
# Stored data for newform 47040.2.a.fd, downloaded from the LMFDB on 19 June 2026.
{"Nk2": 188160, "analytic_conductor": 375.6162911081029, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [5, 1], [7, -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": [47040, 1, [1471, 44101, 31361, 18817, 42241], [134, 134, 134, 134, 134]], "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": 134, "hecke_orbit_code": 598978750473877440, "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": "47040.2.a.fd", "level": 47040, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 5, 7], "level_radical": 210, "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{3}-q^{5}+q^{9}+3q^{11}+q^{13}-q^{15}+\\cdots", "related_objects": ["EllipticCurve/Q/47040/fd"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "47040.2.a", "trace_display": [0, 1, -1, 0], "traces": [0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 3, 0, 1, 0, -1, 0, 0, 0, 7, 0, 0, 0, 5, 0, 1, 0, 1, 0, 0, 0, 6, 0, 3, 0, 0, 0, -3, 0, 1, 0, 3, 0, 8, 0, -1, 0, -1, 0, 0, 0, 0, 0, -5, 0, -3, 0, 7, 0, 4, 0, -8, 0, 0, 0, -1, 0, 0, 0, 5, 0, 6, 0, 14, 0, 1, 0, 0, 0, 16, 0, 1, 0, 16, 0, 0, 0, 0, 0, -6, 0, 0, 0, 6, 0, -7, 0, -16, 0, 3, 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, -1, 0, 0, 0, 1, 0, 3, 0, 1, 0, -1, 0, 0, 0, 7, 0, 0, 0, 5, 0, 1, 0, 1, 0, 0, 0, 6, 0, 3, 0, 0, 0, -3, 0, 1, 0, 3, 0, 8, 0, -1, 0, -1, 0, 0, 0, 0, 0, -5, 0, -3, 0, 7, 0, 4, 0, -8, 0, 0, 0, -1, 0, 0, 0, 5, 0, 6, 0, 14, 0, 1, 0, 0, 0, 16, 0, 1, 0, 16, 0, 0, 0, 0, 0, -6, 0, 0, 0, 6, 0, -7, 0, -16, 0, 3, 0]}