# Stored data for newform 384.4.d.d, downloaded from the LMFDB on 21 May 2025. {"Nk2": 6144, "analytic_conductor": 22.656733442204395, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 8, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": 1, "char_values": [384, 2, [127, 133, 257], [2, 1, 2]], "cm_discs": [], "conrey_index": 193, "dim": 4, "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 8, "has_non_self_twist": 1, "hecke_cutters": [[5, [8, 0, 1]], [7, [-200, 0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511005107650944, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 8, "hecke_ring_index_factorization": [[2, 3]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "384.4.d.d", "level": 384, "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": false, "level_primes": [2, 3], "level_radical": 6, "minimal_twist": "384.4.d.d", "nf_label": "4.0.256.1", "prim_orbit_index": 2, "qexp_display": "q+3\\beta_1 q^{3}+\\beta_{2} q^{5}-5\\beta_{3} q^{7}-9 q^{9}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "384.4.d", "trace_display": [0, 0, 0, 0], "trace_hash": 829055651682029678, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.787", "prec": 17}, {"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "122.428", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4980.074", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.759", "prec": 17}, "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, 0, 0, 468, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, -572, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, 448, 0, 0, 0, 0, 0, 0, 0, -1352, 0, 0, 0, 0, 0, 0, 0, 324, 0, 0, 0, 0, 0, 0, 0, -936, 0, 0, 0, 0, 0, 0, 0, -712, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 5512, 0, 0, 0, 0, 0, 0, 0, 3724, 0, 0, 0, 0, 0, 0, 0, -3024, 0, 0, 0, 0, 0, 0, 0, -11416, 0, 0, 0, 0, 0, 0, 0, 2272, 0, 0, 0, 0, 0, 0, 0, 1224, 0, 0, 0, 0, 0, 0, 0, 3520, 0, 0, 0, 0, 0, 0, 0, 2516, 0, 0, 0, 0, 0, 0, 0, -4368, 0, 0, 0, 0, 0, 0, 0, 3072, 0, 0, 0, 0, 0, 0, 0, -9960, 0, 0, 0, 0, 0, 0, 0, 7536, 0, 0, 0, 0, 0, 0, 0, 4160, 0, 0, 0, 0, 0, 0, 0, 6240, 0, 0, 0, 0, 0, 0, 0, -4212, 0, 0, 0, 0, 0, 0, 0, -11304, 0, 0, 0, 0, 0, 0, 0, -13416, 0, 0, 0, 0, 0, 0, 0, 12432, 0, 0, 0, 0, 0, 0, 0, 27528, 0, 0, 0, 0, 0, 0, 0, 7712, 0, 0, 0, 0, 0, 0, 0, -6720, 0, 0, 0, 0, 0, 0, 0, -25064, 0, 0, 0, 0, 0, 0, 0, -15028, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, 8320, 0, 0, 0, 0, 0, 0, 0, 12424, 0, 0, 0, 0, 0, 0, 0, -16848, 0, 0, 0, 0, 0, 0, 0, -19520, 0, 0, 0, 0, 0, 0, 0, 17192, 0, 0, 0, 0, 0, 0, 0, 2112, 0, 0, 0, 0, 0, 0, 0, 26952, 0, 0, 0, 0, 0, 0, 0, 16620, 0, 0, 0, 0, 0, 0, 0, -936, 0, 0, 0, 0, 0, 0, 0, -31808, 0, 0, 0, 0, 0, 0, 0, 3200, 0, 0, 0, 0, 0, 0, 0, 18864, 0, 0, 0, 0, 0, 0, 0, 14328, 0, 0, 0, 0, 0, 0, 0, -20504, 0, 0, 0, 0, 0, 0, 0, -23568, 0, 0, 0, 0, 0, 0, 0, -15912, 0, 0, 0, 0, 0, 0, 0, -25096, 0, 0, 0, 0, 0, 0, 0, 5148, 0, 0, 0, 0, 0, 0, 0, 56760, 0, 0, 0, 0, 0, 0, 0, 25896, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, -20160, 0, 0, 0, 0, 0, 0, 0, -43008, 0, 0, 0, 0, 0, 0, 0, 35184, 0, 0, 0, 0, 0, 0, 0, -18880, 0, 0, 0, 0, 0, 0, 0, -2912, 0, 0, 0, 0, 0, 0, 0, -5616, 0, 0, 0, 0, 0, 0, 0, 2856, 0, 0, 