# Stored data for newform 891.2.e.k, downloaded from the LMFDB on 28 March 2024. {"label": "891.2.e.k", "space_label": "891.2.e", "level": 891, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45036271185167227, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2195634778965343858, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [4, -2, 1]], [5, [1, 1, 1]], [7, [4, -2, 1]]], "qexp_display": "q+(2-2\\zeta_{6})q^{2}-2\\zeta_{6}q^{4}-\\zeta_{6}q^{5}+(2+\\cdots)q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 3564, "analytic_conductor": 7.114670820096082, "hecke_ring_index": 1, "level_radical": 33, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.013", "prec": 17}, "analytic_rank_proved": true, "char_values": [891, 3, [650, 244], [2, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [3, 11], "conrey_indexes": [298, 595], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.895", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.867", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "97.916", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [2, 0, -1, 2], "traces": [0, 2, 2, 0, -2, -1, 0, 2, 0, 0, -4, -1, 0, -4, -4, 0, 4, -4, 0, 0, -2, 0, 2, 1, 0, 4, -16, 0, -8, 0, 0, -7, -8, 0, -4, -4, 0, 6, 0, 0, 0, 8, 0, 6, 4, 0, 4, -8, 0, 3, -8, 0, -8, -12, 0, 2, 0, 0, 0, -5, 0, -12, -28, 0, -16, -4, 0, 7, 4, 0, -4, -6, 0, 8, 6, 0, 0, 2, 0, 10, -8, 0, 32, 6, 0, 2, -12, 0, 0, 30, 0, -16, 2, 0, 16, 0, 0, 7, 12, 0, -16, -2, 0, 16, 0, 0, -12, 36, 0, 20, 2, 0, -8, -9, 0, 1, 0, 0, -20, -4, 0, -1, 24, 0, -14, -18, 0, 16, 0, 0, 8, 18, 0, 0, 28, 0, 0, 7, 0, -10, 4, 0, -6, 8, 0, 0, 8, 0, -6, 10, 0, -2, 0, 0, 8, -7, 0, 7, -20, 0, -8, 4, 0, 8, 16, 0, -12, 12, 0, -3, 8, 0, -24, 6, 0, -8, 4, 0, 30, -30, 0, 14, -16, 0, 0, -3, 0, 2, 32, 0, 0, -17, 0, -4, -14, 0, 6, -4, 0, 0, 0, 0, 4, 0, 0, 8, 64, 0, -32, 0, 0, -12, 12, 0, 36, -12, 0, -28, 20, 0, -2, 8, 0, -19, -32, 0, -36, -18, 0, -15, -2, 0, 0, 48, 0, 16, -10, 0, 8, 30, 0, 8, -4, 0, 48, 3, 0, 0, 0, 0, -18, -46, 0, -2, 16, 0, -16, 2, 0, 6, 16, 0, 72, -14, 0, 6, 0, 0, 14, 20, 0, -56, -8, 0, -14, 4, 0, 2, -40, 0, 0, 18, 0, -4, 6, 0, 8, 32, 0, -26, 0, 0, -8, -24, 0, -5, 0, 0, 40, 4, 0, -12, 4, 0, 0, 24, 0, 16, 4, 0, 14, -12, 0, 1, 28, 0, -40, -13, 0, 0, 8, 0, 4, 0, 0, -32, 8, 0, 0, 16, 0, -7, -24, 0, 48, 7, 0, 22, 6, 0, 4, 14, 0, 40, 0, 0, -12, -28, 0, -30, -32, 0, 16, 21, 0, 3, -30, 0, -30, -40, 0, -38, 14, 0, 16, -4, 0, 17, 8, 0, -12, -12, 0, 26, -4, 0, 0, 0, 0, -10, 0, 0, 34, 1, 0, 2, -16, 0, -28, 15, 0, -2, 0, 0, -4, -20, 0, -4, 0, 0, -16, -2, 0, -28, 8, 0, 0, -3, 0, 30, -16, 0, 32, -20, 0, -12, -32, 0, 0, -20, 0, -22, -48, 0, 0, -8, 0, 24, -36, 0, -12, -36, 0, -22, -28, 0, -20, 0, 0, -40, 0, 0, 32, 11, 0, -15, 38, 0, -16, 70, 0, -16, -18, 0, 36, 8, 0, 12, -60, 0, -4, -12, 0, 11, 0, 0, 48, -54, 0, 28, 16, 0, 0, 6, 0, 0, 16, 0, 120, -20, 0, -12, -16, 0, -2, -14, 0, 46, 0, 0, -6, 8, 0, 0, 0, 0, -56, -6, 0, -20, 18, 0, -46, -52, 0, 