# Stored data for newform 538.8.a.d, downloaded from the LMFDB on 16 April 2026.
{"Nk2": 34432, "analytic_conductor": 168.0631437104575, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [269, -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": [538, 1, [271], [1]], "cm_discs": [], "conrey_index": 1, "dim": 43, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_orbit": 4, "hecke_orbit_code": 13510799016329754, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "538.8.a.d", "level": 538, "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": true, "level_primes": [2, 269], "level_radical": 538, "minimal_twist": "538.8.a.d", "prim_orbit_index": 1, "related_objects": [], "relative_dim": 43, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "538.8.a", "trace_display": [344, 123, 1249, 2292], "traces": [43, 344, 123, 2752, 1249, 984, 2292, 22016, 38034, 9992, 9236, 7872, 20734, 18336, 45412, 176128, 73650, 304272, 29172, 79936, 121999, 73888, 292888, 62976, 922452, 165872, 361146, 146688, 564477, 363296, 430638, 1409024, 443001, 589200, 933371, 2434176, 1358862, 233376, 1743349, 639488, 1869846, 975992, 1398712, 591104, 3495454, 2343104, 2157317, 503808, 7543237, 7379616, 230971, 1326976, 5925672, 2889168, 1107773, 1173504, 9117130, 4515816, 2165139, 2906368, 5047648, 3445104, 5691679, 11272192, 12361273, 3544008, 4415992, 4713600, -7538249, 7466968, 6241518, 19473408, 3473436, 10870896, -5305402, 1867008, -3658634, 13946792, 15661969, 5115904, 38608119, 14958768, 12126950, 7807936, 9453663, 11189696, 41966326, 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