# Stored data for newform 256.12.a.p, downloaded from the LMFDB on 15 January 2026.
{"Nk2": 36864, "analytic_conductor": 196.69585422325474, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 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": [256, 1, [255, 5], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 10, "field_disc": 407249023013505639396569079326739790684684448521216, "field_disc_factorization": [[2, 10], [7, 2], [23, 1], [353, 1], [999840527660258387833, 2]], "field_poly": [-20440645894144, 0, 760691642368, 0, -5521716928, 0, 8617108, 0, -5011, 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": [[3, [-23616501181712148139121664, 0, 2820473894112854402304, 0, -58059024148420992, 0, 415491272352, 0, -1121932, 0, 1]], [5, [-46208751498243071728497409638400000000, 0, 12886904566420501696672768000000, 0, -922914430681034275840000, 0, 24403540255091200, 0, -264891952, 0, 1]], [7, [53374179670054702907392, 5740462575196131328, -342941398016, -5087977856, -16808, 1]]], "hecke_orbit": 16, "hecke_orbit_code": 67553994611884288, "hecke_ring_generator_nbound": 13, "hecke_ring_index": 2437194452343092416207650816, "hecke_ring_index_factorization": [[2, 85], [3, 2], [7, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 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": false, "label": "256.12.a.p", "level": 256, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2], "level_radical": 2, "minimal_twist": "8.12.b.a", "prim_orbit_index": 1, "qexp_display": "q-\\beta _{1}q^{3}+(-2\\beta _{1}-\\beta _{4})q^{5}+(3362+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 10, "rm_discs": [], "sato_tate_group": "11.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "256.12.a", "trace_display": [0, 0, 0, 33616], "trace_hash": 2182696963311792910, "trace_moments": [{"__RealLiteral__": 0, "data": "0.219", "prec": 17}, {"__RealLiteral__": 0, "data": "8.604", "prec": 17}, {"__RealLiteral__": 0, "data": "9.078", "prec": 17}, {"__RealLiteral__": 0, "data": "387.525", "prec": 24}, {"__RealLiteral__": 0, "data": "414.713", "prec": 24}, {"__RealLiteral__": 0, "data": "23913.289", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 10, 0, 0, 0, 0, 0, 33616, 0, 472394, 0, 0, 0, 0, 0, 3391792, 0, 2639732, 0, 0, 0, 0, 0, 45357808, 0, 41502654, 0, 0, 0, 0, 0, 442035392, 0, -54732216, 0, 0, 0, 0, 0, 431459312, 0, 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