# Stored data for newform 2178.4.a.bd, downloaded from the LMFDB on 05 October 2026.
{"Nk2": 34848, "analytic_conductor": 128.50615999250306, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, -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": [2178, 1, [1937, 1333], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 12, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[5, [-111, -12, 1]], [7, [-354, 6, 1]], [17, [1053, 72, 1]]], "hecke_orbit": 30, "hecke_orbit_code": 130604389260855426, "hecke_ring_generator_nbound": 7, "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": "2178.4.a.bd", "level": 2178, "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, 11], "level_radical": 66, "minimal_twist": "242.4.a.i", "nf_label": "2.2.12.1", "prim_orbit_index": 1, "qexp_display": "q-2q^{2}+4q^{4}+(6+7\\beta )q^{5}+(-3+11\\beta )q^{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": "2178.4.a", "trace_display": [-4, 0, 12, -6], "trace_hash": 1407798615729613486, "trace_moments": [0, {"__RealLiteral__": 0, "data": "2.006", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "9.815", "prec": 14}, 0, 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