# Stored data for newform 256.12.a.l, downloaded from the LMFDB on 11 February 2025.
{"Nk2": 36864, "analytic_conductor": 196.69585422325474, "analytic_rank": 1, "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": 8, "field_disc": 63165033366336862474046991160977010944, "field_disc_factorization": [[2, 8], [3, 4], [55191967073771377, 2]], "field_poly": [17099916310116, -1034018012664, -244021939416, 7141379724, 904265037, -119616, -59846, -4, 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, [-7245913968, -120671424, -386472, 496, 1]], [5, [539199774781501901635584000000, 0, -172816621342660362240000, 0, 14409198549504000, 0, -233050752, 0, 1]], [7, [24148847943577292207005370038389571584, 0, -61153868756812705504407060480, 0, 46044286693002510336, 0, -11962624512, 0, 1]]], "hecke_orbit": 12, "hecke_orbit_code": 49539596102402304, "hecke_ring_generator_nbound": 13, "hecke_ring_index": 81064793292668928, "hecke_ring_index_factorization": [[2, 53], [3, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -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.l", "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": "64.12.b.c", "prim_orbit_index": 1, "qexp_display": "q+(-124+\\beta _{1})q^{3}+\\beta _{3}q^{5}+(-\\beta _{3}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "11.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "256.12.a", "trace_display": [0, -992, 0, 0], "trace_hash": 1190891525616606395, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.217", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "254.222", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12653.609", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 8, 0, -992, 0, 0, 0, 0, 0, 620744, 0, -789408, 0, 0, 0, 0, 0, -757680, 0, -4654304, 0, 0, 0, 0, 0, 75476504, 0, -318700352, 0, 0, 0, 0, 0, 364632288, 0, -434569728, 0, 0, 0, 0, 0, -2247301968, 0, -2061364640, 0, 0, 0, 0, 0, 8106635080, 0, 13152891456, 0, 0, 0, 0, 0, -16668532576, 0, -18124353696, 0, 0, 0, 0, 0, 58331328768, 0, 74512677920, 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