# Stored data for newform 46.2.c.b, downloaded from the LMFDB on 20 April 2024.
{"label": "46.2.c.b", "space_label": "46.2.c", "level": 46, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503737099878446, "dim": 10, "is_polredabs": true, "nf_label": "10.0.2357947691.1", "trace_hash": 293195220785264347, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [121, 121, -121, -242, 242, -99, 55, 0, 11, 0, 1]]], "qexp_display": "q+\\zeta_{22}q^{2}+(-\\zeta_{22}+\\zeta_{22}^{4}+\\zeta_{22}^{7}+\\cdots)q^{3}+\\cdots", "char_order": 11, "char_parity": 1, "char_degree": 10, "char_conductor": 23, "char_orbit_label": "c", "char_is_real": false, "Nk2": 184, "analytic_conductor": 0.3673118492978898, "hecke_ring_index": 1, "level_radical": 46, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 22, "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": "0.004", "prec": 17}, "analytic_rank_proved": true, "char_values": [46, 11, [5], [8]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 23], "conrey_indexes": [3, 9, 13, 25, 27, 29, 31, 35, 39, 41], "field_disc": -2357947691, "field_disc_factorization": [[-1, 1], [11, 9]], "field_poly": [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.770", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "320.023", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22513.768", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c11", "trace_display": [1, 0, -4, -7], "traces": [0, 10, 1, 0, -1, -4, 0, -7, 1, -19, 4, -2, -11, 2, -15, 11, -1, -9, 19, 2, 7, 33, 2, 21, 0, -11, 9, 0, 15, -2, 0, 11, 1, -11, -13, -17, 3, -18, -13, 0, 4, 5, -22, -21, -2, -10, -10, -22, -11, 24, -22, -11, -20, -7, 11, 3, 7, 11, 24, 43, 11, -3, 33, -23, -1, 41, 11, -1, 2, 33, 6, -11, 8, -28, 18, 44, 2, 30, 0, 34, 7, 13, 6, -3, -11, 8, -34, -33, -9, -49, -45, -52, -1, -88, -11, -36, 0, 16, 20, 6, -11, -12, 0, 30, -24, -22, 7, 10, 0, 22, -3, -55, 4, 14, 22, -15, 20, 49, 23, 25, -11, -37, 3, 33, 0, 9, 23, 6, 1, 22, 14, -1, 22, 36, 12, 33, -13, -6, -33, 48, -17, -22, 0, 15, 14, -8, -38, 44, -7, 15, 11, -14, 20, 49, -30, 33, 0, 32, -23, 22, 4, -62, -2, -3, -17, 0, 3, -27, 33, -79, 14, -61, 1, -27, -11, -55, -2, -55, -28, -72, -21, 46, 19, 22, 1, 82, 0, -40, 33, -99, -19, 24, 0, 7, -38, -110, 24, -51, 5, -29, -11, 33, 12, 19, 22, -24, 102, 25, 2, 15, 22, 97, -7, 55, -54, -7, -33, 66, -22, 44, -8, 73, -22, -6, -4, 55, 19, 50, 11, 14, 15, 88, 