# Stored data for newform 45.2.e.b, downloaded from the LMFDB on 13 January 2026. {"Nk2": 180, "analytic_conductor": 0.3593268090957617, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [45, 3, [11, 37], [2, 3]], "cm_discs": [], "conrey_index": 16, "dim": 6, "field_disc": -954288, "field_disc_factorization": [[-1, 1], [2, 4], [3, 3], [47, 2]], "field_poly": [27, -9, -6, 3, -2, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [9, 15, 28, 1, 6, 1, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503874538831917, "hecke_ring_generator_nbound": 4, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "45.2.e.b", "level": 45, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 5], "level_radical": 15, "minimal_twist": "45.2.e.b", "nf_label": "6.0.954288.1", "prim_orbit_index": 3, "qexp_display": "q+(-\\beta _{1}+\\beta _{2}-\\beta _{4}-\\beta _{5})q^{2}+\\beta _{4}q^{3}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "45.2.e", "trace_display": [-1, 1, -3, -5], "trace_hash": 810449350294801849, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.846", "prec": 17}, {"__RealLiteral__": 0, "data": "2.311", "prec": 17}, {"__RealLiteral__": 0, "data": "139.240", "prec": 24}, {"__RealLiteral__": 0, "data": "227.572", "prec": 24}, {"__RealLiteral__": 0, "data": "6080.743", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, "traces": [0, 6, -1, 1, -5, -3, -4, -5, 6, -7, 2, 2, 17, -4, 9, 1, -5, -4, -23, 8, -5, 0, 4, -3, 15, -3, -4, -2, 10, 7, 11, -8, -17, 20, 4, 10, 10, 12, 2, -14, -3, 13, -33, -10, -44, 2, -6, -13, -10, 2, -1, -4, 12, -4, 5, -4, 9, -2, 17, 2, -22, -1, 84, 33, -30, -4, -2, -11, 22, 39, 9, -20, 15, -16, 16, -2, 12, 0, -4, -2, 10, -19, -58, 15, -27, 2, -28, -26, 24, -18, 1, 20, -39, -42, 31, -4, 13, 18, -80, 22, 10, -6, 28, -6, 18, -9, 22, 30, 23, 6, 4, -16, 13, -16, 20, -3, 38, -4, -44, 0, 9, 13, -25, -5, -8, 6, 30, 26, 21, -32, 2, 18, -32, -10, 6, 19, -48, 12, 45, -24, -5, 20, -28, 32, -41, -14, -40, 44, -22, 13, -7, -22, -36, -14, 36, -8, -4, 18, 42, -22, -17, 18, 10, 84, 47, -4, -27, -33, 6, 15, -8, -28, 84, -36, -13, -5, 10, 14, 3, -28, -17, -18, 0, -26, -33, -6, 24, -20, -14, -39, -4, 40, 13, 12, -2, 16, -2, -48, -52, -16, -3, 57, -30, -3, -8, 13, -32, -6, 0, -16, 18, -18, 10, 28, -9, 20, -36, -52, 25, 40, 22, -16, 16, 9, 78, 5, 112, -2, 26, 31, 3, -30, -9, 60, -14, 26, 10, 12, -18, 20, 23, 29, 34, 1, 54, 2, -73, -24, -42, 0, -1, -72, -3, -72, -61, -16, 27, 54, 26, -28, -24, -13, -12, -50, 48, 2, 0, -3, -71, 14, -40, -40, 10, 0, -24, 2, -48, -2, 16, 84, -18, 33, -101, -17, -46, -14, -20, 6, -10, -62, 17, 80, 0, -30, -2, 2, 0, 8, 110, 30, 5, 8, 32, -48, 0, 2, 68, 38, 12, 32, -42, 