# Stored data for newform 285.2.a.d, downloaded from the LMFDB on 06 September 2025. {"Nk2": 1140, "analytic_conductor": 2.275736457606491, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [5, -1], [19, 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": [285, 1, [191, 172, 211], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 28, "field_disc_factorization": [[2, 2], [7, 1]], "field_poly": [-7, 0, 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": [[2, [-7, 0, 1]], [7, [-6, 2, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798915666205, "hecke_ring_generator_nbound": 2, "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": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "285.2.a.d", "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.a.d", "nf_label": "2.2.28.1", "prim_orbit_index": 1, "qexp_display": "q+\\beta q^{2}-q^{3}+5q^{4}+q^{5}-\\beta q^{6}+(-1+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "285.2.a", "trace_display": [0, -2, 2, -2], "trace_hash": 470291384588819443, "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "1.948", "prec": 17}, {"__RealLiteral__": 0, "data": "0.202", "prec": 17}, {"__RealLiteral__": 0, "data": "9.569", "prec": 17}, {"__RealLiteral__": 0, "data": "1.670", "prec": 17}, {"__RealLiteral__": 0, "data": "66.102", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 2, 0, -2, 10, 2, 0, -2, 0, 2, 0, 6, -10, -6, -14, -2, 22, -8, 0, -2, 10, 2, 14, 8, 0, 2, -14, -2, -10, 2, 0, 12, 0, -6, 0, -2, 10, 2, 0, 6, 0, -14, 14, 6, 30, 2, -28, 8, -22, 2, 0, 8, -30, 12, 0, 6, -42, 2, -42, 12, -10, -12, 0, -2, 26, -6, -14, 8, -40, -8, -14, 4, 0, 20, -14, -2, -10, -20, 14, -8, 22, 2, 14, 12, 10, -8, -14, -2, 42, -18, 0, 20, 40, -12, 28, -2, 0, 10, 28, 6, 10, 8, 0, 0, -42, 2, -28, 0, -10, 0, 14, -2, -22, -8, 0, 8, 10, -6, -28, 8, 0, 10, 28, 14, 60, 2, -14, 8, 0, -6, -14, -2, -30, 2, 56, -2, 0, 12, 28, 4, -10, -8, -28, -32, 22, 2, 0, -2, 10, -20, 0, 4, 0, -8, -56, 12, 30, -16, -56, -12, 0, 20, 0, -10, -70, -6, 0, -32, 42, 6, 0, -2, 30, 0, 42, -2, 66, -12, 42, -4, 10, 24, 56, 12, -84, 2, 0, -24, 40, 2, 0, -14, -26, -18, 42, 6, 10, -8, 14, 4, 0, -8, -28, 40, 40, -14, 56, 8, -66, -6, 14, -16, 60, -4, 0, 6, 0, -12, -28, -20, 30, 24, 14, -16, -70, 2, 0, -32, 10, 28, -28, 20, -126, -36, -14, 8, 60, 8, 56, 26, -22, 12, 84, -2, -60, 2, -14, 6, 0, -12, 0, -38, -10, -4, 0, 8, -10, -32, 14, 12, -30, 2, 70, -12, -42, 12, 14, 18, 40, -18, 0, -20, -88, -20, 0, 6, -40, -20, -84, 12, -42, -38, -28, 14, 20, 2, -84, 0, 0, -2, -42, -10, 100, 32, -28, 12, -42, -6, 56, 4, -10, 8, 56, -8, -22, -12, 0, 4, -100, 0, 0, 30, 42, 24, 28, -2, -40, -12, 28, -36, 26, 0, -28, 8, 10, -6, -14, 0, 42, -36, -14, 44, 60, 2, 28, 8, 22, 14, 84, 8, -40, 36, 0, -16, -42, -8, 0, 52, -10, 4, -14, 6, 70, -20, 28, 4, -90, -8, 28, -14, 0, 2, -28, -10, 100, 20, -28, -2, 88, -14, -14, 16, -60, 26, -56, -2, 84, 36, 14, 20, -10, -8, -70, -16, 0, -20, 14, 6, 50, -12, 14, -32, 84, 2, 112, -8, 30, -4, -28, -2, 22, 6, -56, -36, 40, 2, 28, -8, 0, -24, 14, -12, 0, 16, -28, 12, -70, -4, -14, 62, 10, 36, -56, 8, -84, -8, 28, -16, 0, 32, -14, -4, -22, -50, -84, -2, 0, -8, 0, -24, 42, 2, 56, 64, -10, -18, -56, 20, -26, -46, 0, -28, -40, -4, -28, 20, 0, 32, 28, 8, 40, -12, 56, -34, 