# Stored data for newform 384.4.f.d, downloaded from the LMFDB on 25 April 2024. {"label": "384.4.f.d", "space_label": "384.4.f", "level": 384, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13511142546604416, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 2285816296354542392, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-32, 0, 1]], [23, [-144, 1]]], "qexp_display": "q+(\\zeta_{8}-2\\zeta_{8}^{2})q^{3}-2\\zeta_{8}^{2}q^{5}-2\\zeta_{8}^{3}q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 24, "char_orbit_label": "f", "char_is_real": true, "Nk2": 6144, "analytic_conductor": 22.656733442204395, "hecke_ring_index": 72, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.757", "prec": 17}, "analytic_rank_proved": true, "char_values": [384, 2, [127, 133, 257], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [191], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 3], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.864", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "123.169", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4904.628", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 576, 0, -372, 0, 0, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 220, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 2880, 0, -712, 0, 0, 0, 0, 0, 0, 0, -2268, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 576, 0, 2600, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, -3456, 0, 1724, 0, 0, 0, 0, 0, 0, 0, -3888, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, -8640, 0, 128, 0, 0, 0, 0, 0, 0, 0, 5184, 0, 0, 0, 0, 0, -8736, 0, 0, 0, 0, 0, 0, 0, -9792, 0, -11948, 0, 0, 0, 0, 0, 0, 0, -4968, 0, 0, 0, 0, 0, -6048, 0, 0, 0, 0, 0, 0, 0, -8064, 0, 13528, 0, 0, 0, 0, 0, 0, 0, 13392, 0, 0, 0, 0, 0, 5184, 0, 0, 0, 0, 0, 0, 0, -5184, 0, -14976, 0, 0, 0, 0, 0, 0, 0, -3348, 0, 0, 0, 0, 0, -8640, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 9368, 0, 0, 0, 0, 0, 0, 0, 5256, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 5184, 0, -11648, 0, 0, 0, 0, 0, 0, 0, -20736, 0, 0, 0, 0, 0, 22464, 0, 0, 0, 0, 0, 0, 0, 20736, 0, 9284, 0, 0, 0, 0, 0, 0, 0, 16200, 0, 0, 0, 0, 0, -12192, 0, 0, 0, 0, 0, 0, 0, 31680, 0, -2152, 0, 0, 0, 0, 0, 0, 0, -19944, 0, 0, 0, 0, 0, 14688, 0, 0, 0, 0, 0, 0, 0, 17856, 0, 44344, 0, 0, 0, 0, 0, 0, 0, 13824, 0, 0, 0, 0, 0, 38880, 0, 0, 0, 0, 0, 0, 0, 16704, 0, -24844, 0, 0, 0, 0, 0, 0, 0, -31104, 0, 0, 0, 0, 0, -20928, 0, 0, 0, 0, 0, 0, 0, -1152, 0, -11520, 0, 0, 0, 0, 0, 0, 0, 31608, 0, 0, 0, 0, 0, 5184, 0, 0, 0, 0, 0, 0, 0, 8640, 0, -2456, 0, 0, 0, 0, 0, 0, 0, -16848, 0, 0, 0, 0, 0, 20736, 0, 0, 0, 0, 0, 0, 0, 11520, 0, 10216, 0, 0, 0, 0, 0, 0, 0, 1980, 0, 0, 0, 0, 0, -41376, 0, 0, 0, 0, 0, 0, 0, -27648, 0, -34136, 0, 0, 0, 0, 0, 0, 0, 14976, 0, 0, 0, 0, 0, -9504, 0, 0, 0, 0, 0, 0, 0, -20736, 0, 20736, 0, 0, 0, 0, 0, 0, 0, 47088, 0, 0, 0, 0, 0, 17280, 0, 0, 0, 0, 0, 0, 0, -78912, 0, -16256, 0, 0, 0, 0, 0, 0, 0, -3888, 0, 0, 0, 0, 0, -53664, 0, 0, 0, 0, 0, 0, 0, -44928, 0, 34276, 0, 0, 0, 0, 0, 0, 0, -29448, 0, 0, 0, 0, 0, -38880, 0, 0, 0, 0, 0, 0, 0, 576, 0, -65664, 0, 0, 0, 0, 0, 0, 0, -25920, 0, 0, 0, 0, 0, 31104, 0, 0, 0, 0, 0, 0, 0, -53568, 0, -15112, 0, 0, 0, 0, 0, 0, 0, 41472, 0, 0, 0, 0, 0, -29472, 0, 0, 0, 0, 0, 0, 0, -6336, 0, 