# Stored data for newform 33.2.e.b, downloaded from the LMFDB on 23 April 2024. {"label": "33.2.e.b", "space_label": "33.2.e", "level": 33, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538831905, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 1812923668782081515, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -4, 6, 1, 1]]], "qexp_display": "q+(-1+2\\zeta_{10}-\\zeta_{10}^{2})q^{2}+\\zeta_{10}^{3}q^{3}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "e", "char_is_real": false, "Nk2": 132, "analytic_conductor": 0.2635063266702253, "hecke_ring_index": 1, "level_radical": 33, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "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": "0.012", "prec": 17}, "analytic_rank_proved": true, "char_values": [33, 5, [23, 13], [5, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 11], "conrey_indexes": [4, 16, 25, 31], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.870", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "45.109", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "934.601", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [-1, 1, -3, 1], "traces": [0, 4, -1, 1, -9, -3, 1, 1, 13, -1, 2, -11, -6, 7, -4, -2, 1, 12, 4, -10, 3, 4, 4, -8, 7, 6, 2, 1, -6, 6, 3, -12, -30, -9, 12, 3, -9, 9, -10, -7, -6, -3, -1, 0, 36, 2, -3, 17, 14, 6, 6, 3, 3, 4, 6, 2, 12, -5, -24, -6, -3, -21, -27, 1, 13, -14, -4, -6, -27, 3, 3, 15, -7, 14, -26, -1, 60, 1, -2, -11, 13, -1, -3, 13, -9, -9, 15, 24, -37, -24, 2, 3, 3, 12, 17, 5, -15, 3, 36, 4, -36, 3, 3, 22, 9, -3, -1, 17, -6, -48, -8, 16, -1, -19, -25, 11, -36, -3, 29, -12, -14, 19, 54, -7, 42, -17, 1, 14, 8, -15, -4, 2, 24, -10, -6, -2, -21, -17, 3, -27, -3, 8, -50, -28, 26, 18, -26, -6, -24, -3, 19, 10, -25, -18, 16, 24, 12, -24, 44, -4, 15, 3, 4, 16, 18, 13, -2, 35, 13, 24, -9, 5, 45, 36, -6, 14, -14, -34, 11, 3, 3, -17, 3, -24, -1, 7, -28, -3, -102, -1, -15, -13, -13, 14, 33, 4, -36, -6, -11, 0, 27, 6, -42, -6, 27, -4, -48, 7, -22, 30, 2, 0, 6, 20, 17, -15, -13, -13, 12, -4, -12, 66, -9, -21, -15, 1, -19, -27, 45, 14, 6, -11, 72, 15, 2, -9, 51, 11, 3, 1, 12, 60, -21, -4, -9, -12, -2, -5, 16, 7, 28, -54, -6, 17, -36, -21, 27, -56, -15, 1, 9, 6, 27, 6, -28, -8, 10, -11, -9, -18, -2, -20, 3, 7, -62, -34, -18, -54, 63, 13, 1, -32, 43, 14, 15, 10, -13, 8, 0, 53, 18, -3, 6, 41, 24, -28, 88, 1, 22, -29, -39, -15, 10, -3, -95, -3, -3, 