# Stored data for newform 891.2.a.q, downloaded from the LMFDB on 20 April 2024. {"label": "891.2.a.q", "space_label": "891.2.a", "level": 891, "weight": 2, "hecke_orbit": 17, "hecke_orbit_code": 72057594071483259, "dim": 4, "is_polredabs": true, "nf_label": "4.4.22545.1", "trace_hash": 91798385278771615, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [13, 8, -9, -1, 1]], [5, [31, 29, -9, -4, 1]], [7, [4, 5, -6, -1, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+(3+\\beta _{3})q^{4}+(1-\\beta _{1}-\\beta _{3})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3564, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 7.114670820096082, "hecke_ring_index": 1, "level_radical": 33, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "analytic_rank_proved": true, "char_values": [891, 1, [650, 244], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 11], "conrey_indexes": [1], "field_disc": 22545, "field_disc_factorization": [[3, 3], [5, 1], [167, 1]], "field_poly": [4, 5, -6, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.707", "prec": 17}, {"__RealLiteral__": 0, "data": "0.126", "prec": 17}, {"__RealLiteral__": 0, "data": "37.548", "prec": 20}, {"__RealLiteral__": 0, "data": "7.668", "prec": 17}, {"__RealLiteral__": 0, "data": "588.796", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [11, -1]], "trace_display": [1, 0, 4, 1], "traces": [0, 4, 1, 0, 11, 4, 0, 1, 0, 0, 1, 4, 0, 7, 1, 0, 17, -5, 0, 9, -10, 0, 1, 14, 0, 14, 22, 0, -1, -6, 0, -2, -34, 0, 16, -8, 0, 3, 3, 0, 12, -2, 0, -21, 11, 0, 2, -7, 0, -15, 23, 0, -10, -6, 0, 4, 18, 0, -21, 2, 0, 15, -20, 0, 16, 19, 0, 14, -7, 0, -38, -3, 0, 22, -36, 0, 42, 1, 0, 11, -34, 0, -17, 18, 0, 13, -24, 0, 0, -6, 0, 19, 67, 0, -19, -30, 0, 26, 15, 0, -8, -19, 0, 11, 87, 0, -3, 9, 0, 7, 1, 0, 8, -9, 0, 2, 9, 0, -1, -26, 0, 4, 3, 0, 20, 45, 0, -25, -60, 0, -50, -30, 0, 24, -16, 0, 3, 20, 0, 1, -49, 0, -36, 7, 0, -27, -32, 0, -36, 5, 0, 17, 6, 0, 1, -23, 0, 23, 41, 0, -31, -13, 0, -32, -16, 0, -15, -12, 0, 27, 73, 0, -57, -3, 0, -1, 17, 0, -42, -6, 0, 37, 7, 0, -48, 54, 0, -5, -26, 0, -63, -4, 0, 16, -31, 0, -42, -44, 0, 15, 81, 0, -37, -6, 0, -29, -70, 0, -52, 9, 0, -15, -30, 0, -18, -21, 0, -5, -20, 0, -10, -23, 0, -77, 23, 0, -21, 42, 0, 18, 53, 0, -69, 21, 0, -25, 34, 0, -44, 3, 0, 13, 1, 0, 45, -15, 