# Stored data for newform 114.2.i.b, downloaded from the LMFDB on 28 September 2023.
{"label": "114.2.i.b", "space_label": "114.2.i", "level": 114, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504149416738930, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 760543505555790370, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [9, 0, 36, -30, 0, 3, 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": "0.015", "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": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.822", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "99.136", "prec": 20}, {"__RealLiteral__": 0, "data": "25.024", "prec": 20}, {"__RealLiteral__": 0, "data": "2935.857", "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, -3, 3], "traces": [0, 6, 0, 0, 0, -3, 0, 3, -3, 0, 6, 12, -3, -21, 0, -3, 0, 3, 6, 6, -12, -9, 3, -15, 0, 9, 0, -3, -9, 15, 6, 3, 0, 3, -6, -6, 0, 6, 0, 0, 6, -9, 0, -9, 3, 6, 12, -21, 0, 0, -3, 3, 15, 30, 0, -9, -6, -18, -12, 27, -3, -9, 9, 9, -3, -6, -6, -15, 12, 12, -6, 9, 0, 12, -6, 6, 9, 42, 6, 15, -3, 0, -9, -3, 3, -36, 18, 6, 12, -48, -3, -6, 3, -9, -30, -48, 6, 18, -36, 3, 18, 12, 12, -21, 6, 12, 3, 15, 0, -9, 0, 12, -9, -12, -9, 72, 15, -21, -36, -3, -3, -21, 3, -9, -9, 3, 3, -18, 0, -9, 21, -24, -24, 12, -12, 6, 3, 30, -15, 36, 3, 15, -18, -39, -3, -27, 12, 9, -6, -33, -27, 12, 6, -24, 42, 3, 15, 9, 15, 3, 6, 42, 0, -12, 9, 9, -3, 36, 9, 69, 54, 0, -6, -24, 6, 27, 3, 9, -3, 15, 6, 9, 27, 3, 3, 3, 9, -27, -21, -6, 24, -24, 0, 3, -45, -24, -36, -21, 12, -21, -27, 6, -15, -15, -6, -36, 21, 12, 0, -15, -6, -3, -6, 9, 6, 12, -3, -12, 9, 39, -18, 15, 12, -9, 0, 9, 51, -18, -12, 60, -63, -48, -21, 33, -21, -9, 0, 15, 42, -12, 6, -18, -18, 0, 18, -45, -18, 6, -6, -48, 3, -57, 0, -27, 12, -27, 0, 24, 3, -15, 21, -21, -15, 57, -6, -36, 9, 6, -15, -21, -3, 18, 3, 27, 3, 84, 12, -51, 3, 0, -6, -42, 6, 54, -18, -12, -12, 9, 0, 45, 63, 27, -3, 39, 27, -90, -3, 12, -33, -12, 18, 27, 27, 30, -18, -6, 3, 81, 6, -33, 3, -15, 0, -45, 9, 3, -9, 102, 30, 63, -3, 51, 6, -6, 6, -48, -15, -9, 18, -78, -18, -27, -48, -6, 0, 3, 9, 18, -66, -30, -36, 42, 6, -84, 18, 9, 39, -36, 6, -21, -33, 6, -6, 9, 0, 0, 51, -3, -12, -12, -12, 60, -96, 45, 48, 138, -9, 27, 12, 9, 12, -3, 3, -15, -27, -51, 15, -24, -9, -24, -12, -24, -15, 36, 0, 9, 3, 3, 12, -3, 3, -63, 0, 39, 15, 66, 3, 54, 36, -36, 6, -33, -6, -42, -6, -3, 