# Stored data for newform 256.4.b.b, downloaded from the LMFDB on 18 April 2024. {"label": "256.4.b.b", "space_label": "256.4.b", "level": 256, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503668413956352, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1835593505151644698, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [4, 0, 1]], [7, [20, 1]]], "qexp_display": "q+iq^{3}-3iq^{5}-20q^{7}+23q^{9}-7iq^{11}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "b", "char_is_real": true, "Nk2": 4096, "analytic_conductor": 15.104488961469597, "hecke_ring_index": 2, "level_radical": 2, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [256, 2, [255, 5], [2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [129], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.967", "prec": 17}, {"__RealLiteral__": 0, "data": "0.174", "prec": 17}, {"__RealLiteral__": 0, "data": "15.667", "prec": 20}, {"__RealLiteral__": 0, "data": "2.627", "prec": 17}, {"__RealLiteral__": 0, "data": "154.165", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, -40], "traces": [0, 2, 0, 0, 0, 0, 0, -40, 0, 46, 0, 0, 0, 0, 0, 24, 0, -132, 0, 0, 0, 0, 0, -344, 0, 178, 0, 0, 0, 0, 0, -256, 0, 56, 0, 0, 0, 0, 0, -216, 0, -404, 0, 0, 0, 0, 0, -816, 0, 114, 0, 0, 0, 0, 0, -168, 0, -648, 0, 0, 0, 0, 0, -920, 0, 648, 0, 0, 0, 0, 0, 1400, 0, 836, 0, 0, 0, 0, 0, 1488, 0, 842, 0, 0, 0, 0, 0, 8, 0, 164, 0, 0, 0, 0, 0, 1944, 0, -2244, 0, 0, 0, 0, 0, -1576, 0, -480, 0, 0, 0, 0, 0, 632, 0, -1084, 0, 0, 0, 0, 0, 2640, 0, 2270, 0, 0, 0, 0, 0, 3424, 0, -1192, 0, 0, 0, 0, 0, 1200, 0, 972, 0, 0, 0, 0, 0, 1512, 0, -24, 0, 0, 0, 0, 0, -344, 0, -3036, 0, 0, 0, 0, 0, -2760, 0, 6880, 0, 0, 0, 0, 0, 2104, 0, -1438, 0, 0, 0, 0, 0, -3560, 0, -1288, 0, 0, 0, 0, 0, 1192, 0, -1896, 0, 0, 0, 0, 0, -3936, 0, -2116, 0, 0, 0, 0, 0, -8232, 0, -808, 0, 0, 0, 0, 0, -7912, 0, 4536, 0, 0, 0, 0, 0, 3576, 0, 5120, 0, 0, 0, 0, 0, -1792, 0, 4094, 0, 0, 0, 0, 0, -1120, 0, -4604, 0, 0, 0, 0, 0, 8048, 0, -7172, 0, 0, 0, 0, 0, -17496, 0, 2712, 0, 0, 0, 0, 0, -1584, 0, -13276, 0, 0, 0, 0, 0, 3448, 0, 8280, 0, 0, 0, 0, 0, -3280, 0, 4320, 0, 0, 0, 0, 0, -5888, 0, -8252, 0, 0, 0, 0, 0, 8080, 0, -1114, 0, 0, 0, 0, 0, 3864, 0, 2800, 0, 0, 0, 0, 0, 5560, 0, -3576, 0, 0, 0, 0, 0, 11112, 0, 4108, 0, 0, 0, 0, 0, -56, 0, 6456, 0, 0, 0, 0, 0, -8056, 0, 16320, 0, 0, 0, 0, 0, 2424, 0, 14372, 0, 0, 0, 0, 0, 11440, 0, -4128, 0, 0, 0, 0, 0, -10800, 0, 1700, 0, 0, 0, 0, 0, 21976, 0, -38770, 0, 0, 0, 0, 0, 1744, 0, -9292, 0, 0, 0, 0, 0, 5136, 0, 216, 0, 0, 0, 0, 0, 20480, 0, 3360, 0, 0, 0, 0, 0, 22704, 0, 8472, 0, 0, 0, 0, 0, 12960, 0, 11196, 0, 0, 0, 0, 0, -4424, 0, 1676, 0, 0, 0, 0, 0, -8136, 0, 5144, 0, 0, 0, 0, 0, -18768, 0, -11748, 0, 0, 0, 0, 0, -13584, 0, -18628, 0, 0, 0, 0, 0, 7656, 0, 2622, 0, 0, 0, 0, 0, -10664, 0, -7300, 0, 0, 0, 0, 0, -12960, 0, 31724, 0, 0, 0, 0, 0, -8752, 0, -3072, 0, 0, 0, 0, 0, -3352, 0, 8344, 0, 0, 0, 0, 0, 38144, 0, 17064, 0, 0, 0, 0, 0, -38856, 0, -5384, 0, 0, 0, 0, 0, -3864, 0, -28000, 0, 0, 0, 0, 0, -4536, 0, -16680, 0, 0, 0, 