# Stored data for newform 920.2.e.b, downloaded from the LMFDB on 12 January 2026.
{"Nk2": 3680, "analytic_conductor": 7.346236985957796, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 2, "char_parity": 1, "char_values": [920, 2, [231, 461, 737, 281], [2, 2, 1, 2]], "cm_discs": [], "conrey_index": 369, "dim": 14, "field_disc": -2363030496997458313216, "field_disc_factorization": [[-1, 1], [2, 18], [94943383, 2]], "field_poly": [8, -32, 64, -20, 24, -116, 297, -26, 2, -10, 39, -2, 0, 0, 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": [[3, [4, 0, 149, 0, 1095, 0, 1431, 0, 766, 0, 195, 0, 23, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503874538832792, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "920.2.e.b", "level": 920, "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": [2, 5, 23], "level_radical": 230, "minimal_twist": "920.2.e.b", "prim_orbit_index": 2, "qexp_display": "q-\\beta _{8}q^{3}+\\beta _{3}q^{5}+(\\beta _{7}-\\beta _{13})q^{7}+(1+\\cdots)q^{9}+\\cdots", "related_objects": [], "relative_dim": 14, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "920.2.e", "trace_display": [0, 0, 2, 0], "trace_hash": 98282722780477344, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.445", "prec": 20}, {"__RealLiteral__": 0, "data": "5.127", "prec": 17}, {"__RealLiteral__": 0, "data": "857.088", "prec": 24}, {"__RealLiteral__": 0, "data": "1415.887", "prec": 27}, {"__RealLiteral__": 0, "data": "89442.224", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 14, 0, 0, 0, 2, 0, 0, 0, -4, 0, -14, 0, 0, 0, -6, 0, 0, 0, 14, 0, -12, 0, 0, 0, -14, 0, 0, 0, 22, 0, -20, 0, 0, 0, -2, 0, 0, 0, 48, 0, -32, 0, 0, 0, -26, 0, 0, 0, 34, 0, -14, 0, 0, 0, -38, 0, 0, 0, 22, 0, 10, 0, 0, 0, -38, 0, 0, 0, 6, 0, -28, 0, 0, 0, -24, 0, 0, 0, 64, 0, -10, 0, 0, 0, -50, 0, 0, 0, 48, 0, -14, 0, 0, 0, -30, 0, 0, 0, 122, 0, -58, 0, 0, 0, -44, 0, 0, 0, 54, 0, -36, 0, 0, 0, -4, 0, 0, 0, 82, 0, 52, 0, 0, 0, -34, 0, 0, 0, 36, 0, -28, 0, 0, 0, -94, 0, 0, 0, 62, 0, -36, 0, 0, 0, -30, 0, 0, 0, 102, 0, 6, 0, 0, 0, 20, 0, 0, 0, 24, 0, -8, 0, 0, 0, -72, 0, 0, 0, 32, 0, 36, 0, 0, 0, -48, 0, 0, 0, 56, 0, -34, 0, 0, 0, 10, 0, 0, 0, 38, 0, -92, 0, 0, 0, -30, 0, 0, 0, 72, 0, -88, 0, 0, 0, -96, 0, 0, 0, 112, 0, -18, 0, 0, 0, 8, 0, 0, 0, 36, 0, -40, 0, 0, 0, 0, 0, 0, 0, 8, 0, 62, 0, 0, 0, -58, 0, 0, 0, 6, 0, 40, 0, 0, 0, 4, 0, 0, 0, 144, 0, -106, 0, 0, 0, -18, 0, 0, 0, 46, 0, 10, 0, 0, 0, -30, 0, 0, 0, 142, 0, 0, 0, 0, 0, -6, 0, 0, 0, 94, 0, -104, 0, 0, 0, -76, 0, 0, 0, 6, 0, -38, 0, 0, 0, -32, 0, 0, 0, -14, 0, 24, 0, 0, 0, 6, 0, 0, 0, -2, 0, -56, 0, 0, 0, -34, 0, 0, 0, 24, 0, 108, 0, 0, 0, -56, 0, 0, 0, 0, 0, -2, 0, 0, 0, -6, 0, 0, 0, -44, 0, -64, 0, 0, 0, -12, 0, 0, 0, 126, 0, -74, 0, 0, 0, -20, 0, 0, 0, -12, 0, 44, 0, 0, 0, 46, 0, 0, 0, 96, 0, -58, 0, 0, 0, -126, 0, 0, 0, 42, 0, 44, 0, 0, 0, -76, 0, 0, 0, 42, 0, 0, 0, 0, 0, 24, 0, 0, 0, 110, 0, -40, 0, 0, 0, -54, 0, 0, 0, -136, 0, -116, 0, 0, 0, -62, 0, 0, 0, 84, 0, 70, 0, 0, 0, -4, 0, 0, 0, -166, 0, -36, 0, 0, 0, 30, 0, 0, 0, -42, 0, -24, 0, 0, 0, 44, 0, 0, 0, 184, 0, 98, 0, 0, 0, 58, 0, 0, 0, -146, 0, -108, 0, 0, 0, -94, 0, 0, 0, 58, 0, 192, 0, 0, 0, -22, 0, 0, 0, 60, 0, 32, 0, 0, 0, 104, 0, 0, 0, -64, 0, -106, 0, 0, 0, 82, 0, 0, 0, -70, 0, 44, 0, 0, 0, 0, 0, 0, 0, 32, 0, 48, 0, 0, 0, 36, 0, 0, 0, 14, 0, -36, 0, 0, 0, 28, 0, 0, 0, -14, 0, 118, 0, 0, 0, -42, 0, 0, 0, -60, 0, -68, 0, 0, 0, 34, 0, 0, 0, -150, 0, -160, 0, 0, 0, -12, 0, 0, 0, 24, 0, 0, 0, 0, 0, 50, 0, 0, 0, 4, 0, 166, 0, 0, 0, 4, 0, 0, 0, -112, 0, -18, 0, 0, 0, 132, 0, 0, 0, -146, 0, 182, 0, 0, 0, -20, 0, 0, 0, 6, 0, -12, 0, 0, 0, 140, 0, 0, 0, -84, 0, 72, 0, 0, 0, 14, 0, 0, 0, -98, 0, 0, 0, 0, 0, 38, 0, 0, 0, -94, 0, 168, 0, 0, 0, 102, 0, 0, 0, -136, 0, -116, 0, 0, 0, 100, 0, 0, 0, 36, 0, 10, 0, 0, 0, -30, 0, 0, 0, -184, 0, -2, 0, 0, 0, 36, 0, 0, 0, -76, 0, -142, 0, 0, 0, -72, 0, 0, 0, -224, 0, 104, 0, 0, 0, 52, 0, 0, 0, -152, 0, -92, 0, 0, 0, -2, 0, 0, 0, -140, 0, -82, 0, 0, 0, 46, 0, 0, 0, -206, 0, 76, 0, 0, 0, 216, 0, 0, 0, 112, 0, 176, 0, 0, 0, 90, 0, 0, 0, 44, 0, 60, 0, 0, 0, 38, 