3, 6, 3, -18, -9, 3, 21, -27, -15, -54, 6, -6, 75, 6, 12, 27, 6, 15, -6, 30, 9, 45, 51, 6, -24, 39, 0, 18, -18, -63, -42, -6, 6, 42, 9, 9, -39, -66, -3, 9, -18, -15, 3, -24, 9, -72, -21, -63, -72, 24, 18, -84, 12, 3, 54, -81, -48, -9, 6, 21, -57, 18, 0, -21, -36, 9, 9, -57, 18, 135, 24, -24, -12, -9, -3, -9, 39, -3, 45, -105, -3, 21, 18, 39, 9, -48, -9, 90, -45, 36, -9, -63, -3, 6, 3, 0, -3, 93, -9, 36, -36, -3, 18, 3, 9, 15, 6, 6, 24, -15, -9, -54, 6, -15, -6, -42, 15, 9, -6, -33, 57, -30, 3, 9, 72, 0, -36, 90, -3, 72, 21, 60, -21, 27, 6, -33, 45, 48, 12, 21, -6, -117, -42, -9, 30, 60, -24, 3, 27, 3, -9, 69, 3, -18, 12, 18, 3, 15, 6, 99, -9, 9, -18, -30, -21, -102, -39, 3, 9, -132, 0, 66, -3, -6, -63, -96, 12, 27, -51, -24, 3, 3, 0, -15, 54, -39, 12, 15, 3, 27, -6, -18, -21, 99, -3, -51, 27, 21, 36, 6, -6, 120, -9, -6, 3, 183, -6, 63, 81, -9, -21, -36, 12, -24, 3, 3, -15, 3, -21, -18, 30, -60, 84, 33, -6, -6, -30, -3, -15, -24, -24, 135, -9, 9, -3, 108, 6, -48, 42, 48, -24, -102, 0, -45, -30, 9, -15, -39, 21, 45, -9, -3, -42, 51, 0, -90, -66, -30, 6, 12, 6, -135, -63, -9, -51, -93, 3, 45, 27, -27, -39, -60, -30, -18, 27, 45, 33, -204, 0, 36, -9, 12, -9, -111, 9, 3, -15, 42, -18, 21, 6, 9, 57, 33, -36, -6, 0, -48, -24, 27, 36, 6, -36, -21, 0, -9, -3, 51, -12, 27, -12, 6, 60, 27, 6, -24, 81, -78, 9, -57, -18, 42, 48, -3, -33, -93, -9, 3, 48, 36, -15, -75, -9, -6, -24, 108, 42, 63, 0, -117, -45, 51, -45, 93, 48, -96, 15, -3, -24, -51, 0, -36, 81, 72, 15, 54, 0, -54, 12, 27, 36, 63, -3, -3, -36, -12, 33, 78, -9, 27, 27, 15, -102, 45, 12, 81, -9, -21, 9, -24, -6, 3, -39, -78, 3, 75, 3, 30, -27, 9, -21, -102, -9, 90, -27, -48, 39, 168, -6, -36, -9, 15, -6, 42, 6, 18, -15, 18, -57, 111, -24, -54, -60, -42, 18, -27, 30, -126, -21, -15, 18, 39, 12, 27, -54, -18, 15, 135, -27, 54, 66, -6, 51, -60, -6, 81, 27, 3, 9, -126, -21, 93, 3, -45, -87, -21, 9, -114, 60, 33, -30, 39, 105, 21, 39, -18, 39, 42, 0, 117, -24, -3, -18, 114, 63, 108, 9, -24, -15, -84, 39, -159, 15, 3, 9, -6, 0, 60, -30, -27, 33, -96, -6, 0, 45, -6, 138, -84, 12, 126, 9, -12, -42, -33, -3, 18, 36, -9, 6, -105, -63, -36, 27, 12, 24, -90, 0, 72, -60, -15, -24, 24, 3, 0, -36, -81, -27, 18, -21, -33, -75, -33, 6, -129, -6, -108, -12, 12, 0, -45, 15, 57, -15, -15, 27, 87, -42, 9, 9, -6, 15, 69, 15, -174, -66, 30, 42, 108, 30, -27, -12, -9, 36, -75, 6, 72, 42, -57, 54, 21, -30, -96, 42, 12, 