# Stored data for newform 285.2.i.f, downloaded from the LMFDB on 14 May 2025. {"Nk2": 1140, "analytic_conductor": 2.275736457606491, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 19, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [285, 3, [191, 172, 211], [3, 3, 2]], "cm_discs": [], "conrey_index": 106, "dim": 10, "field_disc": -232208922080448, "field_disc_factorization": [[-1, 1], [2, 6], [3, 9], [13577, 2]], "field_poly": [16, -52, 189, 1, 125, -18, 56, -2, 9, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [16, -52, 189, 1, 125, -18, 56, -2, 9, -1, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22518547926221085, "hecke_ring_generator_nbound": 19, "hecke_ring_index": 3, "hecke_ring_index_factorization": [[3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 3, 1, 3, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "285.2.i.f", "level": 285, "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": [3, 5, 19], "level_radical": 285, "minimal_twist": "285.2.i.f", "prim_orbit_index": 3, "qexp_display": "q+(-\\beta _{1}-\\beta _{2})q^{2}-\\beta _{4}q^{3}+(-1-\\beta _{3}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 5, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "285.2.i", "trace_display": [1, 5, -5, 4], "trace_hash": 36021346136958342, "trace_moments": [{"__RealLiteral__": 0, "data": "0.105", "prec": 17}, {"__RealLiteral__": 0, "data": "9.112", "prec": 17}, {"__RealLiteral__": 0, "data": "3.272", "prec": 17}, {"__RealLiteral__": 0, "data": "329.985", "prec": 24}, {"__RealLiteral__": 0, "data": "45.227", "prec": 20}, {"__RealLiteral__": 0, "data": "20982.698", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.008", "prec": 17}, "traces": [0, 10, 1, 5, -7, -5, -1, 4, -12, -5, 1, 10, -14, 8, 4, 5, -7, -10, -2, 5, 14, 2, -2, 2, -6, -5, -4, -10, -10, 7, 2, -18, 23, 5, -25, -2, -7, 12, -37, 16, 6, -12, -4, 8, -16, 10, -40, -6, 7, 30, -2, 10, 4, -8, -1, -5, 72, -2, 76, 1, 7, -7, -15, -2, 28, -16, 2, 14, -2, 4, 4, 27, 6, -26, 18, -10, -56, 28, -2, -23, -7, -5, 36, -24, -20, -10, 2, 14, 0, 9, 1, -46, 52, -9, 90, 2, 46, -10, -21, -5, -7, -19, -50, -20, -48, 2, 10, 36, 7, 7, -2, 6, 20, 8, -14, -4, 14, 8, 10, -34, -6, 68, -112, 12, 75, 10, -8, 16, 33, -8, 2, -44, -32, -40, -40, 5, -60, -60, -20, -22, 20, -12, -36, -4, 14, -14, 28, 15, -78, 9, -1, 18, -66, 20, -92, 9, -4, 18, 58, -16, -46, 8, 1, -24, 60, 5, -3, -2, 36, 3, 50, -7, -8, -18, 38, -2, -82, -1, 132, -42, -7, 4, 44, -14, -24, -6, 15, 56, 51, -4, 14, 66, 14, -38, 2, -8, 3, 28, 4, -27, 6, 28, -28, -2, -1, -12, 82, 2, -68, 17, 8, 9, 53, -27, 3, 8, 12, -36, -5, 26, 32, 28, -18, 42, -10, -5, 41, -96, -49, -62, 20, 14, -54, -6, 2, 12, -112, 23, 62, 114, -14, 11, -43, 5, 10, -15, 72, 58, 144, -12, 1, 13, -10, 26, -20, -20, -29, -8, 4, 132, 4, 7, -32, 44, 0, 16, -124, 18, -98, 7, -1, -27, 151, -92, 30, -5, -52, 4, -82, 9, -36, -32, 45, -34, -120, 7, 176, -12, 23, -85, -38, 10, 176, -4, 21, 1, -60, -10, -66, 4, 7, -46, 33, -38, -5, 14, -25, -90, -28, -10, -15, -48, -96, 16, 66, 4, -40, 32, 5, -83, -14, 18, -184, 16, 14, 8, 42, -7, 54, -42, -4, 68, 33, -6, 10, -28, -20, -8, -39, 4, 1, -54, 23, 20, -48, -2, 78, 38, -14, 108, -8, -8, 110, 100, 20, 27, 48, 34, 114, 