# Stored data for newform 418.2.e.b, downloaded from the LMFDB on 05 May 2024.
{"label": "418.2.e.b", "space_label": "418.2.e", "level": 418, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538832290, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1114801644585988182, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [0, 1]], [5, [1, 1, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}-\\zeta_{6}q^{4}+(-1+\\zeta_{6})q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1672, "analytic_conductor": 3.33774680448952, "hecke_ring_index": 1, "level_radical": 418, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [418, 3, [343, 287], [3, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 11, 19], "conrey_indexes": [45, 353], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.893", "prec": 17}, {"__RealLiteral__": 0, "data": "0.057", "prec": 17}, {"__RealLiteral__": 0, "data": "10.573", "prec": 20}, {"__RealLiteral__": 0, "data": "1.809", "prec": 17}, {"__RealLiteral__": 0, "data": "91.888", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, 0, -1, 2], "traces": [0, 2, -1, 0, -1, -1, 0, 2, 2, 3, -1, 2, 0, -2, -1, 0, -1, 0, -6, -1, 2, 0, -1, 6, 0, 4, 4, 0, -1, 8, 0, -20, -1, 0, 0, -1, 3, 6, -7, 0, -1, 2, 0, 8, -1, -6, -12, 0, 0, -12, -8, 0, -2, 9, 0, -1, 2, 0, -16, 14, 0, 0, 10, 3, 2, 4, 0, -12, 0, 0, -1, -6, 3, 0, -3, 0, 8, 2, 0, 11, -1, -9, 2, 14, 0, 0, 8, 0, 2, -14, 3, -2, 6, 0, 0, -7, 0, -5, 6, 3, 4, -10, 0, 12, -2, 0, -18, 34, 0, 10, -1, 0, -1, 4, 0, -12, 8, 6, 14, 0, 0, 2, 0, 0, 10, -18, -6, -20, -1, 0, -2, 20, 0, -1, 24, 0, 0, 23, 0, 5, 2, 0, -6, -2, -6, -16, 0, 0, -3, 4, 0, -18, -1, 0, -1, 10, 0, -21, 11, 0, 2, 6, -9, -8, -4, 0, -7, -9, 0, 9, 0, -24, -16, -22, 0, 4, -1, 0, 28, -32, 3, 5, 4, 0, 6, -3, 0, 0, 0, 0, 8, -36, 0, -4, -5, 0, 6, 4, -6, -10, 4, 0, 20, 8, 0, 2, -6, -18, 4, -1, 0, -13, 9, 0, -17, 8, 0, -20, 10, 0, 2, 0, 0, 16, -1, -12, -2, 50, 0, -2, 6, 0, 8, 18, 6, 0, -28, 0, 0, -10, 0, -10, -1, 0, 0, 6, 0, 16, -20, 0, 9, 12, 3, 6, 40, 0, -1, 21, 0, 6, -2, -24, 20, 3, 0, -18, -7, 0, -12, 21, 0, -15, 0, 0, -46, 4, 0, -4, -10, -30, -1, -20, 0, 7, 12, 0, 4, 2, 3, 17, 8, 0, 0, 0, 0, 14, 6, 0, 4, 12, 0, 8, 9, 0, -7, 0, 0, 23, -1, 0, 10, -20, 0, 21, -21, -6, -22, -22, 0, 8, -1, 0, -12, 0, 18, 8, 4, 0, 2, 0, 0, -8, -7, 9, 18, 24, 0, 8, 9, 0, 0, -20, 3, -26, 8, 0, -22, 3, 0, 56, -8, 0, -1, 22, 0, -6, -14, 0, 16, -3, -6, -37, -10, 0, -2, 0, 0, -10, -12, 12, -3, 9, 0, -8, 0, 0, 0, 16, 0, 4, -1, 0, 18, -8, 0, -1, -4, 48, 10, 23, 0, 0, -12, 0, -2, 11, 3, 27, 20, 0, -8, -10, 0, 20, -10, -9, -16, 6, 0, -10, -4, 0, -6, 14, -18, -7, -2, 0, -7, 0, 0, 15, -13, 0, 9, 0, 0, 0, -17, 0, -16, -5, 0, -30, 10, 0, -20, -48, 0, -29, -1, -18, 0, -22, 0, 28, 16, 0, 2, -10, -12, 2, -2, 0, -25, 4, 0, 76, 1, 0, 6, -26, 0, 32, -16, 0, 18, 12, -12, -12, 0, 0, 14, 8, 0, -32, 0, -27, 5, 32, 0, -6, 20, 0, -1, -5, 0, -4, 0, 0, 6, 15, 0, 0, -2, -6, 