# Stored data for newform 114.2.i.a, downloaded from the LMFDB on 19 April 2024.
{"label": "114.2.i.a", "space_label": "114.2.i", "level": 114, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 549789368434, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 315104364981473426, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [81, 162, 162, 90, 36, 9, 1]]], "qexp_display": "q+\\zeta_{18}q^{2}+\\zeta_{18}^{4}q^{3}+\\zeta_{18}^{2}q^{4}+(-1+\\cdots)q^{5}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 19, "char_orbit_label": "i", "char_is_real": false, "Nk2": 456, "analytic_conductor": 0.9102945830425964, "hecke_ring_index": 1, "level_radical": 114, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 18, "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": "0.026", "prec": 17}, "analytic_rank_proved": true, "char_values": [114, 9, [77, 97], [9, 7]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 19], "conrey_indexes": [25, 43, 55, 61, 73, 85], "field_disc": -19683, "field_disc_factorization": [[-1, 1], [3, 9]], "field_poly": [1, 0, 0, -1, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "5.943", "prec": 17}, {"__RealLiteral__": 0, "data": "3.376", "prec": 17}, {"__RealLiteral__": 0, "data": "114.949", "prec": 24}, {"__RealLiteral__": 0, "data": "223.328", "prec": 24}, {"__RealLiteral__": 0, "data": "4525.503", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c9", "trace_display": [0, 0, -9, 9], "traces": [0, 6, 0, 0, 0, -9, 0, 9, 3, 0, 0, 0, -3, 15, -6, -9, 0, -9, -6, -12, 0, -3, 9, 9, 0, 9, 0, -3, -3, -9, 0, -9, 0, 9, 0, -36, 0, 18, 18, 0, 0, 27, -6, -21, -9, 0, 0, 27, 0, -12, 3, 9, -3, 0, 0, -9, 18, 18, -36, 9, 9, -3, 21, -3, -3, -18, 0, -3, 0, 0, 36, 9, 0, -12, -6, 6, 9, 18, 12, -21, -9, 0, -27, -9, 9, 18, -6, -18, 0, 0, 9, 24, -9, 33, -18, 36, -6, -54, -24, 9, -18, -36, 0, -9, 12, 0, 9, -9, 0, 9, -18, 6, -3, 0, 9, -36, -9, 15, 18, 9, -9, 15, 9, -27, 33, -27, -9, 18, 0, -21, 9, 18, 0, 0, -36, 0, -9, 18, -9, 6, 9, -9, 18, -27, -3, 9, 12, -39, -12, 9, -9, 12, -6, 0, 0, 81, -3, -3, 21, -9, 0, 0, 0, 18, -9, -9, 27, 36, 3, 33, -18, 0, -18, -36, 0, 69, 9, 9, 27, 9, 0, 27, -3, -9, 9, -45, 21, 9, 27, -18, -36, 0, 0, -21, -27, -18, 24, -45, 0, 51, -9, -18, 27, -9, 0, -54, 21, 0, 0, -27, 18, -3, -18, 9, 18, 0, 3, 48, -9, -21, 18, -27, -6, -57, -6, 9, -63, 18, 6, 36, 9, 36, -9, 27, -15, 9, -18, -3, -18, 0, 0, -30, 18, 0, 24, 9, -18, -84, -18, -18, 9, -45, 6, 9, -12, -9, 0, -36, -9, 39, -9, 9, -27, 9, 0, -36, 21, 54, -3, -63, 9, 0, 9, 3, 27, 0, 0, 21, -27, -12, -36, 72, 18, -54, 54, 0, 36, 45, 0, 9, 45, 27, 9, 9, -15, 0, 9, 0, -9, 18, -18, -57, 9, 54, 18, 54, 