24, 6, 28, 0, -23, -11, 19, -9, 0, -22, 4, 0, 19, -36, 11, 95, 0, 22, 24, -80, -78, -13, -28, 0, -1, -44, -22, -27, 19, -49, 23, -39, 0, -17, -25, -11, -23, -19, 22, 3, -9, -55, 6, 22, 0, -96, 29, -22, -5, 39, 0, -30, -11, 0, 7, -31, -3, -64, -14, -22, 5, -48, -44, -4, -15, -22, -70, 24, 44, 51, -85, -22, -20, -12, 28, -28, -25, -99, 11, 34, 0, 44, 67, 62, 23, -24, 33, 18, 7, 198, 7, -26, 13, 110, -30, 88, 6, 121, 0, 81, 30, 120, -28, 40, -11, -32, -9, -121, -14, -66, -16, -14, 54, 22, -6, 47, -22, 51, 55, -77, 13, -2, 88, 0, -16, 0, 28, 78, -12, -7, 86, -66, 36, -13, -22, -144, 21, -4, 39, -5, -11, -62, -15, -66, -11, -7, 33, 77, -14, 11, -57, -9, -11, -23, -7, 8, 5, 0, -110, -130, -24, -165, 40, -84, -5, 85, -59, -22, 0, 40, -66, 0, 10, -14, -19, 41, 0, 32, -42, 55, 30, 26, 41, -34, -24, -33, -15, 7, 44, -17, 46, -55, 7, -55, -22, 1, -56, 11, 7, -10, 33, -18, -44, 99, -22, 2, -44, 14, -3, -28, -73, 3, -22, 79, -60, 77, -7, -14, -11, -23, 47, 22, -6, 45, 44, -56, 96, 0, 7, 48, 0, 125, -2, 44, 71, 13, 71, -150, 22, 11, 1, 145, 33, 11, 14, -34, 9, 52, -11, -151, -22, 88, -48, -46, -22, 19, -19, 55, -8, 31, 22, 92, 92, 24, -33, -88, 66, -5, -13, 44, 69, 10, 23, 18, 46, 88, 6, 4, 11, 57, 1, 44, 33, 21, -55, -22, 38, 0, 25, 6, -83, -10, -23, -143, -5, 44, -22, 21, -38, -173, -30, 12, 11, -136, -43, 55, -80, -117, 0, -16, 19, -88, 20, -11, -88, 146, -61, -13, 0, -106, -44, 40, -69, -88, 4, -115, -11, -123, -6, 22, -39, 3, -11, 12, 8, 69, 11, -91, 0, -113, -29, 11, 20, -132, 14, 36, -24, -22, 14, 67, 110, 19, 6, 42, 37, -38, 77, -33, -7, 22, 4, -6, 44, -21, 15, 22, -13, -82, 11, 125, 92, 190, -58, 61, -22, 56, -2, -33, 1, -22, -6, -6, 50, 55, 25, 37, -55, 113, 44, -22, 76, 53, 44, -96, -44, 0, -1, 124, -62, 95, 43, -209, 35, -20, 0, 51, -18, 44, 4, 74, 88, 12, 37, -66, 59, 29, -24, 9, 11, 22, -25, 64, -11, 117, 27, 73, -11, 3, -11, 90, -81, 44, -41, 1, -10, 108, -16, 33, 4, -50, 11, -53, -78, -11, 64, -109, -11, 156, -8, 55, -55, 10, -39, 9, -74, -110, 1, -52, 88, -106, -27, -2, -25, 5, -22, -76, -29, -121, 33, -55, -66, -30, 9, -11, -31, 4, -88, -49, -22, -146, -28, 88, 0, -17, 60, -55, -78, 106, -21, -109, -70, 77, 2, 22, 33, -129, 19, 38, 2, 31, 44, 44, 34, 22, 12, -68, -51, -122, 49, 77, -28, -64, 0, -50, 51, -167, 26, -95, 66, -202, -33, 11, 7, 21, 33, 15, 44, -77, -52, 19, 11, -66, 57, -13, 75, 13, 0, 55, 12, -11, -48, 29, -8, 110, -5, -154, -11, 