44920, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, -20736, 0, 0, 0, 0, 0, 0, 0, -58752, 0, 18596, 0, 0, 0, 0, 0, 0, 0, -60912, 0, 0, 0, 0, 0, 25920, 0, 0, 0, 0, 0, 0, 0, 40896, 0, 49680, 0, 0, 0, 0, 0, 0, 0, -6408, 0, 0, 0, 0, 0, -62208, 0, 0, 0, 0, 0, 0, 0, 60480, 0, -16856, 0, 0, 0, 0, 0, 0, 0, 2376, 0, 0, 0, 0, 0, 26784, 0, 0, 0, 0, 0, 0, 0, -22464, 0, 62208, 0, 0, 0, 0, 0, 0, 0, 55296, 0, 0, 0, 0, 0, 98496, 0, 0, 0, 0, 0, 0, 0, 79488, 0, -24192, 0, 0, 0, 0, 0, 0, 0, -67068, 0, 0, 0, 0, 0, 5280, 0, 0, 0, 0, 0, 0, 0, -30528, 0, -55168, 0, 0, 0, 0, 0, 0, 0, -53784, 0, 0, 0, 0, 0, 51840, 0, 0, 0, 0, 0, 0, 0, 119232, 0, -83240, 0, 0, 0, 0, 0, 0, 0, 20736, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, 158976, 0, 145152, 0, 0, 0, 0, 0, 0, 0, 88128, 0, 0, 0, 0, 0, -3360, 0, 0, 0, 0, 0, 0, 0, 62784, 0, -23328, 0, 0, 0, 0, 0, 0, 0, -33480, 0, 0, 0, 0, 0, 85536, 0, 0, 0, 0, 0, 0, 0, 35136, 0, -97428, 0, 0, 0, 0, 0, 0, 0, 43632, 0, 0, 0, 0, 0, 5184, 0, 0, 0, 0, 0, 0, 0, -125568, 0, -71552, 0, 0, 0, 0, 0, 0, 0, 23400, 0, 0, 0, 0, 0, 12000, 0, 0, 0, 0, 0, 0, 0, 126144, 0, 178560, 0, 0, 0, 0, 0, 0, 0, 124416, 0, 0, 0, 0, 0, -46656, 0, 0, 0, 0, 0, 0, 0, 73728, 0, -52560, 0, 0, 0, 0, 0, 0, 0, -173232, 0, 0, 0, 0, 0, 36288, 0, 0, 0, 0, 0, 0, 0, -34560, 0, -33848, 0, 0, 0, 0, 0, 0, 0, 51840, 0, 0, 0, 0, 0, 79584, 0, 0, 0, 0, 0, 0, 0, -13824, 0, -75524, 0, 0, 0, 0, 0, 0, 0, 15552, 0, 0, 0, 0, 0, -80352, 0, 0, 0, 0, 0, 0, 0, -157248, 0, -39296, 0, 0, 0, 0, 0, 0, 0, 119664, 0, 0, 0, 0, 0, -38880, 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, 8, 2, 1, 2, 0], [1, 1, 12, 2, 1, 2, 0], [1, 1, 24, 6, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "384.4.f.c", "char_is_minimal": true, "conrey_index": 191, "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 1, -2, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [9, 0, 0, 3], [0, 0, 0, 0], [0, -10, 5, 0], [0, 0, 0, 0], [0, -24, 12, 0], [0, 0, 0, 0], [24, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [0, 0, -9, 0], [0, 0, 0, 0], [0, -24, -6, 0], [0, 0, 0, 0], [144, 0, 0, 0], [0, 0, 0, 0], [-93, 0, 0, 0], [0, 0, 0, 0], [0, 45, -9, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, -26], [0, 0, 0, 0], [90, 0, 0, -15], [0, 0, 0, 0], [0, -32, 16, 0], [0, 0, 0, 0], [0, 24, -12, 0], [0, 0, 0, 0], [216, 0, 0, -36], [0, 0, 0, 0], [0, 0, 0, 36], [0, 0, 0, 0], [0, 0, 81, 0], [0, 0, 0, 0], [0, 48, -42, 0], [0, 0, 0, 0], [576, 0, 0, 0], [0, 0, 0, 0], [55, 0, 0, 0], [0, 0, 0, 0], [0, -72, -18, 0], [0, 0, 0, 0], [0, 0, 182, 0], [0, 0, 0, 0], [0, 0, 0, -20], [0, 0, 0, 0], [108, 0, 0, 9], [0, 0, 0, 0], [0, 138, -69, 0], [0, 0, 0, 0], [0, 168, -84, 0], [0, 0, 0, 0], [432, 0, 0, -18], [0, 0, 0, 0], [0, 0, 0, -48], [0, 0, 0, 0], [0, 0, -279, 0], [0, 0, 0, 0], [0, 144, -288, 0], [0, 0, 0, 0], [720, 0, 0, 0], [0, 0, 0, 0], [-178, 0, 0, 0], [0, 0, 0, 0], [0, -93, 186, 0], [0, 0, 0, 0], [0, 0, 180, 0], [0, 0, 0, 0], [0, 0, 0, -114], [0, 0, 0, 0], [-567, 0, 0, 54], [0, 0, 0, 0], [0, -146, 73, 0], [0, 0, 0, 0], [0, -96, 48, 0], [0, 0, 0, 0], [24, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, -102], [0, 0, 0, 0], [0, 0, 432, 0], [0, 0, 0, 0], [0, -312, -78, 0], [0, 0, 0, 0], [144, 0, 0, 0], [0, 0, 0, 0], [650, 0, 0, 0], [0, 0, 0, 0], [0, -90, -225, 0], [0, 0, 0, 0]]}