0, 0, 0, 0, 0, -33180, 0, 0, 0, 0, 0, 0, 0, -15696, 0, 0, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, 0, 0, 44640, 0, 0, 0, 0, 0, 0, 0, 8160, 0, 0, 0, 0, 0, 0, 0, 55464, 0, 0, 0, 0, 0, 0, 0, 37544, 0, 0, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, 0, 0, -37624, 0, 0, 0, 0, 0, 0, 0, 5048, 0, 0, 0, 0, 0, 0, 0, -34080, 0, 0, 0, 0, 0, 0, 0, -67496, 0, 0, 0, 0, 0, 0, 0, 50756, 0, 0, 0, 0, 0, 0, 0, -11088, 0, 0, 0, 0, 0, 0, 0, 71032, 0, 0, 0, 0, 0, 0, 0, -29120, 0, 0, 0, 0, 0, 0, 0, 12168, 0, 0, 0, 0, 0, 0, 0, -8320, 0, 0, 0, 0, 0, 0, 0, -48328, 0, 0, 0, 0, 0, 0, 0, 1872, 0, 0, 0, 0, 0, 0, 0, -107968, 0, 0, 0, 0, 0, 0, 0, -3536, 0, 0, 0, 0, 0, 0, 0, -11712, 0, 0, 0, 0, 0, 0, 0, 27456, 0, 0, 0, 0, 0, 0, 0, 106720, 0, 0, 0, 0, 0, 0, 0, -2916, 0, 0, 0, 0, 0, 0, 0, 50240, 0, 0, 0, 0, 0, 0, 0, -17056, 0, 0, 0, 0, 0, 0, 0, 76752, 0, 0, 0, 0, 0, 0, 0, 63336, 0, 0, 0, 0, 0, 0, 0, -66664, 0, 0, 0, 0, 0, 0, 0, -46080, 0, 0, 0, 0, 0, 0, 0, -39936, 0, 0, 0, 0, 0, 0, 0, -116480, 0, 0, 0, 0, 0, 0, 0, 8424, 0, 0, 0, 0, 0, 0, 0, 36968, 0, 0, 0, 0, 0, 0, 0, 52416, 0, 0, 0, 0, 0, 0, 0, -28080, 0, 0, 0, 0, 0, 0, 0, 19448, 0, 0, 0, 0, 0, 0, 0, -63756, 0, 0, 0, 0, 0, 0, 0, 103152, 0, 0, 0, 0, 0, 0, 0, 100776, 0, 0, 0, 0, 0, 0, 0, -16352, 0, 0, 0, 0, 0, 0, 0, 6408, 0, 0, 0, 0, 0, 0, 0, -171320, 0, 0, 0, 0, 0, 0, 0, 101280, 0, 0, 0, 0, 0, 0, 0, -29568, 0, 0, 0, 0, 0, 0, 0, -22592, 0, 0, 0, 0, 0, 0, 0, 82880, 0, 0, 0, 0, 0, 0, 0, -59280, 0, 0, 0, 0, 0, 0, 0, -54600, 0, 0, 0, 0, 0, 0, 0, -28392, 0, 0, 0, 0, 0, 0, 0, -4320, 0, 0, 0, 0, 0, 0, 0, 187752, 0, 0, 0, 0, 0, 0, 0, -70492, 0, 0, 0, 0, 0, 0, 0, -21216, 0, 0, 0, 0, 0, 0, 0, -167560, 0, 0, 0, 0, 0, 0, 0, -30816, 0, 0, 0, 0, 0, 0, 0, -34896, 0, 0, 0, 0, 0, 0, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, -5], [0, 0, 0, 0], [-9, 0, 0, 0], [0, 0, 0, 0], [0, 20, 0, 0], [0, 0, 0, 0], [0, 0, -14, 0], [0, 0, 0, 0], [0, 0, 0, -3], [0, 0, 0, 0], [-34, 0, 0, 0], [0, 0, 0, 0], [0, -52, 0, 0], [0, 0, 0, 0], [0, 0, -15, 0], [0, 0, 0, 0], [0, 0, 0, -22], [0, 0, 0, 0], [117, 0, 0, 0], [0, 0, 0, 0], [0, -27, 0, 0], [0, 0, 0, 0], [0, 0, -71, 0], [0, 0, 0, 0], [0, 0, 0, -39], [0, 0, 0, 0], [-60, 0, 0, 0], [0, 0, 0, 0], [0, -40, 0, 0], [0, 0, 0, 0], [0, 0, -96, 0], [0, 0, 0, 0], [0, 0, 0, 42], [0, 0, 0, 0], [26, 0, 0, 0], [0, 0, 0, 0], [0, 252, 0, 0], [0, 0, 0, 0], [0, 0, -9, 0], [0, 0, 0, 0], [0, 0, 0, 122], [0, 0, 0, 0], [-143, 0, 0, 0], [0, 0, 0, 0], [0, -102, 0, 0], [0, 0, 0, 0], [0, 0, -241, 0], [0, 0, 0, 0], [0, 0, 0, -20], [0, 0, 0, 0], [156, 0, 0, 0], [0, 0, 0, 0], [0, 364, 0, 0], [0, 0, 0, 0], [0, 0, -260, 0], [0, 0, 0, 0], [0, 0, 0, 45], [0, 0, 0, 0], [112, 0, 0, 0], [0, 0, 0, 0], [0, -628, 0, 0], [0, 0, 0, 0], [0, 0, -66, 0], [0, 0, 0, 0], [0, 0, 0, 118], [0, 0, 0, 0], [-338, 0, 0, 0], [0, 0, 0, 0], [0, 351, 0, 0], [0, 0, 0, 0], [0, 0, -100, 0], [0, 0, 0, 0], [0, 0, 0, -279], [0, 0, 0, 0], [81, 0, 0, 0], [0, 0, 0, 0], [0, -1036, 0, 0], [0, 0, 0, 0], [0, 0, -34, 0], [0, 0, 0, 0], [0, 0, 0, 213], [0, 0, 0, 0], [-234, 0, 0, 0], [0, 0, 0, 0], [0, 560, 0, 0], [0, 0, 0, 0], [0, 0, -117, 0], [0, 0, 0, 0], [0, 0, 0, 52], [0, 0, 0, 0], [-178, 0, 0, 0], [0, 0, 0, 0], [0, -180, 0, 0], [0, 0, 0, 0]]}