67, -110, 88, -13, 132, 24, 29, -33, -73, 92, 110, -4, 164, -6, 17, 47, 33, 15, 3, 66, 99, 0, 147, 136, -12, 88, 5, 22, 165, 12, 52, 14, 24, -69, -88, 36, -56, -11, -2, -87, 134, -13, -74, 88, -79, 25, 33, -125, -72, -30, 118, -10, 121, -20, -81, -33, 35, -7, 77, -62, -112, -11, -63, 39, 44, -13, -85, 55, 170, 26, 99, 0, 92, 0, 20, -23, 152, 56, 2, 55, -40, 26, -11, -67, 41, 0, 24, -48, -121, -77, 2, 55, 57, -22, -158, -123, 118, 44, -139, -3, -209, 3, 92, -16, -74, -48, 77, -36, -79, -55, 42, 42, -106, 60, 0, 0, -46, 18, -44, 124, -55, -22, 36, 23, -242, 8, -14, 88, -164, -16, 25, 10, 79, 11, -50, 12, -33, 14, 37, -55, -18, 26, -88, -48, -99, -88, 88, -4, -68, -9, -48, -55, 29, -5, -33, 9, -6, 50, 41, 150, -44, -33, -69, 22, 38, -34, 55, -2, 117, -33, 23, 55, -132, 8, -35, -54, 8, -53, 11, -41, -174, -22, -68, -168, -129, -22, 116, -165, -116, 4, -99, 13, 38, 11, -93, -107, 55, -3, 170, 110, 56, -36, -11, -53, 69, -22, -72, 73, 121, 18, 89, 20, 45, -11, 176, 88, 82, -33, 34, 27, 77, 2], "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, 23, 3, 1, 11, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "46.2.c.b", "char_is_minimal": true, "conrey_index": 3, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 0, 0, 1, 0, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, -1, 0, -1, 0, -1], [-1, 1, -2, 1, -1, 2, -1, 1, 0, 1], [-2, 1, -1, 2, -3, 2, -1, 1, -2, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, -2, 1, -3, 2, -3, 2, -3, 1, -2], [1, -1, 1, -1, 0, -1, 0, -1, 0, -1], [0, -1, 0, 1, 1, -1, -1, 0, 1, 0], [-1, 0, 0, -1, 0, 0, 1, 0, 0, 1], [1, -1, 1, -1, 0, 1, 3, -1, 3, 1], [0, -2, 1, -1, 2, -3, 2, -1, 1, -2], [1, 2, 1, 2, 1, 2, 1, 0, 1, -1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [-2, 3, 0, 1, -1, 0, -3, 2, 0, 1], [2, -2, 0, -1, -1, 0, -1, 0, -1, -1], [-1, 0, -3, 0, -1, 0, -1, 3, -3, 1], [1, 0, 0, 0, 0, -1, 0, -1, 0, -1], [1, 2, 1, 0, -3, 5, -3, 3, -5, 3], [0, 0, -1, 0, 1, 1, -1, -1, 0, 1], [1, 3, -2, 3, 0, 0, -2, -1, -1, 1], [-1, 0, -1, 1, -2, 1, -1, 2, -1, 1], [-3, 4, -3, 0, -3, 1, -2, 2, -1, 3], [-1, 2, -2, 2, -2, 1, 0, 4, -2, 4], [1, 1, 1, 1, 1, 0, 1, -4, 4, -1], [2, -2, 0, -1, 1, 0, -1, 0, 1, -1], [2, -3, 2, -3, 3, -2, 3, -2, 0, -4], [1, 0, 3, 0, 3, 0, 3, 0, 1, 0], [4, -4, 4, -3, 4, -4, 4, 0, 3, -3], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, -2, 2, 0, 0, -3, 1, 1, 1, -3], [-1, -1, 2, 1, 0, 0, -1, -2, 