40, -12, -11, -38, 34, -26, -26, -56, 40, -56, 24, 18, -26, 150, 148, -118, 5, -138, -16, -4, -62, 49, 32, -138, -28, -33, -14, -44, -16, 28, 21, -2, -56, 96, 44, -71, -23, -16, -8, -12, 4, 14, 69, -20, 0, -98, -5, 256, 72, 60, 25, -72, -120, -82, 94, 20, 12, -56, -44, -82, 142, 10, -109, -123, -6, -84, 20, -72, -64, -9, -8, -4, 29, 7, -6, 60, -7, 218, 70, 56, -1, 0, -15, 112, 4, -156, -18, -30, -9, -152, 54, 1, -6, 43, 9, 24, 92, 48, -68, -113, 10, 52, -75, 92, -76, -4, -9, 15, -8, -8, 26, -45, -18, 48, -4, 116, -7, 208, -8, -6, -19, -23, -54, -22, 16, 19, -10, 2, 44, -18, -12, -21, -9, 30, -52, 28, 10, 105, 30, 3, 14, -7, -4, -80, -26, -36, 38, -112, -3, -40, -36, 25, -50, -68, -5, -164, 10, -4, -90, -78, 18, 96, 18, -38, -4, 200, -4, 47, -12, 82, -25, -5, -2, 58, -24, 66, -18, 144, -21, -92, -270, -14, 9, -63, 8, 214, 7, 22, -20, -69, -7, 4, 113, -48, 52, 82, 6, -35, -14, 30, 124, 20, -56, -80, -156, -51, -4, 56, -2, -66, -126, -23, 30, 4, 33, 36, 2, -14, 132, -100, 38, 14, -132, 4, 82, 66, 8, -55, -62, 6, -93, -20, 14, -78, -12, 2, -34, 36, -54, 52, 54, 12, 78, -22, 14, 15, -34, -14, -172, 106, -4, 56, -30, 1, 54, 66, -24, -72, 60, -82, -116, -150, -2, -6, 30, -34, -5, 316, 88, 84, -12, 4, 117, 90, -9, 50, -32, -53, 6, 160, -54, 33, -63, -3, -4, 52, 16, -164, 0, 6, -35, 2, -18, 42, -72, -10, -44, -84, 52, 132, 112, 16, -27, 26, 14, -60, -4, -36, 62, -37, -42, 20, -73, -20, 264, 46, 5, -114, 136, -41, -4, -60, -48, 6, 156, 7, 120, 134, -31, 34, -10, -20, -10, 132, -14, -1, 44, -108, 30, 21, 6, -10, -70, 4, 48, -176, 6, 22, -34, -56, -9, 72, 46, -84, -102, 124, 8, 30, 57, -2, 3, -7, 148, -80, 22, -55, 7, 43, 82, 66, 10, -56, -14, -10, -116, -44, 15, -104, -10, 36, -5, 156, 50, -308, 16, 72, 9, -146, 12, 52, -108, -1, -3, -198, 26, -52, -9, 10, -20, 154, 52, -48, 276, -10, -68, 78, -10, -115, -184, -58, -97, -92, -16, 260, 14, 2, 9, 12, 66, -144, 78, 8, 105, 208, -7, 219, 18, -64, 148, 71, -44, -116, -268, 0, -50, 214, 8, -120, -128, -50, 120, 23, 9, 102, 112, 98, -16, -180, -7, 78, 194, -2, -41, -64, 27, -96, 12, 302, -8, -212, -46, -30, -45, 15, -74, -180, -10, 28, 42, -104, 172, -3, 2, 104, -246, -41, 4, -182, 18, -110, -102, 36, -28, 86, -64, -6, 3, -45, 8, -358, 34, -25, 108, -60, -56, -28, 5, -132, -74, 88, 45, 4, 12, 128, 28, -23, -18, 12, -170, 6, 103, 38, -2, 36, 20, -32, 4, 88, -60, 107, -2, -82, -94, 42, -118, -106, 2, -254, 12, -30, -8, -66, -5, -288, 234, -132, 21, 144, -4, -30, -21, 14, 284, 48, 46, -264, -8, -33, -32, -72, -19, -22, 90, 50, -216, 28, 7, 191, 148, 25, -124, 48, 90, 192, 48, -56, -6, 56, 10, 8, 7, -30, -3, -330, -24, 115, 56, -48, 12, 260, 32, 51, -57, 132, 72, -94, 2, -88, 62, -20, -4, 23, 64, -150, 106, -5, -33, -186, -166, -28, -54, 14, -28, 228, -18, 19, -38, -92, -8, 132, 20, -4, 42, 7, -4, 146, -8, 208, -72, -42, 81, -6, -14, -30, -2, -54, -14, -106, -84, -88, -8, -2, -58, -183, 34, 48, 54, 66, 16, 5, -12, -12], "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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, -1, 0, 0, 0, -1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, -1, -1, 0, 0], [0, 0, 1, -1, 0, 0, -1, -1, 0, 0], [-1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, -1, 0, 1], [-1, 0, 