9, -81, -36, 51, -81, -27, 0, -9, 39, 9, -27, 0, 0, 45, 9, 45, -18, 0, 6, 24, 39, 9, 0, 36, -18, -63, -18, 6, 0, 27, -3, 6, -6, -36, 18, -18, 12, -24, -6, -9, -27, -18, 0, 9, -27, -12, 0, -45, 18, 54, 9, 9, 18, 0, 0, -12, -12, 9, -48, 72, 3, 33, 0, -9, 0, -45, -9, 39, -9, 9, 9, 72, 3, 36, 0, -24, 27, 0, 0, -99, 21, 9, 12, -45, -27, 9, 12, -45, 9, -36, -9, -48, 0, 60, 6, 81, 12, -84, 36, 9, -45, 18, 9, 54, 27, -27, -21, 99, -9, 36, 12, -54, -27, -18, 0, -45, 12, -9, 18, 0, 27, 33, 45, 18, 36, -81, 0, 6, -6, 9, -42, 0, 18, 24, 9, -39, -9, 0, -9, 9, -96, -9, 9, -36, -9, 54, -27, -9, -54, -144, 0, 36, -24, 9, 18, -45, -36, -9, -18, -45, 45, 0, 0, 33, 18, -3, -9, -9, -54, -27, 0, 18, -36, -117, 9, 51, 45, -9, 9, 81, 3, 21, -24, 33, 99, -54, -27, 18, 9, -36, 33, -45, 27, -12, -9, 0, 45, -63, 3, 72, 18, -39, 18, -81, 9, 51, -6, 6, 36, 9, 15, 18, -60, 9, 18, 36, 9, 15, 18, 27, -9, -54, 9, 9, 36, 36, -12, 162, 9, 90, -15, 18, 63, 63, 0, -75, -27, -6, 0, -63, -24, 51, 0, -21, 54, 0, 0, -21, -45, -45, -21, -81, 9, -24, 0, -18, -9, 81, -18, 9, -27, -3, 18, 54, -27, -18, -27, -9, -45, 36, 0, 30, -33, 6, 9, 54, -12, -45, -33, -18, -27, -63, 24, -45, -54, 27, 6, 135, -9, 9, 0, 0, 27, -9, 3, -63, 57, 15, 18, -18, 0, 36, 9, -90, -45, 117, 0, 117, 81, -27, 9, 36, 30, 72, -9, -9, 27, 27, 15, -54, 42, -36, 0, -9, 36, -84, -24, 15, -9, 0, 18, 39, 9, -27, -9, -18, 18, 24, 0, 72, -18, 18, 0, -81, 48, 69, -39, 27, -21, -63, -27, 9, -36, -63, 18, -72, -42, 18, -18, 54, -18, -9, 9, -57, 27, -9, -9, -27, -15, 9, -3, -18, 36, -78, 9, 27, -45, -36, -18, -36, 21, -84, -21, -27, 9, 3, 27, 0, -90, -27, 18, -27, -105, 27, -48, -54, 0, -54, 0, -45, 18, -90, -18, -21, 0, -27, 9, 45, 0, 9, -18, 18, 36, 99, 0, 48, -81, 90, 27, 27, 18, 24, 48, -3, -45, 63, -21, -15, 36, 90, -9, 27, -27, 42, 36, 36, 54, 27, 12, -9, -27, 45, 9, 45, 0, -84, -9, -45, -72, 9, 6, -84, 93, 36, 9, -18, 36, 84, 36, -9, 0, -9, -3, -111, -36, 18, -27, 90, 21, -39, -27, -21, -18, 27, 36, -27, -9, 9, -39, -36, -18, 9, 27, 18, -45, 27, 9, 6, -51, 45, 51, -126, 21, -90, -9, 0, 99, -72, -12, -72, -57, 63, 0, 72, 0, -72, 9, 0, 45, -45, 0, 78, 132, 24, 0, 117, -18, 18, 9, 27, 36, 99, 0, -27, -36, -90, -3, 27, -15, -54, 36, 18, 45, -36, -36, 117, 45, 9, -9, -72, -27, -27, -9, 27, 27, 45, 9, 78, 60, -27, -18, 27, -9, 87, -9, -90, -27, 54, 0, 45, -72, 33, 6, 36, 45, 96, -9, -24, 27, -144, -21, -39, 21, -9, -9, -18, 12, 114, 18, -27, -9, 144, 12, -60, -63, 0, 18, -72, 0, -18, 3, 18, -54, -81, -3, 36, 54, -3, 0, -81, 9, 54, -81, -36, 72, -18, 0, -144, -96, 9, 60, -162, -9, 72, -18, 27, -63, -36, -9, 69, 39, 51, 0, 45, -18, 186, 0, -36, 72, 27, 3, -147, -39, 