18, 9, 8, -1, -31, 1, 17, -24, -2, -99, 43, -4, 6, -26, 3, -2, 15, 6, -17, -19, -12, 9, 18, -7, 40, -18, 9, 55, 12, 1, 32, -56, -1, 54, 48, -30, -13, -75, 4, 36, 16, -54, -21, -6, 8, 90, -48, 6, 5, 69, 12, 3, 18, -6, 39, -22, 41, -18, -18, 51, -18, 23, 7, 17, 1, 3, -68, -33, 12, 44, 18, 4, -33, -15, 16, 2, -9, -18, -12, 24, -15, -63, 63, 4, -54, -78, -27, -31, 22, 21, -48, -15, -10, 69, -66, 6, -11, 87, -3, -36, -21, 6, -8, 1, 7, -12, 11, 2, -6, -30, -18, 25, 14, 3, -34, 15, -8, 8, 3, -45, 21, -102, 3, -30, 24, 14, -74, -13, -18, 108, 0, -14, 120, 9, -24, 21, 62, -51, 13, -21, -7, 17, 38, 26, -13, 114, 30, 58, 4, 25, 52, 4, 3, -21, -30, 4, 74, -6, 1, -15, 37, -12, 6, 26, -6, -82, 15, 66, -20, -18, -1, 1, 32, 15, 7, 0, -8, -114, -6, 1, 21, -132, -16, -12, 11, -3, -72, -10, -3, -88, -15, -8, 14, -18, -35, -99, -28, 7, -6, 12, 16, 6, -65, -6, 16, 61, 10, 129, -14, 90, -53, -34, 29, -8, -20, 6, 36, 78, 6, 36, -66, -31, -56, -3, -6, 45, -29, -11, -14, 18, -23, 132, 6, 12, 69, 75, -3, -45, 36, 2, 57, 72, -6, -19, -60, -9, 11, -129, -7, 27, -86, -27, 45, 2, -42, -152, 39, -78, 18, 14, 1, 120, -48, -5, -14, 33, 48, 3, 8, -17, -10, 53, 1, -18, -13, 42, -16, 108, 11, -94, 27, 36, -15, -23, 31, -29, 2, -19, 24, -12, 15, -4, 38, -27, 29, 30, 9, -60, 22, -58, -16, 105, 6, -3, 6, 18, 6, -57, 14, -43, 0, -22, -49, -39, -7, -31, -11, 12, 24, 22, 20, 144, -18, 3, -51, -77, 0, -22, 2, 9, 48, 96, 10, -26, 32, 48, -10, 12, 0, -30, 2, -12, -21, -2, -12, 54, 7, -12, -29, -12, 14, -17, -84, -3, 106, -25, -21, 11, 0, 9, 18, -75, -29, 12, 24, -30, 51, -78, -6, -24, -28, -56, 12, 27, -8, 93, -80, 15, 24, 52, -14, -75, 7, -1, -52, -216, -9, 16, 9, 78, 21, -21, -15, -39, 50, 3, -70, -52, -16, 12, -13, 69, 72, 5, -11, -103, 34, 12, 31, -18, 4, -42, 91, -12, 18, 69, 0, 42, 84, 16, -50, -9, -1, 12, 90, 9, -30, 87, -18, 30, 9, 2, -3, -27, 0, 1, -15, 69, -4, -23, -12, 108, 28, 17, -12, 163, 54, 18, 20, -9, -5, 122, 13, 50, -51, -34, -12, -72, 21, -54, -28, 18, -62, -12, -34, -39, -41, -30, 37, -39, 9, -157, -5, -24, -20, -24, -6, 84, 18, -27, -12, -84, -36, 22, -36, 13, -78, 27, 3, -45, 90, -10, -24, -75, 1, 144, -76, -36, -11, -1, -42, 61, -9, -3, -49, 36, -70, 94, -32, -33, 60, -28, -7, -21, -71, -38, -59, 184, 4, 46, -40, 3, 77, -6, 54, 9, 18, 27, -70, -195, 2, -66, 51, -6, -7, -34, 22, -30, -8, 52, -4, -24, 16, 18, 7, -15, -31, 51, 5, 59, 120, 3, -84, 