24, 24, 48, -68, -15, -20, 40, 52, 26, 15, 9, 51, 32, 79, 8, -32, -25, 63, -57, 28, -26, -30, -2, -6, -11, -57, 20, -3, -100, 22, 0, 22, 2, -60, -36, 24, 2, -25, 35, -18, 34, -16, -36, -14, 10, 15, 12, 16, -24, 30, -66, 31, -19, 2, 8, 47, 34, -6, -58, -32, -18, -132, 14, -28, 1, 51, -80, 9, 20, 12, 61, 2, -18, 12, 0, 196, -58, -196, 21, -16, 36, 36, -6, 0, 4, 26, -52, 62, 12, -5, 6, 93, -16, 108, 29, -78, 16, -54, 30, 29, -36, -22, 36, 39, -30, -26, 8, -20, 22, 39, 2, -80, 121, -60, 2, -112, 23, 9, 20, -28, -60, -7, 20, -60, -17, -85, 30, -88, 20, -48, -80, 40, 15, 52, 9, -83, 43, 43, 140, 22, 68, 28, -20, -4, -10, -24, 2, -90, -4, 78, -15, -12, 46, 41, 0, -48, -44, 4, 38, 31, -22, 30, 32, -90, -4, -24, -2, 88, -30, -8, 4, -7, -51, 15, -36, 23, -84, -51, 32, 40, -20, 170, 26, 32, -14, 184, 48, 99, -76, -5, 3, -42, 46, -15, 12, 30, 78, -57, -49, -26, 56, -118, -8, -36, -6, 116, -20, 66, -48, 18, -38, 10, -22, 30, 9, 44, 0, -20, -6, -44, -44, -4, -8, 12, -15, -63, -16, -107, -8, -25, -26, -10, -31, 8, -3, 12, -55, 48, -73, -8, 40, -33, -46, -60, 32, -40, -12, -42, -24, 13, -20, -15, -33, -113, -16, 78, -30, 168, -66, -4, -60, 4, 76, -15, 6, 23, 12, -11, 14, -19, 57, 58, -8, 96, 32, -72, -75, 88, -16, 22, 0, 26, 28, -74, 0, -85, -62, 36, 58, -24, -18, -12, 6, 84, 13, 42, 47, -26, 99, -25, 92, -64, -4, 83, 34, -6, 24, 34, -12, 16, -27, 60, 15, -10, -3, 106, 20, 74, -32, -39, 128, 54, 20, 38, -13, 10, 8, 16, 86, -42, -3, 6, -41, -51, 28, -20, 98, -123, 16, 2, 60, -58, -62, -32, 18, -142, 32, -162, 8, -8, 2, -66, -40, -27, 20, -100, 138, -33, 32, -3, 26, -69, -92, -16, -17, -186, 12, 4, 38, 24, -20, 84, -156, -44, -24, 15, -57, -66, -4, -15, -22, 168, 36, 88, -24, 84, -34, -31, 48, -5, -134, -4, -8, -22, -31, -84, 18, 64, -61, 56, 102, -18, 42, 36, -16, -26, -112, 150, -12, -5, 56, 3, -74, 59, 7, -41, 15, -24, 2, 80, 32, 101, 66, 36, -4, -21, -120, -5, 68, -22, -68, 30, -43, 108, 13, 92, -99, 80, -21, -4, 38, 49, 42, 26, 44, 120, 32, -82, -30, 18, -9, -166, -31, -232, -8, 48, -4, 19, -51, -18, -18, -100, 192, 124, 16, 78, -48, 45, -8, -22, 56, -60, 25, -164, 18, -66, -82, 108, -32, 42, -48, 84, -48, 38, 14, 120, 40, -30, -20, 34, 21, -204, 8, -132, -9, 0, 107, -78, 52, -5, 4, -63, 10, -16, -42, 76, 12, -92, -42, -94, -9, 84, -3, 0, -16, 30, 206, 15, -74, -27, -108, 8, 4, 88, -33, -8, 174, -16, 88, -3, -20, 50, 102, 2, -30, 38, -86, 46, -123, 4, -48, -88, 4, 42, -4, -30, 20, -20, 14, -42, 15, 102, 22, 79, 72, -16, 11, 110, -12, 8, 38, 114, 22, -72, -5, -88, 52, -28, 24, 10, 14, 44, -6, 4, 8, 75, -90, 18, 35, -6, -68, -82, -46, 59, 14, -15, -60, -2, -216, 7, 16, -92, -18, -12, 9, -130, 1, 44, -90, 0, -82, 