# Stored data for newform 549.2.a.g, downloaded from the LMFDB on 07 June 2024. {"Nk2": 2196, "analytic_conductor": 4.383787070968293, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [61, -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": [549, 1, [245, 307], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 148, "field_disc_factorization": [[2, 2], [37, 1]], "field_poly": [1, -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": [[2, [-1, -3, 1, 1]], [5, [13, -9, -1, 1]]], "hecke_orbit": 7, "hecke_orbit_code": 27021597797777957, "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": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "549.2.a.g", "level": 549, "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": false, "level_primes": [3, 61], "level_radical": 183, "minimal_twist": "61.2.a.b", "nf_label": "3.3.148.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{2}+(\\beta _{1}+\\beta _{2})q^{4}+(\\beta _{1}-\\beta _{2})q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "549.2.a", "trace_display": [-1, 0, 1, -3], "trace_hash": 812385600430309596, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.964", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "23.856", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "281.805", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.004", "prec": 17}, "traces": [0, 3, -1, 0, 1, 1, 0, -3, -3, 0, -9, -13, 0, -9, 3, 0, -3, 2, 0, 0, -1, 0, 11, -5, 0, 4, -1, 0, 5, -4, 0, -2, 3, 0, 8, -11, 0, -6, -14, 0, 9, -3, 0, -14, -9, 0, -5, 4, 0, -10, 12, 0, -15, 2, 0, -13, -5, 0, 10, -29, 0, 3, 32, 0, -11, 17, 0, 9, 2, 0, 1, -14, 0, -1, -12, 0, 32, 15, 0, 13, 19, 0, -7, 8, 0, -18, -4, 0, 11, 4, 0, -7, 3, 0, 20, -4, 0, 10, 4, 0, -8, 10, 0, 12, 25, 0, -14, -26, 0, 13, 37, 0, -13, 9, 0, 7, 0, 0, -15, 8, 0, 30, -1, 0, -30, -21, 0, -18, 33, 0, 43, -8, 0, 18, 35, 0, -12, -3, 0, -3, 13, 0, 36, 35, 0, -20, 13, 0, 30, -9, 0, 3, -18, 0, -13, -34, 0, -10, 21, 0, 7, 3, 0, 10, -25, 0, 16, 32, 0, 20, -16, 0, -6, 10, 0, 0, 9, 0, 4, -42, 0, -20, -9, 0, 7, -6, 0, 0, 16, 0, -18, -31, 0, -20, -38, 0, -26, 29, 0, -50, -8, 0, -4, 14, 0, 39, -18, 0, 41, -14, 0, 22, 10, 0, 10, 14, 0, 4, -31, 0, -5, -26, 0, -11, 7, 0, -47, -11, 0, -9, 17, 0, -6, 40, 0, -56, 15, 0, 2, 38, 0, 7, -68, 0, 1, 18, 0, -36, 0, 0, 29, -38, 0, 15, -16, 0, 13, -2, 0, 24, -21, 0, -10, 28, 0, 18, 0, 0, -31, 10, 0, -2, -22, 0, -57, -4, 0, 4, -1, 0, -3, -28, 0, 34, -34, 0, -29, -29, 0, -31, 2, 0, 13, 2, 0, 15, -12, 0, 7, 19, 0, 4, -51, 0, -36, 1, 0, 7, -19, 0, 4, -15, 0, -30, 60, 0, -43, -58, 0, 26, -57, 0, -5, 4, 0, -20, 12, 0, 35, 32, 0, -13, -40, 0, 26, -39, 0, 26, 36, 0, 2, 40, 0, 9, 24, 0, 14, -32, 0, 14, 4, 0, -29, 15, 0, -38, -32, 0, -22, -14, 0, 39, 60, 0, 13, -39, 0, -38, 9, 0, 0, -6, 0, 24, -26, 0, -40, -8, 0, 18, 64, 0, 11, 37, 0, 45, -20, 0, -2, 34, 0, -12, 32, 0, -41, 1, 0, 6, 26, 0, -12, 28, 0, 2, 26, 0, -4, 12, 0, -2, 41, 0, 36, 29, 0, 8, -29, 0, 88, -50, 0, 2, -28, 0, 2, 20, 0, -3, -54, 0, 52, -2, 0, -44, -2, 0, 23, 14, 0, -44, -19, 0, -44, 4, 0, 24, -31, 0, 29, 29, 0, 5, 19, 0, -75, 5, 0, 90, -27, 0, 11, -6, 0, 36, -16, 0, -10, 21, 0, -5, -48, 0, 29, 52, 0, -28, -8, 0, -44, -22, 0, -18, -31, 0, 58, 78, 0, 20, -3, 0, 52, -8, 0, 16, 70, 