# Stored data for newform 1089.2.e.c, downloaded from the LMFDB on 17 June 2025.
{"Nk2": 4356, "analytic_conductor": 8.695708780117434, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [1089, 3, [848, 244], [1, 3]], "cm_discs": [], "conrey_index": 364, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, -1, 1]], [5, [1, 1, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007474166203457, "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, 9, 3, 1, 3, 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": false, "label": "1089.2.e.c", "level": 1089, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [3, 11], "level_radical": 33, "minimal_twist": "99.2.e.a", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+(1-\\zeta_{6})q^{2}+(-2+\\zeta_{6})q^{3}+\\zeta_{6}q^{4}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1089.2.e", "trace_display": [1, -3, -1, 4], "trace_hash": 166737920565266131, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.013", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.021", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "107.132", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.012", "prec": 17}, "traces": [0, 2, 1, -3, 1, -1, 0, 4, 6, 3, -2, 0, -3, -2, -4, 3, 1, -8, -3, -12, 1, 0, 0, 4, -9, 4, -4, 0, 8, 6, 3, -7, 5, 0, -4, -8, 6, 6, -6, 6, -3, -2, 12, 6, 0, -6, 8, 7, 0, -9, -4, 12, 2, -18, 9, 0, 12, 18, -6, 7, 0, 0, -14, -12, 14, -2, 0, -11, -4, -12, -4, 18, 9, -8, 3, 0, -6, 0, 6, 8, -2, -9, -4, -12, -12, 4, -6, 0, 0, 12, -3, -16, -4, 21, -7, 6, -15, 19, -18, 0, 8, -4, 0, 13, -6, 12, -9, 36, -9, 4, 0, -9, -4, 15, 0, 4, 12, -12, 14, -16, 9, 0, 0, 6, 7, -18, -24, -4, -3, 0, 2, -6, 0, -24, -22, 9, -24, -5, -12, -2, -4, 0, 9, 0, -3, -12, -4, 27, 3, -4, 12, -16, -36, -12, 0, -7, 0, 7, -8, 27, 5, 32, -18, -22, 2, 0, 12, 12, 0, 9, 8, -18, 12, 0, 18, -16, 0, -21, 6, -18, -3, 14, -8, 0, 12, -3, 21, 0, 14, 36, 12, 13, -21, 4, -19, 0, 9, -32, 0, -6, 12, 33, 4, -24, 12, -2, 26, 24, -4, 0, 0, 6, -9, -27, 18, -12, 0, -56, 2, 12, 0, 8, 0, -16, 40, -12, 30, -18, 18, 6, -4, 0, 18, -48, -6, -14, -7, 0, 16, 6, 3, 10, 0, 27, 0, -9, 6, 12, -21, 0, -9, 56, 12, 0, -2, -12, 17, -22, 18, 12, -4, -18, -12, -16, 0, 9, 24, -18, 11, -34, 0, 44, -4, 24, 5, 0, 0, -2, -4, -42, -24, 6, 21, 28, 9, -18, 0, -16, 30, -2, -6, 0, -4, 12, 27, 7, 18, 0, -8, 8, -12, -24, 16, 0, -6, 0, 12, 56, 0, -39, 7, 21, 18, -14, 14, -12, 16, -22, 0, 0, -7, -54, 16, 48, 9, -16, -11, -6, -6, -28, 0, -1, -24, 9, 24, -11, 12, -22, -9, -45, -4, 0, 18, -16, 18, 0, 0, 4, -18, 30, -32, 18, 0, 18, -21, -9, 6, 0, -9, 