10, -6, 0, 32, 9, 0, -24, -16, 3, 20, -12, 0, -20, 21, 0, 0, 2, 0, -42, -6, 0, 0, -3, 0, 4, -62, -24, 7, -40, 0, 3, 0, 0, -13, 9, 84, 8, -8, 0, -17, -12, 0, 21, -12, 0, -8, -15, 0, 0, 10, 0, 1, 23, 0, -8, -64, 0, 11, 2, 0, 5, 30, 60, -32, -1, 0, 40, -34, 0, -2, 7, -9, -6, 20, 0, -74, -2, 0, 2, -24, 3, 50, -34, 0, 8, 14, 0, 9, 0, 6, 0, -26, 0, 10, -28, 0, -3, -14, 0, 0, -8, 0, 12, 16, 0, 84, 8, 36, 9, -1, 0, -16, 8, 0, 0, 0, 0, -4, 23, 0, 2, 15, 0, 92, -20, 0, 10, -14, 0, -11, -42, 0, 42, 0, 3, 22, 11, 0, 44, 40, 0, 12, -16, -36, -1, -39, 0, 16, 6, 0, 0, 36, -9, 14, 8, 0, 4, -36, 0, 20, 2, 0, 0, 15, 0, 11, 4, 0, 14, -7, -18, -48, -9, 0, -12, 0, 0, 88, 8, 0, -18, -72, 0, -5, 0, 0, 10, 52, 21, -46, 13, 0, 8, 18, 0, -100, 44, 3, 3, -10, 0, 0, -28, 0, 4, 36, 0, -3, 2, 0, -11, -10, 0, -43, 12, 66, -14, -60, 0, 4, 16, 0, -3, -8, 3, 12, 26, 0, 5, -32, 0, -26, -2, -54, 0, 0, 0, -72, 20, 0, 6, -12, -6, -4, 6, 0, -18, -41, 0, 4, 4, 21, 0, 34, 0, -8, 0, 0, 16, 9, 0, 50, -2, 0, -7, -72, 0, 10, 18, 0, -8, -56, 0, -2, -1, 0, 8, -38, -24, -40, -5, 0, -46, 14, 0, -6, 0, 0, 6, -21, 0, 22, -2, 0, -22, 4, 3, 0, 27, 0, -10, 42, 0, 0, 4, 42, -10, 0, 0, -12, -40, 0, -10, -88, 18, -23, 8, 0, -3, 4, 0, 56, 20, 6, 2, 20, 0, 16, 12, 0, 14, 8, 36, -20, -7, 0, -2, 0, 0, 18, 8, 0, 0, 16, 0, -35, 15, 0, 26, 9, 0, 2, -18, 0, 0, 18, 0, 30, 0, 3, 34, 0, 0, 14, 8, 0, 10, -64, 0, -22, 60, 0, 10, 11, 0, -24, 10, -30, 6, -18, 0, 18, -29, 0, -1, -28, 36, -20, 0, 0, 44, 35, 0, -20, -14, -9, -32, 0, 0, 16, -1, 0, 5, -80, 24, 0, 2, 0, 4, -10, 0, 38, -25, 30, -2, -24, 0, 14, -38, 0, 1, 20, 0, -78, -12, 0, -26, 24, 0, 12, -16, 18, 8, 6, 0, 6, -36, 0, -6, 0, 6, -16, 24, 0, 0, -24, 0, 24, 14, 0, 8, -10, 0, 0, 4, 0, 0, -34, -27, 18, 5, 0, -64, 23, 0, 138, 12, 51, -10, -4, 0, 1, 2, 0, 10, 20, 0, 5, 2, 0, 0, 66, 0, -14, -12, 60, 15, -14, 0, -2, 0, 0, -14, 96, 3, -4, 10, 0, -6, 20, 0, -52, 32, 0, -18], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "418.2.e.b", "char_is_minimal": true, "conrey_index": 45, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [-1, 1], [0, 0], [0, -1], [-1, 1], [0, 0], [1, 0], [1, 0], [0, 3], [0, -1], [1, 0], [0, 0], [0, -2], [-1, 1], [0, 0], [-1, 1], [0, 0], [-3, 0], [-3, 5], [1, 0], [0, 0], [-1, 1], [0, 6], [0, 0], [0, 4], [2, 0], [0, 0], [0, -1], [0, 8], [0, 0], [-10, 0], [0, -1], [0, 0], [0, 0], [-1, 1], [3, -3], [3, 0], [-2, -3], [0, 0], [-1, 1], [2, -2], [0, 0], [8, -8], [0, -1], [-3, 0], [-6, 0], [0, 0], [0, 0], [-6, 0], [-4, 0], [0, 0], [-2, 2], [0, 9], [0, 0], [-1, 1], [1, 0], [0, 0], [-8, 0], [14, -14], [0, 0], [0, 0], [10, -10], [0, 3], [1, 0], [2, 0], [0, 0], [0, -12], [0, 0], [0, 0], [0, -1], [-6, 6], [0, 3], [0, 0], [-3, 3], [0, 0], [5, -2], [1, 0], [0, 0], [11, -11], [0, -1], [-9, 9], [0, 2], [7, 0], [0, 0], [0, 0], [0, 8], [0, 0], [1, 0], [0, -14], [3, -3], [0, -2], [6, -6], [0, 0], [0, 0], [-2, -3], [0, 0], [-5, 5], [6, -6], [0, 3], [4, -4]]}