# Stored data for newform 229.2.e.a, downloaded from the LMFDB on 14 June 2024. {"Nk2": 916, "analytic_conductor": 1.8285742062873207, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 229, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 6, "char_parity": 1, "char_values": [229, 6, [6], [5]], "cm_discs": [], "conrey_index": 95, "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, [3, 0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 274911461605, "hecke_ring_generator_nbound": 3, "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, 229, 5, 1, 6, 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": true, "label": "229.2.e.a", "level": 229, "level_is_powerful": false, "level_is_prime": true, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [229], "level_radical": 229, "minimal_twist": "229.2.e.a", "nf_label": "2.0.3.1", "prim_orbit_index": 5, "qexp_display": "q+(1-2\\zeta_{6})q^{2}+(1-\\zeta_{6})q^{3}-q^{4}-3\\zeta_{6}q^{5}+\\cdots", "related_objects": ["Genus2Curve/Q/52441/a"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "229.2.e", "trace_display": [0, 1, -3, -3], "trace_hash": 1630447864956428868, "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "2.031", "prec": 17}, {"__RealLiteral__": 0, "data": "0.088", "prec": 17}, {"__RealLiteral__": 0, "data": "12.173", "prec": 20}, {"__RealLiteral__": 0, "data": "0.636", "prec": 17}, {"__RealLiteral__": 0, "data": "97.667", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.177", "prec": 17}, "traces": [0, 2, 0, 1, -2, -3, -3, -3, 0, 2, -9, 0, -1, 0, 3, -6, -10, 12, 6, -5, 3, 0, 0, 3, -3, -4, 0, 10, 3, 3, 0, -3, 0, 0, 0, 9, -2, 1, -15, 0, -9, 3, 6, 8, 0, 6, 3, 9, -5, -4, 12, 6, 0, -12, 0, 0, 3, -10, 3, 21, 6, 20, 3, -6, -2, 0, 0, 3, -12, 3, 9, -9, 6, 27, -3, 4, 5, 0, 0, -27, 15, -1, -3, -15, 0, -18, 0, 3, 0, -9, -18, 0, -3, 0, -9, -15, 9, 1, 12, 0, 4, 0, -18, -19, 0, 9, 0, 0, -10, 0, 0, -1, 15, 15, 0, 0, -3, 0, -21, -18, 0, -22, 0, 0, 3, -6, -6, -9, 0, 4, 0, -9, 0, 15, 3, -15, 0, 27, -3, -33, -9, 0, -27, 0, -10, 0, 27, 4, -1, -3, 12, -11, -15, 12, 0, 9, 0, 39, 27, -6, 27, -6, 3, 3, -3, 0, 45, 3, 6, 26, -54, 10, -8, -3, -3, 0, 0, 0, -9, -21, -6, -7, 0, 10, 3, -6, 6, 0, -9, -15, 45, 9, -1, -7, -3, 0, 4, 0, 0, 0, 12, 3, 24, -6, -6, -9, 57, 0, 0, 0, -9, 9, 12, -18, -12, -12, 0, 3, 48, 27, 0, 0, -3, -21, -9, -16, 15, 0, 10, 22, -18, 0, 3, -12, 0, -27, -21, 0, 18, -15, 30, -19, 0, 16, -20, 24, -6, 0, 3, 15, 0, 0, 6, 0, -9, -36, 38, 39, -12, 0, 0, 0, -9, 0, 0, 18, 15, -9, -3, 51, -45, 16, -60, 0, 27, 0, -3, -19, -33, -6, 9, 0, -18, 0, 9, 15, 0, -3, -18, 38, -18, -1, -27, -60, 12, -63, -3, 0, -9, 0, -4, -12, 33, 12, 25, -30, 36, 29, 0, 19, 9, 3, 0, 0, -39, 0, 27, 0, 18, 0, 3, -6, 0, -30, 1, 0, 3, 24, -3, -9, 0, -9, 15, 4, 9, 0, 0, -4, 0, 15, 18, 0, -30, 0, 0, -9, -9, 3, -3, 0, -24, 0, 0, -21, -42, -27, 9, 0, -21, -33, -18, -6, 21, -11, 0, 0, -30, -17, -15, 6, 0, 18, 0, 1, 0, -3, -9, 0, 15, -27, 15, -9, -9, -33, 21, 0, -21, 8, -1, -9, 0, 18, 12, -9, -72, 81, 0, 68, 12, 15, 20, 36, -3, 0, 0, 6, 0, 0, -18, -19, -9, 27, 19, -21, 12, 90, 0, -33, 0, 63, -9, -19, -9, 18, 0, -24, 0, -30, 0, 