# Stored data for newform 414.2.e.a, downloaded from the LMFDB on 11 May 2024.
{"label": "414.2.e.a", "space_label": "414.2.e", "level": 414, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 274911461790, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1102771686872624678, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [16, 4, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{2}+(1+\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1656, "analytic_conductor": 3.305806643681008, "hecke_ring_index": 1, "level_radical": 138, "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": "0.014", "prec": 17}, "analytic_rank_proved": true, "char_values": [414, 3, [47, 235], [1, 3]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 23], "conrey_indexes": [139, 277], "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": "1.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "12.254", "prec": 20}, {"__RealLiteral__": 0, "data": "1.811", "prec": 17}, {"__RealLiteral__": 0, "data": "114.868", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, 3, -4, 0], "traces": [0, 2, 1, 3, -1, -4, 3, 0, -2, 3, -8, 3, 0, -4, 0, 0, -1, 14, 6, -10, -4, 0, -3, -1, -3, -11, -8, 0, 0, 4, -12, 2, 1, 9, 7, 0, 3, 16, -5, 0, 4, 7, 0, 1, -6, 12, -2, -10, -3, 7, 11, 21, -4, 20, 9, -24, 0, -15, -4, -13, -12, -2, 4, 0, 2, -16, 0, 7, -7, 0, 0, 0, -3, -18, 8, -33, 5, 0, -12, -2, 8, -9, 14, -4, 0, -28, -1, 12, -3, 36, -12, 0, -1, 0, 10, 20, 0, -7, 14, 18, 22, 0, 21, -2, 4, 0, 10, -10, 9, -20, -12, 24, 0, -18, -15, -4, -8, 12, -26, 0, 0, 2, 2, 0, 2, 48, 0, 32, 1, 3, 16, 12, -9, 0, 14, 36, -14, 13, -3, 5, 0, -30, 0, -24, -6, -32, -9, 0, -8, -10, 0, 20, 10, 21, 0, 8, -12, -2, 2, 30, 4, 0, 9, -8, 7, -36, 4, -12, 0, -3, -56, -15, -2, -10, 0, 0, 3, 0, 18, -24, -24, -16, 0, -6, 1, -32, 6, 21, 20, 0, 40, -6, 3, -1, 7, -48, 7, -8, 9, -28, 11, 0, 0, 0, 0, 28, -4, 3, 8, -15, 0, 12, -10, 0, -5, -8, 0, 0, -10, -27, 12, -28, 24, -18, 0, -66, -36, 7, 0, 6, 4, 0, -4, -10, -12, 80, -13, -6, 0, 0, 12, 1, 4, -27, 4, 28, 21, 20, -2, -12, 24, 2, 0, -6, 16, 0, -1, 21, 0, 0, 32, 24, 24, -22, -9, -40, 0, 54, 7, -20, 0, 4, -7, 0, -13, 33, -3, -4, 10, -6, 0, 26, 0, 0, 0, 0, -12, 0, -3, 64, -16, -21, 9, -24, 21, -52, -16, 27, -20, -4, 33, 0, -20, 0, 5, 16, 42, 46, 0, 0, -8, -20, 0, 1, -4, 0, 4, 2, 30, -12, -4, -15, 0, -70, 18, 88, -4, -30, -7, 0, -36, -32, 8, 24, -24, 28, 0, -9, 3, 0, -28, 12, -30, 0, -1, -12, 10, -27, -12, 6, 0, 36, 6, 25, -39, 0, -18, 0, -12, 24, -12, 12, -8, 0, 0, 36, 0, -24, 2, -21, -64, 0, 6, 36, -21, 72, 10, -32, 0, -2, 20, 48, 6, -26, 3, 0, -2, 6, 14, -10, 0, -7, -7, 0, -4, 16, -9, 0, -14, 0, -11, 37, 21, 8, 0, 72, 0, 24, -21, -5, -28, 39, -2, 0, -3, 32, 4, 0, 15, 0, 0, 12, 24, -60, -20, -77, 0, 0, 5, -36, -4, 72, -9, -2, 0, -48, 10, 5, -27, -28, 24, -21, -56, -29, 0, -72, 18, 0, 0, 18, -33, 42, -18, 60, -7, 0, 15, -27, 12, 0, 8, -42, 0, -6, 4, 24, -5, -78, -24, 0, 40, 0, 13, -3, 0, 55, 0, 30, 0, 0, 12, -32, -1, 0, 2, 56, 0, -64, 2, -12, -28, 25, 21, 28, 40, -36, -4, 0, 0, 35, -24, 0, 1, -32, 0, 0, -3, -9, -16, 