0, 0, 0, -22, 0, 66, 0, 0, 0, -30, 0, 0, 0, -30, 0, 64, 0, 0, 0, 108, 0, 0, 0, -38, 0, -112, 0, 0, 0, 78, 0, 0, 0, -132, 0, 240, 0, 0, 0, 128, 0, 0, 0, 72, 0, 110, 0, 0, 0, 150, 0, 0, 0, -350, 0, -98, 0, 0, 0, -104, 0, 0, 0, -12, 0, -28, 0, 0, 0, -10, 0, 0, 0, -192, 0, 30, 0, 0, 0, 34, 0, 0, 0, -110, 0, 36, 0, 0, 0, 96, 0, 0, 0, -6, 0, 148, 0, 0, 0, -100, 0, 0, 0, -20, 0, 60, 0, 0, 0, 86, 0, 0, 0, 64, 0, 38, 0, 0, 0, 56, 0, 0, 0, -194, 0, 222, 0, 0, 0, 4, 0, 0, 0, -144, 0, 68, 0, 0, 0, 106, 0, 0, 0, 64, 0, -84, 0, 0, 0, -184, 0, 0, 0, -84, 0, 12, 0, 0, 0, 210, 0, 0, 0, -142, 0, -18, 0, 0, 0, 190, 0, 0, 0, 130, 0, -136, 0, 0, 0, 108, 0, 0, 0, -92, 0, 242, 0, 0, 0, 48, 0, 0, 0, 146, 0, 70, 0, 0, 0, 232, 0, 0, 0, -88, 0, -154, 0, 0, 0, -34, 0, 0, 0, -28, 0, -56, 0, 0, 0, 96, 0, 0, 0, -314, 0, 206, 0, 0, 0, 190, 0, 0, 0, -150, 0, -106, 0, 0, 0, -128, 0, 0, 0, -192, 0, 64, 0, 0, 0, 58, 0, 0, 0, 12, 0, -4, 0, 0, 0, 152, 0, 0, 0, 152, 0], "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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, -1, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -1, 0, 1, -1, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, -2, -1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, -1, 0, 1, -1, 0, 0, 1, -1, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, -1, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, -1, 1, 1, 0, 0, 0, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, 1, 0, -1, 1, 1, -1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -2, 0, 0, 0, 0, 0, 0, -2, 1, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -2, -1, 0, 1, 3, 0, 0, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 5, 1, -1, -1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 1, 0, -1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, -2, -2, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 3, 1, 0, -1, -1, 0, 0, 0, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, -2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, -1, 0, 1, 1, -1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, 1, -1, -1, -1, 2, -2, -2, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 1, 1, 0, 1, -1, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -3, 0, 1, 0, -1, -1, 0, 0, 0, 2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 0, 1, -1, -1, 1, 3, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 0, 1, 0, -2, -1, 3, -1, -1, 1, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, -1, -1, 0, -1, 1, 0, 0, -2, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 1, -5, -2, 0, 2, 3, 0, 0, -1, 1, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 1, 2, 0, -2, -1, 0, 0, -4, 1, 0, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -4, 0, 0, 1, 3, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -2, -1, -2, 2, 0, -1, 0, 1, -2, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 3, 0, 0, -4, -2, 2, -2, -3, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -1, 2, 1, 0, -1, -3, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 3, 0, 0, -1, -1, -1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 1, -1, 1, 3, -1, -2, 1, 2, -2, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -2, 0, 0, 0, 2, -1, 1, -2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 1, 1, -1, 0, 1, 2, 0, 0, 3, -1, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -4, 1, 0, 1, 5, 1, -1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -2, -2, -1, -2, 0, -2, -1, 0, -1, -1, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 1, -1, 2, -2, 3, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 3, 1, 0, -1, 0, 0, 0, 1, -1, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, 1, 0, -1, 1, 0, 0, 2, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 1, 4, 0, -3, 3, 2, -2, -1, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 1, 1, 3, -2, 0, -1, -1, 2, -1, -3, -3, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 4, -1, 0, 0, 3, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -3, 4, 4, 0, -4, -1, 0, 0, 0, 4, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}