# Stored data for newform 47424.2.a.by, downloaded from the LMFDB on 02 November 2025.
{"Nk2": 189696, "analytic_conductor": 378.6825465457201, "atkin_lehner_eigenvals": [[2, 1], [3, -1], [13, 1], [19, -1]], "atkin_lehner_string": "+-+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [47424, 1, [28159, 38533, 15809, 18241, 27457], [51, 51, 51, 51, 51]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": -1, "hecke_orbit": 51, "hecke_orbit_code": 225179981402126656, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": -1, "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "label": "47424.2.a.by", "level": 47424, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 13, 19], "level_radical": 1482, "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{3}-3q^{5}-3q^{7}+q^{9}-4q^{11}+\\cdots", "related_objects": ["EllipticCurve/Q/47424/by"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "47424.2.a", "trace_display": [0, 1, -3, -3], "traces": [0, 1, 0, 1, 0, -3, 0, -3, 0, 1, 0, -4, 0, -1, 0, -3, 0, -6, 0, 1, 0, -3, 0, 7, 0, 4, 0, 1, 0, -6, 0, 2, 0, -4, 0, 9, 0, -3, 0, -1, 0, 2, 0, -8, 0, -3, 0, 12, 0, 2, 0, -6, 0, 1, 0, 12, 0, 1, 0, -13, 0, 15, 0, -3, 0, 3, 0, -10, 0, 7, 0, 3, 0, -4, 0, 4, 0, 12, 0, 1, 0, 1, 0, 14, 0, 18, 0, -6, 0, -6, 0, 3, 0, 2, 0, -3, 0, 13, 0, -4, 0], "weight": 2, "weight_parity": 1, "id": null, "analytic_rank": null, "analytic_rank_proved": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "hecke_cutters": null, "inner_twists": null, "is_twist_minimal": null, "level_is_powerful": null, "level_is_prime_square": null, "minimal_twist": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null, "qexp": [[0], 1, 0, 1, 0, -3, 0, -3, 0, 1, 0, -4, 0, -1, 0, -3, 0, -6, 0, 1, 0, -3, 0, 7, 0, 4, 0, 1, 0, -6, 0, 2, 0, -4, 0, 9, 0, -3, 0, -1, 0, 2, 0, -8, 0, -3, 0, 12, 0, 2, 0, -6, 0, 1, 0, 12, 0, 1, 0, -13, 0, 15, 0, -3, 0, 3, 0, -10, 0, 7, 0, 3, 0, -4, 0, 4, 0, 12, 0, 1, 0, 1, 0, 14, 0, 18, 0, -6, 0, -6, 0, 3, 0, 2, 0, -3, 0, 13, 0, -4, 0]}