# Stored data for newform 289.2.c.a, downloaded from the LMFDB on 25 April 2024. {"label": "289.2.c.a", "space_label": "289.2.c", "level": 289, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 137472508193, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 1515727066649897396, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 0, 1]]], "qexp_display": "q+\\zeta_{8}^{2}q^{2}+q^{4}+\\zeta_{8}q^{5}+2\\zeta_{8}^{3}q^{7}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 17, "char_orbit_label": "c", "char_is_real": false, "Nk2": 1156, "analytic_conductor": 2.307676618415003, "hecke_ring_index": 4, "level_radical": 17, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.760", "prec": 17}, "analytic_rank_proved": true, "char_values": [289, 4, [3], [3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [17], "conrey_indexes": [38, 251], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "3.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.211", "prec": 17}, {"__RealLiteral__": 0, "data": "125.581", "prec": 24}, {"__RealLiteral__": 0, "data": "1.619", "prec": 17}, {"__RealLiteral__": 0, "data": "4895.030", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 16, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, -16, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, -40, 0, 32, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, -48, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -36, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 96, 0, 48, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -64, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, -32, 0, -68, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 48, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 80, 0, -48, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, -40, 0, -48, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 108, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 104, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -108, 0, 112, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, -24, 0, 32, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 16, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -96, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 64, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 32, 0, 24, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 8, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -16, 0, -48, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 32, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 64, 0, 96, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, -192, 0, -64, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 136, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, -8, 0, -64, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 256, 0, 96, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, -48, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -132, 0, 16, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 17, 2, 1, 2, 0], [1, 2, 17, 3, 1, 4, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "17.2.a.a", "char_is_minimal": false, "conrey_index": 38, "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], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 3, 0], [0, 0, -3, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 0, 4, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, -3, 0, 0], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, 5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-8, 0, 0, 0], [0, 0, -3, 0], [0, -1, 0, 0], [-4, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 3], [0, 0, 0, -3], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 0, -3], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -9, 0], [1, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, 0, -6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -6, 0, 0], [0, 0, 0, 0], [0, 0, 0, -3], [0, 0, -12, 0], [0, 0, 0, 0], [0, 0, 0, -5], [0, 0, 0, 2], [0, 6, 0, 0], [-7, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [4, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -8, 0], [0, -2, 0, 0], [9, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -6], [0, -1, 0, 0], [-9, 0, 0, 0], [0, 3, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-10, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, 4], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 4], [0, 0, 0, 0], [0, -1, 0, 0], [9, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0]]}