64, -18, 34, 7, 0, -8, 4, 0, 11, 8, -12, -6, -36, 0, 10, 0, 27, 21, -24, 36, 32, -6, 6, -13, -29, 0, 0, 8, -18, 38, -33, -6, -16, -27, 18, -16, -16, 0, 26, -3, 0, -4, -17, 33, -14, -8, -9, -48, 0, 36, 0, 2, 0, -13, 56, 12, 24, 10, 6, 0, -5, 12, -13, 12, -21, -54, -16, 0, 0, 18, 0, -6, 60, 9, -28, -28, 18, 2, -24, 0, -14, 0, -54, 16, -1, -9, -6, 16, 12, 28, 46, -24, 0, -15, 0, 18, 8, 54, -6, 12, 0, 8, -12, 0, 8, -6, 0, -24, 54, -6, -88, -7, -21, 21, 0, 24, -24, -32, -27, 12, -4, 0, -6, -10, -48, 0, -38, 27, -74, 0, 33, 9, -8, 0, -24, 24, 0, -14, 36, -36, 25, -9, -36, 28, 28, -36, 8, 0, 0, -2, 6, -12, -16, 22, 0, -44, 13, -18, 0, -12, 0, -6, -6, -36, -40, 6, 48, 16, 28, 0, 7, 18, 42, -48, -4, 0, -18, -33, 27, -17, 0, 9, -20, 22, -21, -20, -2, 0, -22, -10, 0, 0, -36, -36, -32, 2, 9, 2, -80, -21, -24, -4, 0, -6, -14, -21, 15, 56, -72, 54, -6, -18, 32, 0, 0, -8, 32, 21, -6, -1, -12, -6, 48, 57, 0, -24, 6, 24, 5, 0, 42, -7, 48, 3, 44, 0, 32, 4, 9, -8, -4, 0, 2, -48, -66, -32, 0, -12, 8, -30, 72, 0, -28, -24, 32, 28, 0, 0, 15, -39, 25, -14, -36, 42, 24, 6, -11, 14, 0, -7, -24, 12, 74, 24, -18, 22, 2, 27, -18, 0, 27, 6, 30, 0, 16, 16, 18, 24, 64, -27, 0, -8, 84, -11, -31, 0, -6, -4, -12, -56, 34, 0, -49, 1, -24, -36, 48, -9, 48, -12, 0, 11, 0, -60, -22, -44, 36, 18, 0, -45, -76, 12, 0, 0, 10, -36, 10, -8, -18, -6, 18, 12, -35, 0, 0, 8, -2, 0, 8, -30, 72, 16, -4, 0, -36, 0, 21, -18, 16, 0, 13, -18, -24, 36, 28, -48, 0, -9, -18, 32, -30, -3, 104, 17, 0, 7, -24, 0, 33, -48, -54, 8, -24, 0, -6, -11, 0, -20, 0, -6, 32, 3, -36, 36, -50, 63, -4, 20, 36, 0, 72, 0, 11, -7, -84, -12, 32, 0, -38, 16, 0, 18, 36, 0, 8, 26, 24, -58, 14, -51, -16, 0, 66, -4, 36, -36, -56, 57, 0, 33, 12, 6, 0, -32, 54, -18, 7, 18, -14, -16, 0, -8, 120, 0, 0, 13, -27, -3, -5, -72, -28, 40, 18, -34, 0, 0, -16, 14, 51, -12, 60, 9, 28, 24, -66, 0, 11, 0, -36, 0, -24, -4, -20, -15, 24, 39, 0, 28, 80, 12, 50, 12, 0, -14, 36, 6, 12, 0, 63, -10, -16, 36, -7, 13, 0, -6, -18, -42, 0, -9, -84, 16, 12, -27, 2, 0, 36, 108, 38, 0, -15, -6, 24, 30, 48, -45, 0, -14, 3, -28, 0, 0, -22, 12, -57, -48, -36, 12, -18, 14, -36, 0, -14, -27, -10, -8, 0, 1, 8, -27, -8, -12, 0, -32, -42, 12, 9, 12, 0, 23, -84, 12, 72, 0, 72, 45, -7, -48, -12, -36, 12, 16, -27, 0, 0, 6, 0, -6, -48, -36, -104, 12, -84, 12, -18, 0, 12, 16, 78, 60, -21, -21, 54, -24, -63, 27, 0, -36, -28, -44, 0, -7, 0, -21, 8, 14, 0, 0, -15, -24, 8, 24, 0, -48, 52, 27, -26, -6, 0, 4, 20, 21, -18, -12, 54, 20, 4, 0, -50, 0, -72, -19, 40, 0, -16, -37, 24, 0, -18, 0, 0, -18, 6, -16, -3, 18, 16, 24, 84, -12, 48, 0, -88, 