0, -1, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 2, -1, 1, 1, 0, -1], [0, -2, -2, 0, -2, 1, 1, 0, 2, -1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 2, -2], [0, 0, -1, 0, 3, 0, -1, 0, -1, 2], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, -1, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1, 0, 0, 0, -1], [0, 0, -2, 0, 0, 2, 0, 0, 0, 2], [0, -2, 0, 2, 0, 0, 0, 0, 2, 0], [0, 0, 1, 0, 1, -1, 0, 0, 1, -1], [-1, 0, 0, 0, -1, 0, 0, 0, 0, 0], [-1, 0, -1, 2, 0, 0, 0, -1, 0, 1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, 0, 0, -2, -1, 1, 1, 0, -1], [1, 3, 1, -1, 2, -1, -1, 1, -1, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -2, 0, 0, 0, 0, 0, 0], [3, -1, -1, 3, 3, 0, 2, 0, 3, -1], [0, 1, 1, 0, 0, -1, -1, 0, -1, 1], [-3, 5, 1, -4, -4, 1, -3, -1, -4, 2], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [1, 0, 0, 2, 0, 0, -1, -1, 0, 0], [-3, -1, -1, -2, 2, 0, 0, 1, -2, 1], [1, 0, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, -1, 0, -1, 1, 0, 0, -1, 1], [0, 2, 2, 0, 2, 0, 0, 0, 0, 0], [-1, -2, -1, 2, -2, 1, 1, -1, 2, 0], [0, 1, 0, 0, -2, 1, 0, 0, 0, 1], [-2, 2, 0, -4, -2, 0, 0, 0, -4, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -4, 0, 0, 0, 2, 2, 0, 0], [-3, 2, 1, 1, -1, -2, 0, 2, 1, -1], [0, 0, -1, 2, 0, 0, 2, 0, 2, -1], [4, 0, 2, -2, 0, 0, -1, 1, 0, -2], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [3, 0, 1, -1, 3, 0, -2, 0, -1, 1], [0, -1, -2, 0, 0, 1, 0, 0, -2, 1], [-3, -2, -1, 3, -3, 0, 2, 0, 3, -1], [0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 0, 1, 1, 0, 1, -1], [7, 0, 1, 0, 0, 0, 0, 1, 0, -1], [0, 1, 1, 0, -1, 1, 0, -1, -1, 1], [8, 0, 0, 2, 0, 0, -2, -2, 0, 0], [0, -1, 1, 0, 0, -1, 1, 0, -1, -3], [0, 0, 0, 0, -1, 0, 0, 0, -1, 0], [-2, -4, 1, 1, 0, -2, 0, 2, 1, -1], [0, 3, 5, 0, 2, -2, 0, 0, 2, -2], [-1, -1, 0, 0, 0, -1, 1, 1, 0, -1], [0, 0, -4, 1, 0, 0, 2, 3, 0, -1], [-1, 0, 0, 0, 0, 0, -1, -1, 0, 0], [2, 0, 0, 0, 0, 2, -2, -2, 0, 2], [5, 1, 0, -4, 4, 1, -1, -1, -4, 1], [4, 0, 6, -3, 0, 0, -3, -3, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0], [1, 2, 1, -2, 2, -1, -1, 1, -2, 0], [0, -1, -1, 0, -4, -1, -1, 0, -1, 1], [0, 0, 0, 1, 1, -1, 1, 1, 1, -1], [0, 3, 2, 0, 6, -1, -2, 0, 0, 3], [0, -4, -6, 0, -4, 3, 1, 0, 0, 1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 3, 6, -3, -2, -1, -2, 0, -2, -1], [2, 0, 6, 2, 0, 0, 2, 2, 0, 0], [0, 0, 0, 0, 2, -1, -1, 0, -2, 1], [0, 4, 5, 0, 6, -2, -1, 0, -3, 0], [0, 0, 1, -2, 0, 0, -2, 0, -2, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [6, 2, 0, 2, 6, 0, 0, 0, 2, 0], [-3, 0, 0, -1, 0, 0, 1, 2, 0, -1], [-3, 0, -2, 0, 0, 0, 1, 1, 0, 0], [-3, 0, -1, 1, -3, 0, 2, 0, 1, -1], [1, 0, 1, -2, 2, -1, -1, 1, -2, 0], [1, 0, -2, -1, 0, 0, 0, 1, 0, -1], [2, 0, 6, -2, 0, 0, 0, 0, 0, 0], [1, 3, -1, 1, 0, 1, 1, -1, 1, 0], [0, -1, -1, 0, 0, 0, 0, 0, 0, 0], [-9, 1, -2, 2, -12, 3, 1, -3, 2, 1], [0, 4, 4, 0, -8, -2, -2, 0, -4, 2], [0, 0, 0, 0, 1, 0, 0, 0, 2, 0], [7, 0, 0, 6, 0, 0, 0, -1, 0, 1], [0, -1, -1, 0, 1, -1, 0, 1, 1, -1], [3, 0, -1, 3, 0, 0, 1, 0, 0, 1], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, -7, -3, 0, 4, -3, 1, 0, 4, -5], [-1, 1, 1, -1, 0, -1, -1, 1, -1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0]]}