# Stored data for newform 384.3.e.d, downloaded from the LMFDB on 24 April 2024.
{"label": "384.3.e.d", "space_label": "384.3.e", "level": 384, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13511073810350464, "dim": 8, "is_polredabs": true, "trace_hash": 1348472430202732502, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [-176, 368, -108, -4, 1]], [13, [7824, 256, -360, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+\\beta _{3}q^{5}+(1+\\beta _{2})q^{7}+(\\beta _{2}+\\cdots)q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 3456, "analytic_conductor": 10.4632421514354, "hecke_ring_index": 3072, "level_radical": 6, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [384, 2, [127, 133, 257], [2, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [257], "field_disc": 152812191744, "field_disc_factorization": [[2, 16], [3, 2], [509, 2]], "field_poly": [81, 0, 170, 0, 99, 0, 18, 0, 1], "hecke_ring_index_factorization": [[2, 10], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "7.448", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "306.425", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "18857.233", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 4, 0, 8], "traces": [0, 8, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, -24, 0, 16, 0, 0, 0, -40, 0, -44, 0, 0, 0, -56, 0, 8, 0, 0, 0, 32, 0, -104, 0, 0, 0, 136, 0, -80, 0, 0, 0, 72, 0, 176, 0, 0, 0, 192, 0, -40, 0, 0, 0, -160, 0, 264, 0, 0, 0, -280, 0, 80, 0, 0, 0, -80, 0, -348, 0, 0, 0, -408, 0, 72, 0, 0, 0, 192, 0, -368, 0, 0, 0, 336, 0, 160, 0, 0, 0, 96, 0, 432, 0, 0, 0, 488, 0, -80, 0, 0, 0, 160, 0, 472, 0, 0, 0, -576, 0, -176, 0, 0, 0, -8, 0, -544, 0, 0, 0, -376, 0, 88, 0, 0, 0, -192, 0, -752, 0, 0, 0, 904, 0, -416, 0, 0, 0, -144, 0, 780, 0, 0, 0, 808, 0, 32, 0, 0, 0, -512, 0, 912, 0, 0, 0, -632, 0, 272, 0, 0, 0, 88, 0, -904, 0, 0, 0, -1432, 0, -216, 0, 0, 0, 128, 0, -744, 0, 0, 0, 672, 0, 880, 0, 0, 0, -208, 0, 896, 0, 0, 0, 552, 0, 168, 0, 0, 0, 1248, 0, 672, 0, 0, 0, -1272, 0, -400, 0, 0, 0, 304, 0, -808, 0, 0, 0, -152, 0, -304, 0, 0, 0, -640, 0, -928, 0, 0, 0, 576, 0, -1184, 0, 0, 0, 112, 0, 724, 0, 0, 0, 1584, 0, 312, 0, 0, 0, -928, 0, 1120, 0, 0, 0, -496, 0, 272, 0, 0, 0, 144, 0, -816, 0, 0, 0, -920, 0, 256, 0, 0, 0, 160, 0, -664, 0, 0, 0, 1576, 0, 1648, 0, 0, 0, -184, 0, 728, 0, 0, 0, 96, 0, 56, 0, 0, 0, 1792, 0, 304, 0, 0, 0, -216, 0, -656, 0, 0, 0, -352, 0, -704, 0, 0, 0, -1024, 0, 40, 0, 0, 0, -864, 0, -776, 0, 0, 0, 40, 0, -1680, 0, 0, 0, -640, 0, 480, 0, 0, 0, -272, 0, -736, 0, 0, 0, -2240, 0, 568, 0, 0, 0, -1536, 0, 896, 0, 0, 0, 520, 0, 212, 0, 0, 0, -376, 0, -608, 0, 0, 0, 1408, 0, 192, 0, 0, 0, -952, 0, 2112, 0, 0, 0, 96, 0, 152, 0, 0, 0, 1344, 0, 216, 0, 0, 0, 1888, 0, -496, 0, 0, 0, 1296, 0, -1376, 0, 0, 0, 592, 0, -64, 0, 0, 0, 1920, 0, 456, 0, 0, 0, -704, 0, 640, 0, 0, 0, 1040, 0, -2704, 0, 0, 0, 992, 0, -768, 0, 0, 0, -792, 0, 1008, 0, 0, 0, -3168, 0, -176, 0, 0, 0, 1408, 0, 1808, 0, 0, 0, -1136, 0, 848, 0, 0, 0, -824, 0, 1200, 0, 0, 0, 1952, 0, 472, 0, 0, 0, -792, 0, 3120, 0, 0, 0, 480, 0, -1408, 0, 0, 0, -2424, 0, -1320, 0, 0, 0, 3264, 0, -928, 0, 0, 0, -1272, 0, -1168, 0, 0, 0, -1392, 0, 556, 0, 0, 0, 1456, 0, -232, 0, 0, 0, -1344, 0, 944, 0, 0, 0, -3160, 0, -4176, 0, 0, 0, -440, 0, -752, 0, 0, 0, 672, 0, -1320, 0, 0, 0, -3424, 0, -2184, 0, 0, 0, 1768, 0, 1328, 0, 0, 0, -144, 0, 1984, 0, 0, 0, 2928, 0, -992, 0, 0, 0, 960, 0, 1608, 0, 0, 0, 488, 0, 3392, 0, 0, 0, 320, 0, -1160, 0, 0, 0, -2880, 0, 1184, 0, 0, 0, 3168, 0, -1360, 0, 0, 0, 4800, 0, -688, 0, 0, 0, 1328, 0, 2840, 0, 0, 0, -1400, 0, -176, 0, 0, 0, -1696, 0, 2688, 0, 0, 0, -2840, 0, -3664, 0, 0, 0, 1784, 0, -2288, 0, 0, 0, -3640, 0, 1256, 0, 0, 0, -4896, 0, -2144, 0, 0, 0, 296, 0, 1584, 0, 0, 0, -976, 0, 1360, 0, 0, 0, 4320, 0, 1152, 0, 0, 0, 1888, 0, 2464, 0, 0, 0, -3136, 0, 3808, 0, 0, 0, 288, 0, -2892, 0, 0, 0, 1296, 0, -488, 0, 0, 0, 4704, 0, -1352, 0, 0, 0, 968, 0, -2016, 0, 0, 0, -1920, 0, 1616, 0, 0, 0, 4656, 0, 1088, 0, 0, 0, -96, 0, 1288, 0, 0, 0, 960, 0, -4448, 0, 0, 0, -2992, 0, -2760, 0, 0, 0, -3288, 0, -1536, 0, 0, 