# Stored data for newform 693.2.a.e, downloaded from the LMFDB on 01 May 2024.
{"label": "693.2.a.e", "space_label": "693.2.a", "level": 693, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543037109, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 413919239266710939, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 3, 1]], [5, [1, 1]]], "qexp_display": "q+(-1-\\beta )q^{2}+3\\beta q^{4}-q^{5}+q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2772, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 5.53363286007473, "hecke_ring_index": 1, "level_radical": 231, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.025", "prec": 17}, "analytic_rank_proved": true, "char_values": [693, 1, [155, 199, 442], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 7, 11], "conrey_indexes": [1], "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.988", "prec": 17}, {"__RealLiteral__": 0, "data": "0.029", "prec": 17}, {"__RealLiteral__": 0, "data": "9.600", "prec": 17}, {"__RealLiteral__": 0, "data": "1.197", "prec": 17}, {"__RealLiteral__": 0, "data": "64.101", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [7, -1], [11, -1]], "trace_display": [-3, 0, -2, 2], "traces": [0, 2, -3, 0, 3, -2, 0, 2, -6, 0, 3, 2, 0, -4, -3, 0, 13, -4, 0, -2, -3, 0, -3, -8, 0, -8, 11, 0, 3, -8, 0, 8, -15, 0, -4, -2, 0, -2, 13, 0, 6, 0, 0, -8, 3, 0, 2, -4, 0, 2, 12, 0, -21, -20, 0, -2, -6, 0, 17, -8, 0, 8, -22, 0, 4, 4, 0, -4, 24, 0, 3, 0, 0, -24, -7, 0, -33, 2, 0, 0, -13, 0, -10, -4, 0, 4, 12, 0, -6, 20, 0, -4, 18, 0, 11, 2, 0, -16, -3, 0, -12, 8, 0, -4, 32, 0, 40, -34, 0, -24, 3, 0, 13, -4, 0, 8, -27, 0, -13, -4, 0, 2, -2, 0, 42, 18, 0, 0, 9, 0, -11, 4, 0, -2, 31, 0, -28, 12, 0, 0, -3, 0, 10, -4, 0, 8, 41, 0, 27, -16, 0, -12, 46, 0, -3, -8, 0, 40, 10, 0, 15, -8, 0, 20, 30, 0, 36, 20, 0, -8, 4, 0, -12, 12, 0, -8, 13, 0, -30, -12, 0, 0, 11, 0, -16, 2, 0, -4, -21, 0, -13, -12, 0, 12, 24, 0, 3, 16, 0, 24, 24, 0, -2, -8, 0, 0, -24, 0, -41, -2, 0, 8, -60, 0, 51, 8, 0, 8, 26, 0, -3, -12, 0, -16, -15, 0, 36, -36, 0, 12, -2, 0, 44, 8, 0, 4, 63, 0, -4, -10, 0, 8, -3, 0, -18, -2, 0, 24, -64, 0, -27, -16, 0, -8, 10, 0, -9, -6, 0, -2, 21, 0, 14, -6, 0, 20, 13, 0, -81, 12, 0, -6, 4, 0, -28, -8, 0, -4, -20, 0, 6, 28, 0, 6, -30, 0, 11, 0, 0, 14, -17, 0, -51, 16, 0, 8, -34, 0, 9, -4, 0, -8, 8, 0, -43, -8, 0, -24, 3, 0, 22, -24, 0, 12, -70, 0, -30, 8, 0, -8, -4, 0, 2, -36, 0, 16, -45, 0, -40, -4, 0, 8, -96, 0, -50, 4, 0, -32, -8, 0, -24, 8, 0, 2, 24, 0, 22, 0, 0, -4, 12, 0, -15, 62, 0, 0, 30, 0, -22, -16, 0, 4, 30, 0, -21, 24, 0, 12, -22, 0, 7, -20, 0, -12, -4, 0, 32, 26, 0, -12, 33, 0, 58, -40, 0, -2, -8, 0, -24, 28, 0, 56, -6, 0, -54, 0, 0, 12, -16, 0, -52, -16, 0, -36, -18, 0, 17, -2, 0, 32, 10, 0, 84, -8, 0, 4, 45, 0, 13, 24, 0, 18, 8, 0, 100, 16, 0, 8, -51, 0, -12, 42, 0, 16, -22, 0, -6, -32, 0, -30, 6, 0, 28, -52, 0, -20, 44, 0, 4, -36, 0, 0, -96, 0, 74, 4, 0, -16, 2, 0, -18, 68, 0, -8, -67, 0, -42, -32, 0, -4, -11, 0, -76, -8, 0, 8, 24, 0, 25, 24, 