22, -12, 0, 8, -30, -64, 28, 16, -84, 4, 56, -2, 40, 12, -14, 14, 0, 8, -56, -20, 50, 10, 0, 4, 84, 10, 28, -38, 70, -8, 14, 6, 132, 24, 0, 12, 10, 32, -14, -4, -42, 8, -28, -6, 40, -10, 0, -20, 0, 2, -56, 0, -30, 52, 0, 0, -42, -14, -42, -36, -10, 2, -56, -48, -66, 42, -28, 12, 10, 28, -42, 0, 168, 4, -70, 34, -10, 60, -28, -24, 0, 0, -56, -28, 60, -12, 14, -2, 84, 64, -56, -2, 20, -44, 0, -4, -22, 24, 70, 48, -40, -8, 98, -2, -84, -30, 0, 44, -160, 14, 84, 8, 26, -16, 0, 18, 10, -12, -42, 8, 0, -6, 56, -56, -10, -12, -28, 8, 22, 28, -14, 8, -100, -4, 28, 40, 0, 56, -28, 8, 20, 10, 28, -12, 0, -40, 28, -52, -40, -8, 140, 14, -168, 24, -56, 36, 60, -8, -42, -24, 66, 2, -28, 6, -80, -8, -14, -8, -168, 16, -140, 8, -60, -34, -112, 4, 0, -18, 0, -22, 100, -6, 0, -28, 0, 8, -14, 12, -50, 40, 28, -2, -154, 20, -84, 72, -30, -8, 56, -24, 0, 2, -14, 92, -160, 16, 56, -8, 70, -42, -42, -2, 30, 28, 0, -52, 0, 32, 84, -24, -10, 12, 56, -28, 66, -8, 28, -12, 0, -20, 0, 4, 126, 56, -112, 36, -10, 12, 14, -2, 78, -8, -56, 20, -60, -20, -28, -8, 126, 48, -56, -32, -20, -26, 154, 18, 22, -56, 0, -12, 120, 2, -84, -30, 168, 2, 0, -24, 60, 36, -14, -2, -140, 80, 14, -40, 10, -6, -56, 0, 0, -20, 42, 12, -120, 0, 0, -68, 88, 38, 112, 4, 10, -16, 0, 4, 0, -12, 0, 28, -70, -8, 56, -8, 10, 28, -56, 32, -90, -28, -14, 12, 126, -12, 0, 14, 30, -16, 112, -2, 22, -16, -70, 44, -40, 12, -56, 8, 42, 8, 0, -12, 20, 80, -14, -32, 0, -18, 42, 60, -40, 20, -84, 18, -84, -60, 0, -8, 200, 20, -28, -10, 88, -6, -28, 20, -70, 0, 0, -18, 168, -6, -56, 8, 40, 16, 0, 20, -78, -8, 84, -32, -30, -12, -42, 28, 42, 70, -56, 38, -80, 6, 28, -94, 132, -14, 0, 36, -20, 40, 56, -2, 0, -12, 84, 16, 30, 0, -28, -40, 0, 0, 14, 2, -60, -80, 42, -80, -84, 10, 28, -2, -100, -66, -56, -32, 66, -32, 28, -26, 120, -12, 28, -48, 42, -8, 42, 6, -80, -8, -56, -4, -42, -4, 70, 12, 10, -48, -56, -8, 0, 24, -56, -20, -160, 8, 56, 32, 22, 36, 84, 12, 140, -68, 0, 72, -84, -4, 168, 16, 100, 2, 98, 0, -210, 8, 0, -2, -180, -30, -84, -24, -42, 72, -112, -24, 40, -50, -28, -84, 132, 2, 0, 44, 40, -60, 0, 12, 168, 0, -28, -14, 130, 36, 14, -12, -26, 10, 28, 0, 60, -18, 28, -78, 252, -8, 42, 0, -10, 80, -84, 6, -132, -28, 14, -12, 10, 0, -70, 16, -42, -8, 168, 36, 30, 52, 14, -8, 0, -44, 0, 4, -60, 64, 196, -2, 0], "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], [0, 1], [-1, 0], [5, 0], [1, 0], [0, -1], [-1, -1], [0, 3], [1, 0], [0, 1], [3, 1], [-5, 0], [-3, -1], [-7, -1], [-1, 0], [11, 0], [-4, 0], [0, 1], [-1, 0], [5, 0], [1, 1], [7, 3], [4, -2], [0, -3], [1, 0], [-7, -3], [-1, 0], [-5, -5], [1, -3], [0, -1], [6, 0], [0, 5], [-3, -1], [0, -4], [-1, -1], [5, 0], [1, -1], [0, -1], [3, 1], [0, 3], [-7, 1], [7, 1], [3, -1], [15, 5], [1, 0], [-14, 4], [4, 2], [-11, 0], [1, 2], [0, 1], [4, 0], [-15, -5], [6, -2], [0, -1], [3, 1], [-21, -3], [1, 0], [-21, 1], [6, -2], [-5, 0], [-6, 2], [0, 6], [-1, -1], [13, 0], [-3, -1], [-7, -3], [4, 4], [-20, 0], [-4, 2], [-7, -1], [2, -2], [0, 3], [10, 0], [-7, 1], [-1, 0], [-5, 0], [-10, -4], [7, 3], [-4, -4], [11, 0], [1, 0], [7, -7], [6, 0], [5, 5], [-4, 0], [-7, 3], [-1, 3], [21, 9], [-9, 3], [0, 1], [10, 4], [20, -10], [-6, 0], [14, 4], [-1, 0], [0, -5], [5, 3], [14, 1], [3, 1], [5, 0]]}