35, 0, -36, 3, 36, -4, 50, 0, -54, 0, -36, -28, 28, 0, 14, 108, -24, 80, 4, 66, 0, 6, 27, -24, -12, 90, 12, -16, 0, 23, 16, 0, -23, -16, -54, -32, 22, 24, -13, -4, 0, -16, 0, -12, 24, 0, 0, -35, 2, -12, -3, -32, 18, 0, -20, 0, -18, -5, 48, -22, -32, -18, 56, 6, 0, 64, -7, 0, -9, 52, 21, -112, -72, 27, 4, 0, -18, 28, -36, 48, -22, 18, 0, -24, -17, -96, 0, 48, 27, 56, -10, -51, 22, 28, 0, -8, -56, 0, -4, -40, 24, -6, 22, -12, -15, -12, 0, 56, 0, 0, 36, 45, -12, 8, -64, 18, -4, -3, 9, 0, -6, 0, -40, 32, -21, 60, -12, -30, -20, -42, 0, 39, 12, -27, -28, 36, 0, -4, -15, 36, -28, 0, -36, 36, 9, -48, 6, 44, 0, -44, 64, -6, 0, 6, 39, -21, -8, 87, 16, 20, 9, -44, -3, 0, -1, -12, -12, 0, -36, 54, 96, 34, -57, 24, 0, 0, -4, 96, 12, 90, -12, 48, -5, -28, 81, 0, 84, -36, 14, 42, 0, -36, 15, 24, 22, -108, 0, -24, 16, -39, -12, 21, 0, 6, 16, 72, -8, 0, 12, -10, -2, 51, 24, -20, -33, -72, -48, 0, 0, 0, 12, -43, 16, 0, -84, -54, 72, -36, 0, 0, -14, 44, -36, -72, 16, 0, 28, 60, -6, -12, 0, 15, 30, 12, 0, -15, -25, -84, -21, 32, 0, 0, -21, -36, -24, -36, 0, 52, -22, -12, -28, -36, 0, -28, 21, 15, -12, -98, -24, -76, 37, 0, -8, 0, -18, 28, -44, 63, 4, -14, 81, 66, 18, 0, 0, -118, -27, 96, 17, 0, -30, -60, -54, -22, 32, 0, 96, 48, 0, -28, 24, -90, 32, -24, -18, 36, 0, 42, -8, -54, 0, 15, -66, -18, -62, -28, -6, 0, 6, 72, 10, 16, 12, 32, 28, 0, -34, 0, 0, -35, -98, 81, -2, -36, -24, 32, 12, 0, 24, 0, 18, -84, 24, 18, 36, -52, -48, 26, -22, -24, 0, -32, 0, 17, 22, -69, 22, -108, 36, 32, 27, 0, 0, -22, 0, -28, -152, 48, 8, 66, -54, -42, 0, -24, 5, -78, -54, -56, 5, 0, -8, -27, -18, 0, 60, 36, 36, -64, -12, 52, 35, 0, 0, 4, 0, 48, -4, -24, 2, -36, 18, -12, 16, 21, 60, 0, 0, 54, -48, -81, -2, 0, 18, -12, -18, 132, 0, -45, 0, 48, 36, 42, 32, 28, -63, -4, -13, 0, 9, -108, -48, 118, 6, 0, -28, 12, 48, 20, 0, 0, -54, -42, -18, 8, 32, 0, -15, -102, -15, 0, 52, 18, 17, 1, 30, 70, 42, 48, -48, -62, 0, 59, -33, 57, -8, -98, -27, -8, -4, 111, 24, 0, 0, 12, -12, -33, 22, 30, -27, -50, 28, 24, 0, 56, -6, 48, 16, 0, -9, -52, -36, 68, -72, 0, -100, -32, 21, 27, 4, 0, -10, 36, 72, -16, 0, -75, -72, -76, 27, -48, 22, 72, 70, -24, 0, 0, -12, -42, 16, -70, 108, -48, -19, -12, 16, -6, 0, -63, 12, -27, 72, 23, 6, 0, -8, -18, 39, 0, 12, 44, 29, 0, -14, -28, -33, -54, -32, 54, 0, 44, 66, -21, 12, 0, 18, 64, 18, 90, -28, 0, -19, -2, 36, 21, -66, 0, 24, -42, 0, 64, 0, 9, 16, 28, 54, 112, 45, 60, -7, -56, 0, 0, -28, -96, -96, 72, -48, -66, -8, -84, 60, -116, 0, 44, 0, 0, 13, 72, -27, 18, -18, -63, -10, 0, 72, -8, 28, 0, 28, 44, -18, 48, 17, 54, 0, 45, 99, 