0, -3712, 0, -3312, 0, 0, 0, 4168, 0, 1840, 0, 0, 0, 2640, 0, 1296, 0, 0, 0, -1432, 0, -2488, 0, 0, 0, 2240, 0, 1696, 0, 0, 0, -5936, 0, 5632, 0, 0, 0, -912, 0, -736, 0, 0, 0, -3992, 0, 832, 0, 0, 0, 5536, 0, -2480, 0, 0, 0, -1912, 0, -2576, 0, 0, 0, 2400, 0, 3648, 0, 0, 0, 1920, 0, -1472, 0, 0, 0, -4032, 0, 2032, 0, 0, 0, -3032, 0, -4512, 0, 0, 0, 2256, 0, -2288, 0, 0, 0, 200, 0, 1992, 0, 0, 0, -4096, 0, -680, 0, 0, 0, 5568, 0, 1216, 0, 0, 0, -680, 0, 2864, 0, 0, 0, 5704, 0, 3976, 0, 0, 0, -448, 0, 2272, 0, 0, 0, 4616, 0, 5024, 0, 0, 0, -336, 0, -1596, 0, 0, 0, -2448, 0, -1552, 0, 0, 0, 4096, 0, -1296, 0, 0, 0, 4968, 0, -2288, 0, 0, 0, -1936, 0, 480, 0, 0, 0, -4704, 0, 224, 0, 0, 0, -4416, 0, 3664, 0, 0, 0, -2808, 0, -3472, 0, 0, 0, -3120, 0, -448, 0, 0, 0, -4856, 0, -2424, 0, 0, 0, -5056, 0, -1752, 0, 0, 0, -5640, 0, 2000, 0, 0, 0, 1600, 0, 136, 0, 0, 0, 5248, 0, -4208, 0, 0, 0, 3840, 0, -1040, 0, 0, 0, -7488, 0, 4016, 0, 0, 0, -2808, 0, -2480, 0, 0, 0, 6728, 0, 2528, 0, 0, 0, 5152, 0, -1000, 0, 0, 0, 3488, 0, -2896, 0, 0, 0, 3408, 0, 832, 0, 0, 0, 1448, 0, -984, 0, 0, 0, 2016, 0, -776, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "384.3.e.a", "char_is_minimal": true, "conrey_index": 257, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -1, 2, 1, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 0, -2, -2, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, -2, 0, 0, -2, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, 1, 2, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -5, -2, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 1, 2, 4, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 6, 0, 3, 0, 2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 4, -1, 0, 0, -2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, -2, 2, 1, -3, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, 0, 8, 5, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 9, -4, 0, 0, -3, -1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-13, 1, 0, -2, 5, 1, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 6, 0, -6, -6, -2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [17, 1, 2, 0, 0, -2, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-10, 4, -2, 3, 6, 0, 4, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 6, 0, 0, -2, 2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 9, 2, 0, 0, 3, -5, 3], [0, 0, 0, 0, 0, 0, 0, 0], [23, -1, 0, -4, -5, -1, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [4, -12, 0, 1, -4, 4, -4, -4], [0, 0, 0, 0, 0, 0, 0, 0], [22, 4, -2, 0, 0, -2, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -4, -1, -6, 6, 0, 4, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, 0, 0, 8, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-13, -11, 4, 0, 0, 1, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0], [31, 0, 3, 4, 8, 4, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, -12, 0, 2, -6, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-37, 1, 8, 0, 0, 4, -3, 4], [0, 0, 0, 0, 0, 0, 0, 0], [8, 2, -6, 0, 6, -6, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 6, 0, 4, -10, -4, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -12, 4, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-43, 0, -10, 0, -9, -3, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 12, 0, -2, -12, -4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-41, -16, 3, 0, 0, 2, 4, 2], [0, 0, 0, 0, 0, 0, 0, 0], [10, -3, 0, 4, 8, -5, -1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [2, -6, 0, -8, 5, 1, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [16, 8, 16, 0, 0, 8, -8, 8], [0, 0, 0, 0, 0, 0, 0, 0], [-48, 1, 1, -2, 5, -5, -3, 7], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 15, 0, 16, -8, 1, 5, -1], [0, 0, 0, 0, 0, 0, 0, 0], [40, 2, -10, 0, 0, 2, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [27, -11, 4, -5, 8, 1, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0], [8, -24, 0, -4, -16, -2, -8, 2], [0, 0, 0, 0, 0, 0, 0, 0], [5, 13, -2, 0, 0, -5, -1, -5], [0, 0, 0, 0, 0, 0, 0, 0], [55, -3, -2, 4, -10, 4, -1, 4], [0, 0, 0, 0, 0, 0, 0, 0]]}