0, -16, -57, 0, 3, 16, 0, 32, 16, 0, 3, 6, 0, -4, -61, 0, 82, 0, 0, -12, 27, 0, 69, 40, 0, -8, 2, 0, -30, -12, 0, -24, 18, 0, 39, 4, 0, -4, -7, 0, -32, 74, 0, -14, -54, 0, -21, 24, 0, 26, -40, 0, -33, -20, 0, 34, 112, 0, -18, 2, 0, 24, -31, 0, 0, 24, 0, -4, 48, 0, 12, 28, 0, 0, -4, 0, 60, 24, 0, 16, -13, 0, -67, -64, 0, 4, -59, 0, 40, 24, 0, 12, -21, 0, -10, 32, 0, 36, 19, 0, 27, -4, 0, -20, 92, 0, -24, -32, 0, -48, 13, 0, 17, 12, 0, 4, 21, 0, 6, -4, 0, -64, 12, 0, 12, -2, 0, 50, 45, 0, 2, 18, 0, -32, 16, 0, -6, -16, 0, -72, -42, 0, 36, 20, 0, 22, 32, 0, 90, 44, 0, -72, 40, 0, -42, 0, 0, -4, 17, 0, -9, 28, 0, -48, 18, 0, 44, 4, 0, -8, -44, 0, 75, -8, 0, -4, 30, 0, 11, -18, 0, 20, 8, 0, 132, 2, 0, 12, 90, 0, -31, 8, 0, -28, 58, 0, 48, 12, 0, -16, 28, 0, -22, 24, 0, -12, -3, 0, -52, 60, 0, 60, -102, 0, -20, 0, 0, 40, -29, 0, -12, 16, 0, -38, 4, 0, -103, 8, 0, -30, -10, 0, -60, 8, 0, 4, 102, 0, -16, 12, 0, -4, -26, 0, -90, 32, 0, 64, 32, 0, -41, 16, 0, -8, -18, 0, 30, -4, 0, -28, -27, 0, 40, 2, 0, 16, -42, 0, 24, -34, 0, -40, -41, 0, -69, 12, 0, 14, 73, 0, -46, -4, 0, -24, -138, 0, 80, -34, 0, -16, 3, 0, -12, 38, 0, -32, 48, 0, -82, -40, 0, 0, -24, 0, 13, -40, 0, -6, 114, 0, -10, -4, 0, 4, -88, 0, -24, -6, 0, -12, 60, 0, 64, -24, 0, 8, 94, 0, 16, 60, 0, -22, -27, 0, -7, -20, 0, 8, -78, 0, -30, 24, 0, -16, -108, 0, -13, 14, 0, 56, -36, 0, -38, -4, 0, -20, -33, 0, -71, 60, 0, -16, -37, 0, -48, 8, 0, 2, -160, 0, 16, 48, 0, 0, -2, 0, 102, 88, 0, -52, 12, 0, -33, -12, 0, -12, 26, 0, 42, 0, 0, 58, 32, 0, 18, 18, 0, -16, 85, 0, -13, 10, 0, 36, -48, 0, 68, -72, 0, 0, 30, 0, -84, 24, 0, 12, 9, 0, 64, -52, 0, 0, -10, 0, 132, 0, 0, -24, -114, 0, -11, -76, 0, -4, -6, 0, -42, 4, 0, 12, 16, 0, -92, 20, 0, 8, -53, 0, 75, -66, 0, -2, 102, 0, 43, 4, 0, -56, 31, 0, 21, -20, 0, 40, 23, 0, 12, -44, 0, 58, -52, 0, -28, -52, 0, 12, -45, 0, -26, 12, 0, 10, 39, 0, 147, -12, 0, 20, -6, 0, -24, -48, 0, 0, -8, 0, 22, -28, 0, 20, -3, 0, -9, -48, 0, -16, 36, 0, 111, 32, 0, -8, -90, 0, 10, -24, 0, -80, -7, 0, -54], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "693.2.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-1, -1], [0, 0], [0, 3], [-1, 0], [0, 0], [1, 0], [-1, -4], [0, 0], [1, 1], [1, 0], [0, 0], [-1, -2], [-1, -1], [0, 0], [5, 3], [-4, 4], [0, 0], [1, -4], [0, -3], [0, 0], [-1, -1], [-6, 4], [0, 0], [-4, 0], [3, 5], [0, 0], [0, 3], [-3, -2], [0, 0], [2, 4], [-6, -3], [0, 0], [0, -4], [-1, 0], [0, 0], [-3, 4], [3, 7], [0, 0], [1, 4], [-2, 4], [0, 0], [-4, 0], [0, 3], [0, 0], [2, -2], [-1, -2], [0, 0], [1, 0], [4, 4], [0, 0], [-6, -9], [-8, -4], [0, 0], [-1, 0], [-1, -4], [0, 0], [5, 7], [-9, 10], [0, 0], [6, -4], [-6, -10], [0, 0], [-1, 6], [1, 2], [0, 0], [3, -10], [12, 0], [0, 0], [1, 1], [2, -4], [0, 0], [-11, -2], [-1, -5], [0, 0], [-12, -9], [1, 0], [0, 0], [2, -4], [-5, -3], [0, 0], [-2, -6], [4, -12], [0, 0], [4, -4], [4, 4], [0, 0], [-1, -4], [10, 0], [0, 0], [-1, -2], [12, -6], [0, 0], [3, 5], [-1, 4], [0, 0], [-8, 0], [-1, -1], [0, 0], [0, -12]]}