0, 21, -69, 0, 12, 34, 0, 14, 65, 0, -5, 46, 0, -6, -37, 0, 30, -4, 0, 42, 63, 0, 1, 10, 0, 29, -67, 0, -58, 14, 0, 37, 37, 0, -30, -9, 0, -35, -18, 0, 22, 37, 0, 5, 12, 0, 41, -27, 0, -10, -36, 0, -16, -22, 0, -6, -16, 0, 93, 24, 0, 17, -1, 0, 13, 15, 0, -13, -34, 0, 46, 4, 0, -6, -35, 0, -1, -54, 0, 86, -20, 0, 15, 23, 0, -11, 117, 0, -21, 83, 0, -28, -45, 0, 122, -2, 0, -10, -39, 0, 69, -71, 0, 54, -52, 0, -34, -51, 0, -30, 0, 0, -24, 28, 0, 5, 25, 0, 41, 52, 0, 31, 103, 0, 21, -36, 0, 40, 16, 0, -3, -60, 0, 43, -126, 0, 92, 32, 0, -8, 46, 0, 115, -39, 0, 14, 39, 0, 64, -28, 0, -20, 135, 0, -77, -40, 0, -53, -140, 0, 15, 3, 0, 36, -113, 0, -41, -16, 0, -63, 65, 0, 3, 11, 0, 19, -81, 0, -24, 11, 0, -9, 117, 0, -3, 33, 0, -5, 16, 0, 77, 27, 0, -20, 12, 0, -32, 58, 0, 30, -59, 0, 4, 47, 0, -2, -45, 0, 105, -8, 0, 12, -72, 0, 1, -30, 0, -53, 60, 0, 51, 57, 0, -28, -76, 0, -48, -21, 0, -24, -49, 0, -3, -46, 0, 6, -5, 0, 11, -34, 0, -49, -18, 0, -6, 10, 0, -3, 123, 0, 77, 36, 0, 32, 99, 0, -104, -14, 0, 8, 2, 0, -11, -6, 0, -5, -59, 0, 67, 74, 0, -7, -57, 0, -33, 21, 0, -4, -84, 0, 17, -8, 0, 2, 102, 0, 81, 28, 0, -93, -33, 0, 94, -15, 0, 1, -73, 0, 38, -17, 0, -16, 91, 0, 23, 3, 0, 26, -14, 0, 68, 46, 0, -57, -1, 0, -54, -11, 0, 21, 10, 0, -24, 84, 0, -76, -10, 0, 64, 7, 0, -15, 38, 0, -12, 18, 0, -6, -66, 0, -87, -59, 0, 12, 50, 0, -9, -22, 0, -56, 49, 0, 146, 49, 0, 104, -6, 0, 97, 4, 0, -46, -48, 0, 42, 2, 0, 50, 56, 0, 18, -54, 0, 35, -22, 0, 78, -54, 0, -4, -16, 0, 76, -27, 0, -83, 84, 0, 112, -40, 0, -6, -21, 0, 66, -12, 0, -25, -26, 0, -69, 14, 0, 2, -67, 0, -226, -74, 0, -30, 41, 0, 41, 70, 0, 22, 184, 0, -93, -15, 0, 9, 27, 0, 98, 15, 0, -22, 53, 0, 33, -75, 0, 23, -6, 0, -20, -142, 0, 101, -10, 0, -51, -33, 0, -37, 99, 0, 40, -80, 0, -89, 54, 0, -44, -25, 0, -51, 16, 0, 12, 56, 0, 2, -111, 0, -150, 23, 0, 19, 45, 0, 88, 39, 0, 11, 116, 0, 179, -87, 0, -30, 54, 0, 37, 9, 0, 93, -182, 0, -185, 14, 0, -1, 27, 0, -84, 58, 0, -73, -155, 0, -7, 12, 0, 16, 16, 0, 39, -25, 0, -7, 49, 0, -75, 18, 0, -32, -74, 0, 35, -43, 0, -28, -38, 0, -22, -24, 0, -73, -102, 0, 36, 60, 0, -3, 95, 0, -102, 50, 0, -53, -103, 0, -67, -12, 0, 9, 10, 0, 15, 80, 0, -58, -23, 0, -79, 22, 0, -70, 61, 0, 84, -18, 0, -11, -6, 0, -36, 37, 0, -48, 135, 0, -151, 64, 0, -48, -66, 0, -4, 