21, -45, -81, 0, 27, 9, 36, -9, 63, -3, -6, 48, -18, -18, -72, 0, 45, 36, -9, -36, 9, 0, -120, 6, -27, 6, -45, -36, -66, 30, -54, 0, -108, 0, 15, 63, 24, -9, -27, -6, -9, -63, 21, 54, -45, 0, 171, 63, -72, 24, -72, 9, -12, 21, -12, 45, -27, -9, 141, 21, -9, 27], "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, 5, 1, 9, 0]], "char_orbit_index": 9, "prim_orbit_index": 5, "minimal_twist": "114.2.i.a", "char_is_minimal": true, "conrey_index": 25, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [-1, 0, 1, -1, 0, 1], [0, 0, 0, 0, 0, 1], [3, 0, -1, -3, 1, 1], [0, 0, 0, 1, 0, 0], [0, 0, -1, 0, 0, 1], [-1, -1, 0, 2, -1, 0], [0, -2, 1, 0, 1, -2], [-1, 0, 0, 1, 0, 0], [3, -2, 0, -1, -1, 0], [-1, 3, 0, 0, -3, 1], [-2, 1, 0, 1, -2, 0], [0, 0, 0, 0, 1, 0], [-2, 0, -1, 1, 0, -1], [-1, 0, 0, 0, 0, 0], [-2, 1, 2, 0, -2, -4], [0, -1, -1, 0, 2, -1], [0, 3, -1, -1, 0, 1], [2, 0, -2, -1, 0, 1], [2, -1, 0, -1, 2, 0], [0, -1, 0, 0, 1, 0], [0, -3, 0, 3, 3, -1], [0, 3, -2, 0, -1, -1], [0, 0, 0, -1, 0, 0], [-1, -1, 3, 1, 0, -3], [-2, -2, -6, 1, 1, 6], [0, -2, 1, 0, 1, -2], [-3, 5, 1, 3, -6, -6], [0, 0, 0, 0, 0, 1], [1, 0, -1, 1, 0, -1], [1, -2, 0, -2, 1, 0], [-8, 0, 8, 4, -3, -4], [0, -1, 0, 0, 0, 0], [3, -2, -2, 0, 2, 0], [4, -2, 1, -2, 0, -2], [0, 1, 1, 0, 2, -3], [1, 0, -1, -2, 0, 2], [3, 0, -3, 3, 3, 6], [-1, 0, 3, 0, -1, 0], [-3, -3, 1, -1, 3, 3], [-1, 2, 0, -1, -1, 0], [0, -1, 2, 0, -1, -1], [0, 2, -1, 0, -1, 2], [4, 4, -3, 1, -5, 3], [0, 0, -1, 0, 0, 1], [0, 7, -1, -4, -1, 7], [1, 0, -3, -1, 3, 3], [2, -1, 0, -1, -1, 0], [1, 0, 3, -3, 0, -1], [2, -4, 3, -4, 2, 0], [0, 0, 0, 0, -1, 0], [0, 6, -3, -3, 0, 3], [3, -1, -1, 0, 1, 0], [2, 0, 2, 2, -2, -1], [-6, -2, -2, 0, 1, 1], [0, -6, 3, 3, 0, -3], [2, 0, -2, -1, 0, 1], [-3, 5, 3, 5, -3, 0], [6, -3, 5, -5, 3, -6], [0, 1, 0, -1, -1, 3], [-1, 0, 0, 1, 0, 0], [0, 1, 4, -6, 4, 1], [1, 1, 0, -2, 1, 0], [-2, -2, -6, 3, -1, 6], [0, 1, -2, 0, -2, 1], [0, 1, -2, 0, 1, 1], [4, -8, 0, 4, 4, -3], [3, 9, 3, -3, -9, -3], [0, 0, -1, 0, 0, 0], [-5, 0, 5, 6, -3, 1], [0, 3, -2, -2, 0, 2], [1, -3, -3, 0, 3, 0], [2, 4, -2, -1, -2, 0], [3, -4, -4, 0, 8, -4], [3, 0, 1, -2, 0, 2], [-5, 0, 5, 3, 9, -2], [-2, 1, 0, 1, -2, 0], [0, 1, 0, 0, -1, 0], [-6, 3, 0, 3, 3, 3], [-3, -7, 8, 3, -1, -1], [0, -1, 0, 3, 0, -1], [3, 3, -3, 0, -3, 3], [-3, -3, -3, 4, -1, 3], [0, -1, -1, -6, -1, -1], [0, -1, 2, 0, -1, -1], [1, 1, 0, -2, -2, -9], [1, 0, -1, 1, 0, -1], [8, -8, -1, -8, 8, 0], [-2, 0, 2, 1, 0, -1], [5, -3, 6, 1, 0, -1], [-3, 4, 4, 0, 1, -5], [5, 3, -8, 2, 3, 4], [-1, 0, 0, 0, 0, 0], [-9, 4, -9, 0, 0, 0], [-7, 0, 7, 6, -4, -1], [2, -1, 0, -1, 2, 0], [-3, 1, 0, 0, -1, 3]]}