0, -36, -24, -50, -7, -9, -9, 0, 0, -27, 35, 0, -16, 0, 24, 1, 0, -21, -6, 3, 21, 0, 0, -15, 11, 84, 0, 0, -68, -36, 60, 0, 33, 0, 23, -15, 9, 0, 15, 0, -6, -27, 0, -21, 0, 54, 40, 18, -12, 15, 0, 0, 0, 57, -3, 22, -6, 48, 3, 0, 3, 0, -27, 0, 18, 0, 0, 15, 27, 45, -39, 6, 6, -36, 9, -6, 36, 0, 13, 9, -27, 0, -54, 0, -25, -39, 114, -4, 0, 6, -6, 0, -57, 12, -15, 9, -12, 12, -18, 0, -20, 54, 42, -15, 0, 9, -18, 3, -21, -51, 0, 15, -23, 0, 7, 0, 72, 0, 51, -27, 20, 0, 0, -3, 27, 57, -3, 33, -3, -6, 0, -45, 0, -72, -15, 0, 0, -36, 0, -27, -27, 45, -33, 0, 0, 9, -12, -2, 39, 0, -14, 0, 0, -3, 0, 27, 0, 0, 21, -4, 15, -63, -36, -5, -27, 0, 54, 3, 6, 0, 0, 12, 0, 12, 0, 11, 33, 12, -25, 45, -3, -90, 0, -12, -33, -87, -9, 0, 21, 57, -88, -9, 15, 9, 18, 0, 29, 120, 0, -39, 6, 36, -37, 27, 0, 0, 0, 6, 0, 0, 18, 63, 21, -6, -8, 6, -24, -90, 45, 3, 0, 0, -3, -3, 0, 24, 0, -15, 0, 27, -63, 0, -76, -9, 0, 45, 0, 0, 3, -3, -21, -18, 0, -18, 1, 0, -20, -26, -69, -15, 0, -54, 42, 0, -72, -10, 0, -66, -7, -40, 0, -9, 88, 3, 0, 9, 0, -3, 18, -48, -6, 0, -27, 0, -10, 0, -27, 21, -12, 0, 0, 81, -54, -9, -6, 36, 0, 21, 0, -99, 0, -30, 0, 18, 19, 7, -12, 33, 33, 0, 26, -162, 48, -10, 1, -51, 12, -9, 0, 6, 0, 6, 0, -18, 51, 6, -9, 3, -60, 0, 6, 9, 64, -45, -18, 0, 66, 15, 41, 27, 0, 45, -9, 9, -24, -9, 36, -99, 0, 19, 25, 0, 0, 7, 0, 24, 0, -3, 3, 9, -15, 0, 0, 18, 15, 20, -117, 9, 13, 0, 6, 81, -30, 0, 0, 0, 36, 0, -45, -15, 54, -36, 0, 0, 0, -3, 9, 0, 0, 24, 0, 0, 45, 6, 8, 0, 0, -30, -20, 57, 0, 9, -39, -27, 0, 57, 0, 63, -45, 0, 15, 0, 19, 0, -24, 33, 9, 0, -15, 63, -3, -9, -26, 57, -36, -9, -39, 18, 33, 60, -18, 72, 3, 18, 75, 30, -60, -12, 15, 0, 40, 12, 3, 0, -96, 0, -9, 21, 19, -3, 0, -9, 0, 48, 4, -30, 9, -27, 87, 105, -30, 0, -57, 0, -47, 0, -63, 0, 63, -3, 18, 54, 0, 21, -45, 0, 0, -21, 0, 63, -6, 16, -72, 0, 0, 15, 42, 33, 43, 0, -24, 0, 27, 50, 0, 0, -60, -22, 18, 0, 41, -18, -29, -99, 0, 0, 4, 69, -76, -9, 0, -9, 40, 12, 6, 45, 0, 0, 0, 0, 60, 27, -51, -78, 6, -105, 45, 0, 57, 0, 0, 0, 0, 18, -51, -36, -27, 15, 0, 60, -54, 6, -28, 0, 12, 19, -21, 9, -23, 0, -60, 0, -9, -16, 66, 3, 0, -100, 12, -3, 0, -24, -48, 81, -33, -6, -108, 18, 9, 0, 12, 0, 23, -9, -9, 27, 18, -15, -7, 39, 5, 0], "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, -2], [1, -1], [-1, 0], [0, -3], [-1, -1], [-2, 1], [1, -2], [0, 2], [-6, 3], [0, 0], [-1, 1], [0, 0], [0, 3], [-3, 0], [-5, 0], [6, 0], [4, -2], [0, -5], [0, 3], [-1, 2], [0, 0], [1, 1], [-1, -1], [-4, 4], [0, 0], [5, 0], [2, -1], [1, 1], [-3, 6], [-2, 1], [-3, 6], [0, 0], [6, -12], [3, 3], [0, -2], [1, -1], [-10, 5], [0, 0], [-6, 3], [2, -1], [3, 0], [4, 0], [0, 0], [6, -6], [3, -3], [6, -3], [-5, 5], [-4, 4], [4, 4], [6, -6], [0, 0], [-6, 0], [5, -10], [0, 0], [0, 3], [-5, 0], [3, -3], [14, -7], [3, 0], [10, 0], [0, 3], [-2, -2], [-1, 0], [0, 0], [0, 0], [1, 1], [-6, 0], [2, -1], [9, -9], [0, -9], [4, -2], [9, 9], [-1, -1], [0, 4], [0, 5], [0, 0], [0, 0], [-18, 9], [0, 15], [-1, 1], [0, -3], [-15, 15], [1, -2], [0, -18], [4, -8], [2, -1], [0, 0], [-3, -3], [-6, -6], [0, 0], [-1, -1], [-1, 2], [0, -9], [-15, 15], [3, 3], [1, -1], [4, 4], [0, 0], [4, -4]]}