0, -2, 16, 0, 45, -15, 0, 20, 22, 0, -18, 13, 0, 2, 58, 0, 27, -61, 0, 18, 0, 0, 4, -6, 0, -39, 58, 0, -19, -16, 0, -62, 32, 0, -54, -2, 0, -50, 73, 0, 34, -13, 0, 26, 44, 0, -8, 52, 0, -4, 39, 0, -31, 47, 0, -48, 4, 0, -35, -34, 0, -7, 40, 0, 62, -17, 0, 40, 22, 0, 75, -56, 0, 12, 1, 0, -46, 83, 0, -3, -20, 0, 8, 41, 0, 4, -32, 0, -22, -25, 0, 42, 22, 0, -88, 87, 0, -30, -12, 0, 4, 9, 0, 35, -45, 0, 15, -14, 0, -1, 78, 0, -46, 78, 0, -9, -84, 0, -2, -33, 0, 17, -46, 0, 0, -58, 0, 33, -32, 0, -63, -26, 0, -6, 0, 0, 23, 9, 0, 42, 30, 0, 74, -48, 0, 1, -46, 0, -6, -11, 0, 4, 1, 0, 101, -68, 0, -74, -54, 0, 36, 67, 0, 4, -62, 0, 12, -11, 0, 16, 50, 0, -2, -52, 0, -31, -13, 0, -10, 10, 0, 36, -40, 0, -50, 32, 0, -162, -106, 0, 67, -31, 0, 34, 2, 0, -68, 6, 0, 42, 9, 0, -42, 44, 0, 12, -34, 0, 96, 83, 0, 9, 12, 0, -40, 40, 0, 24, -28, 0, -25, 26, 0, 12, -38, 0, 6, -105, 0, -44, 12, 0, 52, 3, 0, -23, -28, 0, -17, -14, 0, 11, -1, 0, -13, 66, 0, 2, -63, 0, -23, 90, 0, -4, -18, 0, -38, -76, 0, -42, 103, 0, 1, 76, 0, -42, 88, 0, -21, 41, 0, -31, 87, 0, -62, -13, 0, 12, -34, 0, 60, 30, 0, -6, -72, 0, 92, -22, 0, 54, -114, 0, -38, 39, 0, -17, -37, 0, -9, -76, 0, -38, 17, 0, 60, -28, 0, -32, 17, 0, 21, -156, 0, -32, -55, 0, -45, -18, 0, 66, 50, 0, -4, 50, 0, -47, 52, 0, -38, -30, 0, -29, -60, 0, 49, 0, 0, -3, -28, 0, 0, -174, 0, 108, 6, 0, -63, 8, 0, -30, -108, 0, -40, 6, 0, 28, 24, 0, -5, 3, 0, 70, -67, 0, -50, 2, 0, -70, 64, 0, -34, 20, 0, 24, -31, 0, -35, -5, 0, -4, 35, 0, 48, -34, 0, -51, 19, 0, 93, 6, 0, 40, 18, 0, 4, 16, 0, 65, 44, 0, 18, -25, 0, -37, 36, 0, -16, -3, 0, 19, -76, 0, -30, 81, 0, 17, -50, 0, -16, -12, 0, -19, -18, 0, 64, -35, 0, -54, 38, 0, -36, -92, 0, -10, -3, 0, -68, 48, 0, 31, 56, 0, 5, 9, 0, 28, 20, 0, 13, 29, 0, -18, 77, 0, -49, 36, 0, -2, 8, 0, -63, 42, 0, 10, -7, 0, 63, 72, 0, 89, 28, 0, -58, -20, 0, 10, -2, 0, -5, -18, 0, -3, 6, 0, -12, -42, 0, 10, 70, 0, 43, 8, 0, -60, 32, 0, -88, -92, 0, -14, -14, 0, 6, 15, 0, 7], "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, 0], [1, 0, 0], [0, -1, 0], [0, 0, 0], [0, 1, 1], [0, 1, -1], [0, 0, 0], [-1, 0, 1], [-1, 0, -1], [0, 0, 0], [-3, 0, -1], [-4, -1, 0], [0, 0, 0], [-3, 0, -2], [1, 0, 0], [0, 0, 0], [-1, 0, -2], [1, -1, 1], [0, 0, 0], [-1, 3, 3], [-1, 2, 2], [0, 0, 0], [2, 5, 1], [-2, 1, 0], [0, 0, 0], [2, -2, 0], [-2, 5, 0], [0, 0, 0], [2, -1, -2], [-1, -1, 1], [0, 0, 0], [1, -5, -1], [0, 3, 2], [0, 0, 0], [3, -1, 1], [-4, 1, 2], [0, 0, 0], [-3, 3, 3], [-3, -5, -3], [0, 0, 0], [4, -3, 0], [-1, 0, -4], [0, 0, 0], [-5, 1, -1], [-1, -6, -5], [0, 0, 0], [-2, 1, -1], [2, -2, 4], [0, 0, 0], [-3, -1, -3], [4, 0, 2], [0, 0, 0], [-4, -3, -1], [0, 2, 0], [0, 0, 0], [-3, -4, 3], [-2, 1, 1], [0, 0, 0], [3, 1, 1], [-11, 4, 1], [0, 0, 0], [1, 0, 0], [9, 5, 5], [0, 0, 0], [-2, -5, 1], [8, -7, 1], [0, 0, 0], [5, -6, -1], [1, -1, -1], [0, 0, 0], [0, 1, -1], [-3, -5, -1], [0, 0, 0], [0, -1, 3], [-3, -3, -3], [0, 0, 0], [9, 5, -1], [5, 0, -4], [0, 0, 0], [6, -5, -4], [8, -5, -1], [0, 0, 0], [-4, 5, 0], [4, -4, -4], [0, 0, 0], [-7, 3, -1], [-3, 5, -1], [0, 0, 0], [3, 2, 4], [2, -2, -4], [0, 0, 0], [-3, 2, 1], [1, 0, -1], [0, 0, 0], [8, -4, 2], [-3, 5, 7], [0, 0, 0], [2, 4, -4], [-1, 7, 1], [0, 0, 0], [-2, -2, 0]]}