1, 1], [-1, -1, 0, -1, 2, -2, 1, 0, 1, 1], [1, 1, -1, -1, 0, -2, 1, -2, 1, -2], [0, -1, 3, -2, 4, 2, 4, -2, 3, -1], [-1, 0, -1, -2, -1, 0, -1, 0, 2, -2], [0, -4, -3, -1, -4, -1, -3, -4, 0, 0], [1, 0, 1, -1, 1, -1, 0, -1, 0, -1], [1, -1, 0, 1, 0, -3, 0, -3, 0, 1], [-3, 4, -1, 4, -3, 0, 2, 0, 0, -2], [-5, 2, -3, 3, -2, 5, 0, 3, -8, 3], [-1, 1, -1, 0, -1, 2, 0, 0, -2, 1], [-5, 0, -6, 3, -6, 5, -5, 6, -3, 6], [-1, 2, 2, -1, 2, 1, -1, -1, -2, 0], [-3, 0, 2, 0, -4, 2, -2, 4, 0, -2], [-1, 0, -1, 0, 0, -1, 0, 0, 1, 0], [4, -3, -3, 3, 3, -4, 0, -4, 4, -4], [-3, 0, 1, 0, -3, 0, -2, 1, -1, 2], [-1, 1, 0, -2, 0, 1, 0, 1, 0, -2], [-4, 3, -2, 2, -2, 2, -3, 4, 0, 2], [0, -3, 0, 0, 1, 0, 0, -3, 0, 0], [1, 0, 2, 0, 2, 0, 1, 0, -3, 3], [0, 1, 0, 0, 0, 1, 0, 0, 0, 1], [1, 1, -1, -1, 0, 0, 1, -2, 1, 0], [3, 2, 3, -2, 5, -5, 2, -3, -2, -3], [4, -2, 1, -2, 1, -1, 2, -1, 2, -4], [6, -4, 4, -6, 0, 0, 2, 1, 2, 0], [0, 1, 0, 3, 0, 3, 0, 3, 0, 1], [0, -1, -1, 1, -1, -1, 0, 0, 2, -2], [3, 1, -1, 1, 0, 1, -1, 1, 3, 0], [0, -2, 5, -7, 7, -5, 2, 0, 0, 5], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [5, 2, 4, 2, 5, 0, 3, 1, -1, -3], [3, -3, 1, -1, 3, -3, 0, -2, 4, -2], [1, 4, 1, 0, -1, -5, 3, -3, 5, 1], [-1, 0, -2, 3, 0, 1, -1, 0, -3, 2], [0, 0, -5, 6, -2, 6, -4, 8, 1, 3], [-1, 0, -2, 1, -2, 3, -3, 2, -1, 2], [-1, 0, -1, 0, -1, 1, 3, -3, -1, 1], [2, -1, 3, -3, 1, -2, 0, -1, 0, -1], [-6, 5, -2, 5, -6, 0, -3, 4, -4, 3], [1, -1, 0, 2, -1, 3, 3, 3, -1, 2], [5, 2, -1, -1, 1, 1, -2, -5, 0, -5], [2, -3, 2, -3, 0, -3, 2, -3, 2, 0], [0, 7, -4, -2, -4, 7, 0, 0, -5, 5], [0, 0, -4, -3, -1, -4, -1, -3, -4, 0], [1, 4, -4, -1, 0, 0, -6, 5, -6, 0], [1, 0, 1, 0, 0, 0, 0, -1, 0, -1], [1, -2, 0, 4, 0, 0, -4, 0, 2, -1], [-1, 2, -2, 1, 0, 1, -4, 1, -4, 1], [0, -3, 4, -1, -5, 3, -5, -1, 4, -3], [2, -5, 6, -3, 6, -5, 2, 0, 2, -2], [2, -2, 2, -1, 0, -1, 2, -2, 2, 0], [-3, -2, -1, 0, 0, 1, 2, 3, 0, -5], [-4, 4, 0, 3, 1, 1, 3, 1, 1, 3], [-1, 0, 0, 0, -1, 0, 1, 1, -1, -1], [-7, 0, -3, 3, 0, 7, 0, 4, 0, 4], [-6, 1, -6, 0, -3, 0, -1, 1, 0, 3], [-3, 0, 5, 0, 3, -3, 3, -3, 0, -5], [0, -1, 2, 2, -1, 2, 1, -1, -1, -2], [-8, 0, -1, 0, 0, -5, 5, 0, 0, 1], [2, -5, 2, 0, 2, -6, 4, -4, 6, -2], [-5, 1, -2, 2, -1, 5, 0, 3, 3, 3], [0, -1, 0, -1, 0, 0, -1, 0, 0, 1], [-2, 2, 0, 3, -3, 5, -12, 5, -3, 3], [4, 0, 1, -7, 7, -1, 0, -4, 0, 0], [1, 1, 2, -1, -1, -1, 2, 1, 1, 0], [-2, -1, -2, 3, -2, -1, -2, 0, -1, 1]]}