45, -3, -21, -58, 0, -7, 156, 82, 78, 44, 12, -33, -156, -12, 0, -23, -36, 69, -15, 24, -17, 74, 6, 10, -36, 28, 62, 107, 77, -14, -22, -1, 126, -35, 18, -26, 17, 29, -32, -78, -21, 42, 2, 0, -73, 14, 0, -77, 12, 13, -1, 41, -110, -7, -108, 18, 6, -27, 3, 25, -8, 57, -30, 50, 36, 66, 19, 22, -90, -9, 1, 60, 45, -39, -98, -39, -16, 9, -9, 3, 24, -76, -66, 11, -4, 2, -60, 18, -66, -18, -115, -43, -24, 8, -1, 61, -6, -66, 172, 17, -4, -13, 7, -3, -90, -13, -3, 46, 113, 0, 9, 42, 9, -18, 21, -8, 201, -79, -36, 71, 72, 12, -69, -14, -9, 37, 18, 17, 15, -60, -8, -70, 75, 25, -45, 15, 18, 6, -71, 1, -124], "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, 11, 3, 1, 5, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "33.2.e.b", "char_is_minimal": true, "conrey_index": 4, "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], [1, 0, 0, 0], [-1, 2, -1, 0], [0, 0, 0, 1], [0, -3, 3, -3], [-1, 0, 0, 1], [-1, 2, -2, 1], [0, 0, -1, 0], [4, -4, 0, 1], [0, -1, 0, 0], [0, 0, -1, 1], [-3, 1, 1, 1], [0, 0, 3, -3], [2, 1, 2, 0], [-1, 1, 0, -1], [0, -1, 0, -1], [-5, 8, -8, 5], [6, -3, 3, -6], [0, 1, -2, 1], [-3, 3, 0, -1], [0, 3, 0, 0], [1, 0, 0, 0], [3, -6, 3, 1], [-3, 0, -2, 2], [4, -5, 4, 0], [1, -1, 0, 3], [0, 1, 0, 1], [1, -1, 1, -1], [0, -3, 3, 0], [0, 0, -6, 0], [1, -1, 0, 0], [-5, 3, -5, 0], [-6, 0, 3, -3], [-2, 0, -1, -2], [3, 0, 0, 0], [1, 0, 1, 0], [-3, 3, 0, 0], [0, 2, -5, 2], [4, -11, 11, -4], [-3, 1, -1, 3], [0, -1, 4, -1], [-2, 2, 0, 3], [-1, 2, -1, 0], [3, 0, 6, -6], [3, 9, -9, 6], [1, 0, 1, -1], [-1, 0, -1, 0], [5, -5, 0, 2], [0, 3, -8, 3], [6, -6, 6, -6], [-4, 9, -9, 4], [0, 3, 3, 3], [3, -3, 0, -6], [1, 1, 1, 0], [1, 0, -1, 1], [1, -1, -2, -3], [1, 0, -4, 4], [-3, 4, -3, 0], [-6, 6, 0, -6], [0, 1, 8, 1], [-3, 3, -3, 3], [-3, -6, 6, 3], [0, -8, 11, -8], [0, 0, 0, 1], [6, -5, 6, 0], [-5, 0, -3, 3], [3, -7, 6, -3], [-3, 0, -3, 3], [-9, 0, -9, 0], [2, -2, 0, -3], [0, 1, -1, 1], [1, 6, -6, -1], [1, -5, 5, -1], [0, 6, -2, 6], [-7, 7, 0, -5], [1, -4, 1, 0], [9, 0, -12, 12], [2, -1, 4, -2], [-1, 0, -1, 1], [0, -11, 0, 0], [5, -5, 0, -2], [0, 0, 1, 0], [-1, 0, 0, 1], [5, -1, 1, -5], [0, -3, 3, -3], [-6, 6, 0, 9], [9, -12, 9, 0], [6, 0, 0, 0], [-10, 12, 3, -6], [-5, 0, 2, -2], [1, -1, 1, 0], [2, -2, 0, -3], [0, 3, 3, 3], [2, 3, -3, -2], [-7, 19, -19, 7], [0, 1, -3, 1], [-3, 3, 0, -6], [3, -6, 3, 0], [6, 0, -6, 6], [1, 2, 0, -2], [-3, 0, 12, -12]]}