36, -84, 0, -2, 0, 42, -8, -3, 30, 0, -30, 16, -58, 12, -24, 12, 0, 22, 14, 0, -1, -80, 39, 0, 28, 54, 20, -7, -36, -10, 42, -36, 52, 2, -24, 7, 40, 0, -1, -26, -12, 66, -20, 0, 0, 4, 0, 5, -64, 6, -8, 0, 63, -26, 39, 30, -72, 0, 0, 0, 37, 60, -7, 12, -18, 0, 22, 3, 6, 32, 0, 16, 0, 0, 30, 18, -96, -48, -9, 21, -10, 52, -12, -8, -68, 27, 0, -10, -42, 4, 42, 33, 21, 0, -21, -40, 8, 0, 18, -5, 0, 8, 80, 21, -4, 23, 84, 0, 15, -6, 25, -16, 9, -40, 0, 12, -41, -1, -45, -2, 112, 0, 84, 2, 0, -2, -64, 0, 28, -24, 0, -8, -27, -15, -43, 0, -12, -35, -72, 9, -78, 44, 0, 4, -28, -30, 48, -14, -27, 0, 44, 0, 0, 32, 0, 4, 0, 48, -8, -12, -54, -28, 6, 0, 6, -18, -99, 6, 8, -54, 0, 28, 21, 6, 2, -15, -104, 0, 0, 1, -40, 0, 28, 20, 0, -54, 20, -12, 49, -6, -15, 0, 48, 0, -80, 3, 120, -25, 0, -39, -34, 0, -12, -36, 2, 0, 48, 12, 0, 12, 48, 12, 0, 6, 3, 8, 44, 6, -12, 0, -54, 72, 7, 6, 6, 24, 84, 1, 42, 21, -22, -32, 0, 0, -30, 0, -40, 72, -24, -42, 0, 72, -10, -10, 3, -16, -160, 0, -40, -1, -9, -20, -42, 48, 0, 12, 84, -52, -52, 0, -14, 0, 0, -1, -8, 3, -44, 7, 0, 10, -35, 48, 0, -14, 36, -14, -8, 36, -4, 4, -66, 8, 0, -18, 16, 0, 0, 14, 26, 0, -70, -22, 54, 74, -27, 21, 0, -8, -30, 0, 82, 36, -98, 0, 6, -24, 16, -21, -5, -10, 0, -56, -8, 0, 38, 2, 0, 0, 24, -6, 8, 16, -12, -4, 49, 15, -48, 30, -18, 0, 4, 0, 13, -12, 78, 12, 24, -30, 0, -10, 0, 77, -8, 0, 26, 0, -60, 10, 30, -36, 15, 4, 0, 36, -28, -9, 80, -1, 96, 0, 6, -48, 28, 20, -42, 10, 0, 0, -28, 28, 0, 12, -4, 21, 14, -28, -156, 29, 18, -24, 0, -144, 27, 36, 50, -30, 48, 0, -12, 9, 16, 33, 140, 21, 0, 18, 32, 0, 51, -14, 0, 0, 46, 15, 12, 27, 24, 6, 0, 63, -76, 4, 69, 42, 0, 0, -88, -12, 6, 8, 22, 0, -35, 5, 0, -39, -168, -12, 4, 0, 3, -40, -32, -6, 7, 26, 0, -6, -37, 6, 36, -55, 6, 0, -106, 60, 48, 0, 0, 0, 0, 0, 27, -64, -15, -2, -4, 0, -22, -2, -105, 28, -24, 27, 0, -32, 132, -2, 1, -12, 54, -56, -30, 50, -54, 0, 16, -28, 0, 20, -2, -72, 104, -2, -96, 0, 56, 12, 10, 70, 0, -48], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 9, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "414.2.e.a", "char_is_minimal": true, "conrey_index": 139, "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], [1, 1], [0, -1], [0, -4], [2, -1], [0, 0], [-1, 0], [0, 3], [-4, 0], [3, -3], [1, -2], [0, -4], [0, 0], [4, -8], [-1, 1], [7, 0], [3, 0], [-5, 0], [-4, 4], [0, 0], [0, -3], [0, -1], [-1, -1], [-11, 11], [-4, 0], [-3, 6], [0, 0], [4, -4], [-4, -4], [0, 2], [0, 1], [6, -3], [7, -7], [0, 0], [3, -3], [8, 0], [-5, 5], [4, -8], [0, 4], [0, 7], [0, 0], [1, -1], [-3, 0], [12, -12], [-1, 0], [-10, 10], [-2, 1], [0, 7], [0, 11], [7, 7], [-4, 4], [10, 0], [3, 3], [-12, 0], [0, 0], [-5, -5], [0, -4], [0, -13], [-8, 4], [-2, 2], [2, 0], [0, 0], [1, 0], [-16, 16], [3, -6], [0, 7], [0, -7], [1, -2], [0, 0], [0, 0], [0, -3], [-9, 0], [8, -8], [-22, 11], [0, 5], [0, 0], [-4, -4], [-2, 2], [4, 0], [-9, 9], [7, 0], [-4, 4], [0, 0], [0, -28], [0, -1], [8, -4], [-3, 3], [18, 0], [0, -12], [0, 0], [-1, 1], [-2, 4], [0, 10], [0, 20], [-1, 2], [-7, 7], [7, 0], [9, 0], [11, 0]]}