# Stored data for newform 1323.4.a.bg, downloaded from the LMFDB on 12 December 2025.
{"Nk2": 21168, "analytic_conductor": 78.05952693759484, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [7, -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": [1323, 1, [785, 1081], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 6, "field_disc": 17962212352, "field_disc_factorization": [[2, 10], [7, 1], [1583, 2]], "field_poly": [-112, 0, 369, 0, -42, 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_cutters": [[2, [-112, 0, 369, 0, -42, 0, 1]], [5, [-2699487, 0, 86103, 0, -585, 0, 1]], [13, [48168, -684, -54, 1]]], "hecke_orbit": 33, "hecke_orbit_code": 144115188142966059, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 648, "hecke_ring_index_factorization": [[2, 3], [3, 4]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "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": true, "label": "1323.4.a.bg", "level": 1323, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 7], "level_radical": 21, "minimal_twist": "1323.4.a.bf", "prim_orbit_index": 1, "qexp_display": "q+\\beta _{1}q^{2}+(6+\\beta _{2})q^{4}+(2\\beta _{1}+\\beta _{3})q^{5}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1323.4.a", "trace_display": [0, 0, 0, 0], "trace_hash": 1794507162237031187, "trace_moments": [{"__RealLiteral__": 0, "data": 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