# Stored data for newform 1386.4.a.w, downloaded from the LMFDB on 22 September 2026.
{"Nk2": 22176, "analytic_conductor": 81.77664726795649, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [7, 1], [11, -1]], "atkin_lehner_string": "--+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [1386, 1, [155, 199, 1135], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 217, "field_disc_factorization": [[7, 1], [31, 1]], "field_poly": [-54, -1, 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": 0, "hecke_cutters": [[5, [-42, 7, 1]], [13, [-1174, 27, 1]]], "hecke_orbit": 23, "hecke_orbit_code": 99079191869261162, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "1386.4.a.w", "level": 1386, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 7, 11], "level_radical": 462, "minimal_twist": "462.4.a.m", "nf_label": "2.2.217.1", "prim_orbit_index": 1, "qexp_display": "q+2q^{2}+4q^{4}+(-3-\\beta )q^{5}-7q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1386.4.a", "trace_display": [4, 0, -7, -14], "trace_hash": 1201200528485004823, "trace_moments": [0, {"__RealLiteral__": 0, "data": "2.038", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "10.439", "prec": 17}, 0, 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