61, -32, -27, -28, 66, 0, -24, 4, 0, 30, 64, -18, -46, 14, 30, -72, 18, 0, 24, 0, 21, 22, -96, 60, 36, 36, 6, 0, 84, 24, 0, -6, 0, 20, 63, 15, -28, 48, 0, 26, -76, 0, 4, 28, 0, 40, 2, 72, 16, 25, 96, 12, 0, -6, 40, 12, -18, 72, -36, 0, 56, -12, 120, 0, 48, 0, -88, 5, 36, 16, -16, 0, 37, -14, 0, -26, -22, 18, -40, 18, 42, -9, -72, 21, -84, 0, 0, -45, 21, -84, -7, -32, 108, 24, -12, -81, 0, -2, 0, 0, 60, 18, 84, 18, -96, -38, 8, 0, 16, -30, -39, -36, -9, 0, 20, 30, -48, 24, 0, 0, 96, 0, 9, -14, 60, 0, 4, -168, 24, 0, 21, 18, -29, 22, -144, 2, -60, -114, 66, 24, 0, 36, -52, 36, -73, -36, -18, -28, 112, -36, 38, 0, 0, -7, -24, -27, -36, -5, -126, 24, 0, 21, 0, -2, -48, 16, 36, 0, 26, 8, -66, 6, 20, 0, -128, -48, -48, 42, -24, 0, 82, 18, -9, 136, 0, 24, -32, 23, 12, -42, -176, -36, -20, 36, 0, 0, -17, 72, -4, 30, 99, -14, 42, 48, -27, 12, 0, -54, 64, 24, -144, -8, -24, 27, -14, 90, -16, 0, -144, -12, 49, 0, -11, 18, 42, -24, -22, 36, 0, -52, -48, -4, 64, 0, -114, -24, 6, -36, 2, 0, 7, -12, -45, -8, -16, 39, 72, 42, 0, 21, 0, 21, -40, 108, 36, -144, 10, -63, 64, 27, 0, 0, 6, -6, -102, -14, 33, -44, 48, -42, 11, -42, 0, 0, -68, 0, 12, -8, 36, -35, -56, -36, 0, 0, -111, 15, -16, 0, 88, 16, 36, -48, 58, -66, 0, 16, -6, 26, 22, -54, -96, -13, 0, 18, -60, 0, -29, -8, 0, 40, 24, -9, -60, 18, 0, 6, 0, -54, -28, 30, -48, -4, -30, -48, 6, -100, -18, 0, -8, 0, 8, -19, -96, 20, -132, 81, 66, -8, 0, -37, -70, 0, 35, 0, -84, -36, -16, 33, -78, 0, 93, -27, -54, -6, 64, 8, 0, 3, -24, 6, 0, 32, 0, -48, -58, 84, -32, 36, 0, 24, -96, 0, 224, -44, 147, -49, -13, -3, -82, 72, 48, 6, 0, 0, -48, 4, -72, -25, -48, 27, -80, -9], "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], [1, 0], [1, -1], [-2, 1], [0, 1], [0, -1], [-1, 2], [4, -4], [3, 0], [3, -3], [-1, 0], [0, 0], [-1, -1], [0, -2], [0, -4], [1, 1], [1, -1], [-4, 0], [0, -3], [-6, 0], [1, -1], [-4, 8], [0, 0], [0, 4], [-6, 3], [4, -4], [-2, 0], [-3, 6], [4, 0], [6, -6], [2, -1], [0, -7], [0, 5], [0, 0], [-4, 4], [-4, 0], [3, 0], [3, 0], [-6, 6], [2, 2], [0, -3], [0, -2], [4, 4], [6, -6], [0, 0], [-3, 0], [4, 0], [7, -7], [-1, 2], [0, -9], [0, -4], [8, -4], [2, -2], [-9, 0], [3, 3], [0, 0], [12, -12], [12, -6], [0, -6], [0, 7], [-1, 2], [0, 0], [-7, 0], [0, -12], [7, 0], [-2, 2], [0, 0], [0, -11], [0, -4], [-4, -4], [-4, 4], [9, 0], [9, -9], [-4, 0], [3, -3], [-4, 8], [0, -6], [0, 0], [4, -2], [8, -8], [-1, 0], [0, -9], [-2, 0], [-12, 12], [-8, 4], [0, 4], [0, -6], [-6, 12], [0, 0], [6, 0], [-3, 3], [-8, 0], [-4, 4], [7, 7], [0, -7], [0, 6], [-5, -5], [19, -19], [-9, 0], [0, 0], [4, 0]]}