84, 48, 0, 27, -63, 78, 3, 15, -24, -45, -27, 21, -48, 15, 18, -45, -81, 84, -48, 96, -9, -90, 9, 42, -63, 57, -3, -21, -57, -3, 3], "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.b", "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, -2, -1, 1, 2, 1], [0, 0, 0, 0, 0, -1], [1, -2, 1, -1, 1, 1], [0, 0, 0, -1, 0, 0], [0, 0, -1, 0, 0, 1], [1, 1, 2, 0, -1, -2], [0, 0, -1, 4, -1, 0], [-1, 0, 0, 1, 0, 0], [-3, 4, 0, -1, -1, 0], [1, -1, 2, -2, 1, -1], [0, -1, -2, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 4, 1, 1, 0, -1], [1, 0, 0, 0, 0, 0], [0, 1, 2, 2, -2, 2], [-2, -1, -1, 0, 0, 1], [-2, 1, -1, 1, 0, -1], [0, 0, 0, 1, -4, 1], [-2, -1, -4, -1, -2, 0], [0, 1, 0, 0, -1, 0], [4, 1, 0, -5, -5, -1], [0, 3, -4, 0, 1, 1], [0, 0, 0, -1, 0, 0], [-1, -1, 1, -1, 2, -1], [4, 4, 2, -3, -1, -2], [0, 0, 1, 2, 1, 0], [1, -1, -1, -1, 2, 2], [0, 0, 0, 0, 0, -1], [1, -4, 1, -1, 4, -1], [-1, 0, -4, 0, -1, 0], [0, 0, 0, -2, -1, -2], [0, -1, 0, 0, 0, 0], [1, 0, 0, 0, 2, -2], [2, 0, -1, -4, -2, 2], [0, 1, 1, 0, -4, 3], [1, 2, 1, 0, 0, 0], [-3, 0, 3, 3, -3, 0], [-1, 2, -1, 2, -1, 0], [-3, -1, -3, 3, 1, 3], [1, 0, 0, -1, -1, 4], [2, 1, 0, -2, -1, -1], [0, 2, 1, 4, 1, 2], [-4, -4, 5, 1, 3, -5], [0, 0, -1, 0, 0, 1], [0, -5, 7, 0, 7, -5], [-1, -4, -1, 1, 5, 5], [0, -1, 0, 1, 1, 4], [1, 0, -3, 3, 0, -1], [4, 2, -1, 2, 4, 0], [0, 0, 0, 0, 1, 0], [-2, -6, -1, 1, 0, -1], [-1, 1, 1, 0, 1, -2], [-4, -2, 2, 2, 2, -1], [-2, -4, -4, 0, 3, 1], [2, 0, 7, 5, 0, -5], [0, 0, 0, -1, -2, -1], [-3, 3, -1, 3, -3, 0], [2, -1, 1, -1, 1, -2], [2, -1, 0, -1, -1, 1], [-1, 0, 0, 1, 0, 0], [0, 5, -2, -2, -2, 5], [-1, -1, 4, 0, 1, -4], [-4, -4, 2, 3, 1, -2], [0, 1, 0, 4, 0, 1], [4, 1, 2, -4, -3, -3], [-2, 0, 0, 2, 2, 1], [3, -3, 3, -3, 3, -3], [0, 0, 1, 0, 0, 0], [7, 0, -7, -10, 1, -3], [-2, -1, 0, 2, 0, -2], [1, 5, 5, 0, -1, -4], [2, -2, 0, -1, 4, 2], [7, -4, -4, 0, -6, 10], [3, 0, -1, -4, 0, 4], [5, 0, -5, -5, 3, 0], [0, -1, -2, -1, 0, 0], [0, 1, 0, 0, -1, 0], [0, 3, 0, -3, -3, 3], [-1, -11, 6, 1, 5, 5], [0, 1, -2, 1, -2, 1], [-7, -7, -9, 2, 5, 9], [3, 3, 1, 0, -3, -1], [0, 3, 1, 2, 1, 3], [4, -1, 0, -4, 1, 1], [-5, 11, 0, -6, -6, -1], [-1, -2, -1, 1, 2, 1], [-6, 10, -9, 10, -6, 0], [2, 0, -2, -3, -4, -1], [-1, 1, -2, -1, 0, 1], [-5, 4, 4, 0, -1, -3], [-7, -5, -4, -2, -1, 4], [1, 0, 0, 0, 0, 0], [-1, 4, 7, 8, 0, -8], [-5, 0, 5, -2, 0, -7], [0, 1, -4, 1, 0, 0], [5, 1, 4, -4, -1, -5]]}