4, -2, 0, -16, -15, 0, 8, -64, 0, 8, 16, 0, -8, -12, 0, 0, -6, 0, -32, 36, 0, 28, 14, 0, 22, 24, 0, 0, 32, 0, -18, 0, 0, 20, -6, 0, -16, -56, 0, 16, -10, 0, -8, -28, 0, 16, 0, 0, -20, -4, 0, -20, -4, 0, -48, -8, 0, -36, -4, 0, -9, -16, 0, 0, 0, 0, 28, -8, 0, 32, 8, 0, 66, -26, 0, 0, -12, 0, 6, 0, 0, -96, -28, 0, 0, 10, 0, 12, 88, 0, 8, 20, 0, -8, -40, 0, -2, -48, 0, 8, -1, 0, 22, 0, 0, 24, 64, 0, -32, 16, 0, 0, -18, 0, 25, 28, 0, -48, 30, 0, -11, -2, 0, 14, -12, 0, 14, 0, 0, 26, -8, 0, 12, 0, 0, 0, 33, 0, -29, -4, 0, 0, -14, 0, 10, -32, 0, -8, 41, 0, 18, 64, 0, 64, -10, 0, -37, 14, 0, 0, 0, 0, 0, 24, 0, -14, -12, 0, -14, 88, 0, 12, 42, 0, -14, 0, 0, 14, -32, 0, -14, 40, 0, -24, 24, 0, -17, -24, 0, -112, -10, 0, -16, 60, 0, -16, 4, 0, 0, 8, 0, -42, 4, 0, 25, 12, 0, 0, 7, 0, -4, 30, 0, -40, 30, 0, 64, -38, 0, -14, 0, 0, -3, 0, 0, -16, -12, 0, 36, -34, 0, 8, -14, 0, 100, -6, 0, 24, -4, 0, 10, 104, 0, -8, 36, 0, 23, 32, 0, 0, 4, 0, -44, -10, 0, 0, -12, 0, 20, 68, 0, 4, -20, 0, -20, -4, 0, -8, -12, 0, -56, 0, 0, -30, 0, 0, 3, -8, 0, 24, 7, 0, 32, 4, 0, -20, -36, 0, 96, -4, 0, 0, -53, 0, 16, -64, 0, -8, -4, 0, -2, 56, 0, 0, 0, 0, -76, 0, 0, 6, -4, 0, 0, 120, 0, -32, -22, 0, -39, 0, 0, -20, -104, 0, 50, -12, 0, 32, -6, 0, 12, 0, 0, -80, 5, 0, 29, 44, 0, -24, 6, 0, -4, -24, 0, 16, 3, 0, -14, 96, 0, 0, -8, 0, 15, 12, 0, -36, 48, 0, -12, -22, 0, 28, 10, 0, 28, 0, 0, 0, -18, 0, 12, 80, 0, 4, -86, 0, 8, 16, 0, -22, 22, 0, 16, -60, 0, 76, 0, 0, 15, 0, 0, 70, 0, 0, 24, -16, 0, 0, -7, 0, 12, 72, 0, 32, -12, 0, 6, -24, 0, -30, 72, 0, 20, 0, 0, 24, 12, 0, 12, 44, 0, 0, 30, 0, 0, -48, 0, -54, -4, 0, 16, 28, 0, -16, -42, 0, -8, -40, 0, 24, 27, 0, -16, 0, 0, 0, 68, 0, 34, 60, 0, 40, -14, 0, -18, -48, 0, -32, -4, 0, 32, 0, 0, -14, 94, 0, -40, 46, 0, 48, 27, 0, -15, -12, 0, 32, -39, 0, 2, 0, 0, 0, 12, 0, -16, -56, 0, 12, 0, 0, -38, -80, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 9, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "11.2.a.a", "char_is_minimal": false, "conrey_index": 298, "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], [1, 0], [2, -2], [0, 0], [0, -2], [0, -1], [0, 0], [2, -2], [0, 0], [0, 0], [-2, 0], [-1, 1], [0, 0], [0, -4], [0, -4], [0, 0], [4, -4], [-2, 0], [0, 0], [0, 0], [-2, 2], [0, 0], [0, 2], [0, 1], [0, 0], [4, -4], [-8, 0], [0, 0], [-4, 0], [0, 0], [0, 0], [0, -7], [0, -8], [0, 0], [-4, 4], [-2, 0], [0, 0], [3, 0], [0, 0], [0, 0], [0, 0], [0, 8], [0, 0], [6, -6], [2, 0], [0, 0], [2, 0], [-8, 8], [0, 0], [0, 3], [0, -8], [0, 0], [-8, 8], [-6, 0], [0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, -5], [0, 0], [-12, 12], [-14, 0], [0, 0], [-8, 0], [-4, 4], [0, 0], [0, 7], [0, 4], [0, 0], [-4, 4], [-3, 0], [0, 0], [4, 0], [6, -6], [0, 0], [0, 0], [0, 2], [0, 0], [10, -10], [-4, 0], [0, 0], [16, 0], [6, -6], [0, 0], [0, 2], [0, -12], [0, 0], [0, 0], [15, 0], [0, 0], [-8, 0], [2, -2], [0, 0], [0, 16], [0, 0], [0, 0], [7, -7], [6, 0], [0, 0], [-8, 0]]}