, 4, -8, -34, 0, -3, 3, 0, -62, 10, 54, 3, -26, 4, -16, -7, -1, -22, 34, -26, -32, -2, -30, 6, -13, 38, 22, -3, 48, 5, -38, -1, -16, 17, 14, -16, -16, 10, -20, -1, 45, -7, -3, -30, 24, 2, 22, -32, -21, 11, 16, 0, -46, -9, 10, 19, 6, 27, -18, -12, 9, 1, 30, 3, -27, 6, -13, 32, 21, 17, -40, 5, 36, -18, 3, -14, -12, -5, 0, 18, -5, -2, -12, 10, -24, 4, 15, 20, 69, 40, -18, -18, -65, -2, 38, 22, -8, 8, 0, 44, 33, 9, 13, -1, -50, 0, -4, 4, 51, 12, -15, 3, -15, 28, -58, 24, -10, 4, 15, 7, -70, -4, -27, -12, -22, -3, 22, 5, -30, -27, 11, 2, 6, 3, 22, -28, -38, 17, -9, 22, 20, -5, 18, -5, 45, 0, -17, 6, -22, 0, 36, -10, 27, 4, 30, 12, 7, 1, 59, -29, -67, -2, -12, 13, -42, 13, -11, -30, -16, -30, 24, 9, -18, -2, 18, 30, -27, 18, 32, -25, 51, -1, -82, -1, -28, 2, -6, 27, 4, -6, -4, -17, 0, -18, -45, 12, 18, 18, -3, -56, 8, 5, 27, -39, -42, 11, 2, 28, 36, 12, -120, -4, 20, -1, 56, 14, -40, -18, -10, 2, 0, 2, -18, -18, -30, 24, -8, -48, 12, 14, -48, -9, -29, -28, -42, -2, 0, -10, 26, 0, -54, -12, -2, -38, -81, 10, -28, -38, 7, -11, -31, -4, 56, 4, 34, 7, 4, 21, 40, -15, 52, 3, -18, 34, 18, -10, 27, -10, 20, 3, -6, -3, -59, 27, 30, -6, -17, -1, 24, -16, 42, 5, -26, -5, -84, -2, 0, -20, -18, -15, 6, 0, -19, 22, 2, 45, -4, -9, 6, 49, 22, -1, -32, -6, 5, -18, 2, 23, 62, -16, 13, -13, -15, 11, 32, 42, 30, -7, -48, 18, 12, 2, -32, -27, 68, 22, -18, 53, -18, -42, 12, 1, 24, 0, -18, -9, -2, 23, 22, 54, 42, 6, -9, -20, -68, 21, 18, -13, 21, 1, 54, -18, 54, -17, -52, -8, -5, -13, 82, 36, -4, -11, 0, -30, 4, 5, -12, -78, 18, 3, 24, 1, 36, -12, -57, -13, 18, -14, 24, 38, 0, -2, -24, -53, 78, -28, -24, 42, -36, 15, 20, -14, 3, 5, 32, -80, 28, -18, -4, 4, -5, 10, -58, 33, -32, -8, 12, -42, -43, -3, 33, -10, 14, 9, 105, -2, 11, -32, 29, -7, -44, -4, 2, 8, 48, 34, -21, 0, 41, 3, 62, -3, -46, 0, -6, 62, 10, -10, -10, -54, 50, -3, -6, 26, 21, -4, -27, 16, -44, 7, -40, 1, -44, 22, -13, -34, -5, 26, 71, 32, 54, 2, -26, 30, 30, -6, 15, 13, 60, -38, 100, -22, -12, 3, 0, -48, 9, -5, 6, 38, -5, 1, 63, 16, 7, -17, 18, -14, 77, 16, -27, 16, 47, -10, -16, 20, -11, 1, -78, -45, 28, 7, 20, 3, 0, 30, -2, -24, 56, -2, -37, -22, 80, 32, 39, 21, 42, -11, -50, -16, 38, 0, 60, 46, -22, 9, -23, -10, 25, -19, -26, -6, -72, -27, -28, 18, -21, 12, 12, -9, -48, -1, 9, -30, 18, -3, 17, 27, 18, -6, -54, 13, -30, -32, 49, -21, 11, -17, -42, 40, -4, -5, 2, -36, -40, 18, -3, -3, 0, 14, 4, 12, 62, 5, 32, 0, 14, -18, 42, 5, -82, 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], [1, -1], [1, 0], [-1, 0], [-1, 1], [2, 1], [-1, 0], [1, -1], [1, 0], [0, -2], [1, -1], [5, -1], [-2, -1], [-1, 1], [1, 0], [0, 3], [-1, 1], [2, 2], [-1, 0], [-1, -2], [0, 2], [3, 1], [-1, 1], [1, 0], [-5, 1], [1, 2], [2, 1], [1, 0], [1, -1], [-4, 3], [-1, 0], [6, 0], [0, -3], [-2, -1], [1, -1], [2, -6], [-2, -2], [8, -5], [1, 0], [-6, 2], [1, 2], [2, -1], [0, -2], [-1, 1], [-3, -1], [0, 0], [1, -1], [0, 5], [-1, 0], [-9, 0], [5, -1], [0, 3], [-1, -2], [0, 2], [-2, -1], [-4, -2], [-1, 0], [3, 3], [-1, 1], [-7, -3], [4, -3], [-1, -2], [1, 0], [-5, 1], [-6, 0], [-4, 4], [0, 3], [0, -3], [2, 1], [0, 0], [-1, 1], [-4, -5], [-2, 6], [1, -1], [2, 2], [-6, -6], [-8, 5], [-1, 3], [-1, 0], [-8, 2], [6, -2], [-6, 2], [-1, -2], [0, -3], [-2, 1], [1, -1], [0, 2], [-12, 2], [1, -1], [7, 2], [3, 1], [-13, 4], [0, 0], [-2, -2], [-1, 1], [5, 3], [0, -5], [6, 0], [1, 0]]}