0, 0, -16720, 0, -32400, 0, 0, 0, 0, 0, -152, 0, 18956, 0, 0, 0, 0, 0, 16896, 0, 34834, 0, 0, 0, 0, 0, -19368, 0, 11160, 0, 0, 0, 0, 0, -13672, 0, 24168, 0, 0, 0, 0, 0, 648, 0, -29760, 0, 0, 0, 0, 0, -32184, 0, -3696, 0, 0, 0, 0, 0, -16840, 0, 31980, 0, 0, 0, 0, 0, -30616, 0, -25084, 0, 0, 0, 0, 0, 19320, 0, 14904, 0, 0, 0, 0, 0, 2904, 0, 29028, 0, 0, 0, 0, 0, 6920, 0, -41372, 0, 0, 0, 0, 0, -19552, 0, -160, 0, 0, 0, 0, 0, -4848, 0, -32796, 0, 0, 0, 0, 0, -3280, 0, 6842, 0, 0, 0, 0, 0, 37832, 0, -5928, 0, 0, 0, 0, 0, 32200, 0, -10500, 0, 0, 0, 0, 0, -22152, 0, 9016, 0, 0, 0, 0, 0, -25416, 0, 19228, 0, 0, 0, 0, 0, 14256, 0, -38880, 0, 0, 0, 0, 0, -8344, 0, 46140, 0, 0, 0, 0, 0, 44880, 0, -13640, 0, 0, 0, 0, 0, 18008, 0, -74520, 0, 0, 0, 0, 0, -15432, 0, 26664, 0, 0, 0, 0, 0, 51192, 0, -9792, 0, 0, 0, 0, 0, 34224, 0, 44032, 0, 0, 0, 0, 0, 38032, 0, 31520, 0, 0, 0, 0, 0, -31992, 0, 8566, 0, 0, 0, 0, 0, 1368, 0, 5656, 0, 0, 0, 0, 0, 43704, 0, 31992, 0, 0, 0, 0, 0, 64048, 0, -5000, 0, 0, 0, 0, 0, -9632, 0, 27916, 0, 0, 0, 0, 0, -34776, 0, -23940, 0, 0, 0, 0, 0, -22784, 0, -12640, 0, 0, 0, 0, 0, 400, 0, 10056, 0, 0, 0, 0, 0, 21680, 0, 32184, 0, 0, 0, 0, 0, 53856, 0, 3772, 0, 0, 0, 0, 0, -19256, 0, -78228, 0, 0, 0, 0, 0, 16152, 0, -96552, 0, 0, 0, 0, 0, -2200, 0, 4984, 0, 0, 0, 0, 0, 15928, 0, -7524, 0, 0, 0, 0, 0, -33640, 0, 48770, 0, 0, 0, 0, 0, -45400, 0, 13784, 0, 0, 0, 0, 0, 44712, 0, 17580, 0, 0, 0, 0, 0, -14784, 0, 456, 0, 0, 0, 0, 0, -21816, 0, -51612, 0, 0, 0, 0, 0, -6056, 0, 94308, 0, 0, 0, 0, 0, -46616, 0, -68480, 0, 0, 0, 0, 0, -33480, 0, 37152, 0, 0, 0, 0, 0, 23840, 0, 41016, 0, 0, 0, 0, 0, -81808, 0, -18984, 0, 0, 0, 0, 0, 54760, 0, -21960, 0, 0, 0, 0, 0, -36248, 0, 20604, 0, 0, 0, 0, 0, 11088, 0, -10108, 0, 0, 0, 0, 0, 69488, 0, -24000, 0, 0, 0, 0, 0, -9976, 0, -25940, 0, 0, 0, 0, 0, -19440, 0, -26814, 0, 0, 0, 0, 0, -3304, 0, 42768, 0, 0, 0, 0, 0, -19224, 0, 47292, 0, 0, 0, 0, 0, -76216, 0, -8712, 0, 0, 0, 0, 0, -37280, 0, -11656, 0, 0, 0, 0, 0, 31600, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "128.4.a.a", "char_is_minimal": false, "conrey_index": 129, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 1], [0, 0], [0, -3], [0, 0], [-20, 0], [0, 0], [23, 0], [0, 0], [0, -7], [0, 0], [0, 27], [0, 0], [12, 0], [0, 0], [-66, 0], [0, 0], [0, 81], [0, 0], [0, -20], [0, 0], [-172, 0], [0, 0], [89, 0], [0, 0], [0, 50], [0, 0], [0, -1], [0, 0], [-128, 0], [0, 0], [28, 0], [0, 0], [0, 60], [0, 0], [0, -79], [0, 0], [-108, 0], [0, 0], [-202, 0], [0, 0], [0, 149], [0, 0], [0, -69], [0, 0], [-408, 0], [0, 0], [57, 0], [0, 0], [0, -66], [0, 0], [0, 345], [0, 0], [-84, 0], [0, 0], [-324, 0], [0, 0], [0, 161], [0, 0], [0, -149], [0, 0], [-460, 0], [0, 0], [324, 0], [0, 0], [0, 101], [0, 0], [0, -172], [0, 0], [700, 0], [0, 0], [418, 0], [0, 0], [0, 89], [0, 0], [0, 140], [0, 0], [744, 0], [0, 0], [421, 0], [0, 0], [0, -339], [0, 0], [0, 198], [0, 0], [4, 0], [0, 0], [82, 0], [0, 0], [0, -540], [0, 0], [0, -128], [0, 0], [972, 0], [0, 0], [-1122, 0], [0, 0], [0, -161], [0, 0]]}