50, 0, 64, -36, 0, -155, 36, 0, -111, 42, 0, 29, 40, 0, -62, 76, 0, 36, 3, 0, 1, -84, 0, 101, -27, 0, 53, -18, 0, -123, -148, 0, -78, 36, 0, -111, 18, 0, -60, -83, 0, -7, 11, 0, 11, -135, 0, -48, 15, 0, 30, -146, 0, -34, 68, 0, -47, 59, 0, -116, 17, 0, -49, 156, 0, -178, 27, 0, -21, 9, 0, 158, 48, 0, 75, -17, 0, -27, -17, 0, 18, 108, 0, -110, 27, 0, 18, 192, 0, 39, -6, 0, -110, 39, 0, -162, 6, 0, 69, -38, 0, -42, -81, 0, -33, -69, 0, 117, 13, 0, -73, -97, 0, -92, -51, 0, -55, 52, 0, -24, -45, 0, 10, 0, 0, -90, -35, 0, 95, -15, 0, 92, -112, 0, -78, -123, 0, 98, 22, 0, 28, 0, 0, -43, 20, 0, 16, 104, 0, 60, 36, 0, -6, 54, 0, 154, 33, 0, -74, -12, 0, 48, -72, 0, 79, -76, 0, 63, 45, 0, 98, -52, 0, 30], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "99.2.e.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [3, 0, 0, 1], [1, -1, 0, -1], [0, 0, 0, 0], [0, 1, 0, 0], [-1, 1, 2, -1], [0, 0, 0, 0], [1, -3, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [1, 1, 1, -1], [0, 2, 0, 1], [0, 0, 0, 0], [5, 1, -2, 2], [-1, -2, 1, 0], [0, 0, 0, 0], [2, 2, 0, 1], [-2, -4, 1, -1], [0, 0, 0, 0], [0, 0, 1, 0], [4, -1, 0, 1], [0, 0, 0, 0], [3, -1, 1, -2], [6, 1, 0, 3], [0, 0, 0, 0], [-1, 3, 1, 1], [-1, 0, -1, 1], [0, 0, 0, 0], [0, 0, -1, 1], [-10, 2, 3, -1], [0, 0, 0, 0], [5, -4, -1, -1], [-2, 1, -2, -1], [0, 0, 0, 0], [1, -1, -2, -2], [-1, 5, 3, 1], [0, 0, 0, 0], [4, -3, -3, -2], [-1, 3, -1, 0], [0, 0, 0, 0], [-5, 0, -1, 0], [3, 0, 0, 1], [0, 0, 0, 0], [-1, -1, 5, -2], [-2, 2, -1, 0], [0, 0, 0, 0], [-4, 0, 1, 0], [7, -4, 1, 2], [0, 0, 0, 0], [-5, 3, 7, 0], [-1, -3, 0, -1], [0, 0, 0, 0], [1, -1, 0, -1], [4, 3, 0, 1], [0, 0, 0, 0], [-6, 1, 0, -2], [1, -1, 0, 1], [0, 0, 0, 0], [4, -1, 0, 0], [-6, 1, 1, -2], [0, 0, 0, 0], [6, 1, -7, 2], [5, -2, -3, -4], [0, 0, 0, 0], [4, -3, -1, -2], [-2, -5, 2, -4], [0, 0, 0, 0], [-9, 1, -3, 0], [-1, 3, -2, 0], [0, 0, 0, 0], [6, -1, -2, -1], [-8, -4, -1, -1], [0, 0, 0, 0], [10, 7, 0, 5], [0, 1, 0, 0], [0, 0, 0, 0], [2, 2, 2, 1], [-9, 0, 0, -2], [0, 0, 0, 0], [-5, 6, -1, 2], [5, 2, -1, 3], [0, 0, 0, 0], [4, -4, 4, 3], [-5, 0, -5, -1], [0, 0, 0, 0], [-1, 1, 2, -1], [0, -4, -2, 0], [0, 0, 0, 0], [4, 3, 0, 0], [19, -2, -3, 4], [0, 0, 0, 0], [-5, 4, -2, 1], [-7, -1, -3, -2], [0, 0, 0, 0], [7, 2, -2, 2], [5, 0, -4, 1], [0, 0, 0, 0], [-3, -4, 7, -1]]}