56, 0, 140, 25, 133, -60, -2, -52, -33, -83, 75, 76, -24, -6, -168, -32, -50, -2, 60, 8, -150, 54, 140, 40, -48, 112, 87, -28, 7, -23, -110, 39, -92, 36, -176, -27, -138, 24, 2, 52, -6, -88, 14, -80, 88, 68, -102, 48, -35, -91, -32, -69, 90, 12, 60, 3, -15, 20, -2, 168, -34, 80, 4, -2, -51, -52, -80, -6, 4, 73, 128, 21, -63, 24, -8, 123, 28, 72, 68, -180, -6, 0, -30, 8, 81, -62, 8, 80, 6], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, -1, 1, 0, -1, -1], [0, 0, 0, 0, 1, 0], [0, 0, -1, 1, -1, 1], [0, 0, 0, 1, 0, 0], [-1, 0, 1, -2, -1, 1], [-2, 1, -1, -2, 1, 1], [0, 1, -1, 0, 2, -1], [-1, -1, 1, 1, 0, -2], [0, 0, -1, 0, 1, 0], [0, 1, -1, 0, 0, 0], [4, 2, -1, 2, 0, 2], [0, 0, 1, 2, 1, -1], [0, 2, 1, -3, 1, 1], [0, 1, 0, 0, 0, 0], [-1, -2, 2, -1, -2, -2], [0, -1, 0, 0, -1, 1], [-2, -1, -1, 2, -1, 2], [2, -1, 0, 0, -1, 1], [-1, -1, 1, -1, 0, 0], [1, -2, -1, 2, -1, -1], [0, -2, 1, 0, 1, -3], [0, -1, -2, 0, -2, 1], [0, -1, 0, -3, 1, -3], [-1, 0, 0, -1, 0, 0], [0, -1, 0, 0, -1, 1], [-2, 0, 2, -4, -2, -1], [2, 1, 3, 0, -2, -1], [3, 0, 0, 3, 2, 2], [2, -1, 1, 1, 0, -2], [0, 4, 1, 2, 1, 3], [0, -1, 0, 6, 0, -1], [2, 1, -2, -2, 1, 1], [0, 3, -3, 0, 2, 2], [2, 0, 1, 0, -1, 0], [1, 4, -4, 2, 6, 2], [2, 1, 2, 0, -1, -1], [0, 1, -1, 0, 0, 0], [-4, 1, 1, -2, 0, -2], [0, 1, -1, 0, -1, 2], [0, -2, 1, -3, 1, -3], [-6, -2, -3, 0, 2, 0], [-2, -3, 3, -2, -2, -2], [-6, -1, 2, 0, -3, 1], [-1, 1, -2, -2, 1, 1], [-3, 1, -4, 0, 5, -1], [-6, 4, -4, -6, 3, 3], [-2, -1, 2, -4, -3, 2], [0, -4, -1, 0, -1, -3], [0, 1, 0, 0, 0, 1], [2, 0, 1, 4, -1, 1], [4, 1, -1, 4, 2, 2], [0, 0, 2, 0, -2, 0], [5, 2, 1, 7, -3, 1], [0, -1, 0, 0, -1, 1], [3, 0, 0, 3, 0, 0], [2, 0, 1, 4, 1, 1], [0, 1, 0, -6, 0, 1], [0, -2, 0, 0, 0, -2], [-2, -2, 2, 2, -2, -1], [1, -3, 3, 1, -2, -2], [12, 3, 0, 0, 3, -3], [6, 1, 3, 0, -1, 0], [-5, -1, -2, 0, 1, 1], [-2, 1, -1, -2, 0, 0], [-2, -3, 5, -4, -2, -4], [0, -1, -3, 2, -3, 2], [0, -2, 1, -6, 1, -3], [9, 1, 0, 3, -1, 3], [3, -1, 1, 3, -2, -2], [-6, 3, -2, 0, 5, -3], [0, -5, 3, -6, -1, -3], [-4, 0, -4, 0, 4, 0], [6, -3, 3, 6, -4, -4], [0, -1, 0, 0, -1, 0], [0, -2, -1, -4, -1, -1], [0, 2, 1, 0, 1, 1], [2, 0, 1, 4, -1, 1], [-2, 4, -4, -2, 4, 4], [1, 0, -2, 0, 2, 0], [-4, -2, -2, -5, -2, 4], [-6, -3, 5, 0, -8, 3], [6, -3, 3, 6, -3, -3], [-8, 3, -4, -7, 3, 5], [0, 0, 1, 0, 1, -1], [0, 4, -3, 6, -3, 7], [-2, 1, 2, 8, 3, -4], [6, 5, -5, 6, 4, 4], [-3, 0, 0, 0, 0, 0], [-2, 0, 2, -4, 1, -1], [4, -1, 0, 0, -1, 1], [-12, -2, 2, -12, -1, -1], [-8, 5, -7, 2, 4, 2], [0, 4, 4, -9, 4, 0], [0, 0, 1, 2, 1, -1], [1, 5, 2, -1, -1, -1], [4, 2, -2, 4, -2, -2], [-12, -3, -2, 0, -1, 3], [4, -2, -1, 2, 3, -1], [1, 1, 0, 0, 1, -1]]}