# Stored data for newform 384.3.b.a, downloaded from the LMFDB on 19 April 2024.
{"label": "384.3.b.a", "space_label": "384.3.b", "level": 384, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 68769808768, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1025531765736441909, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [16, 0, 1]]], "qexp_display": "q+\\zeta_{12}q^{3}+\\zeta_{12}^{3}q^{5}+\\zeta_{12}^{2}q^{7}+3q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "b", "char_is_real": true, "Nk2": 3456, "analytic_conductor": 10.4632421514354, "hecke_ring_index": 64, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [384, 2, [127, 133, 257], [1, 1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [319], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[2, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.715", "prec": 17}, {"__RealLiteral__": 0, "data": "0.982", "prec": 17}, {"__RealLiteral__": 0, "data": "110.275", "prec": 24}, {"__RealLiteral__": 0, "data": "61.986", "prec": 20}, {"__RealLiteral__": 0, "data": "4054.239", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -328, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 0, 0, 440, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -504, 0, 0, 0, 0, 0, 0, 0, -292, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 0, 0, 676, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 0, 0, 632, 0, 0, 0, 0, 0, 0, 0, -912, 0, 0, 0, 0, 0, 0, 0, -504, 0, 0, 0, 0, 0, 0, 0, -704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1656, 0, 0, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 0, 0, 328, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 0, 0, 0, 284, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 0, 0, 1392, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, -648, 0, 0, 0, 0, 0, 0, 0, 1336, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -1224, 0, 0, 0, 0, 0, 0, 0, 1864, 0, 0, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, -1472, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, -3384, 0, 0, 0, 0, 0, 0, 0, -4796, 0, 0, 0, 0, 0, 0, 0, -1104, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, -864, 0, 0, 0, 0, 0, 0, 0, 1224, 0, 0, 0, 0, 0, 0, 0, 2888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4104, 0, 0, 0, 0, 0, 0, 0, -584, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -4104, 0, 0, 0, 0, 0, 0, 0, -1276, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 2232, 0, 0, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, -984, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 0, 0, -2888, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 0, 0, -8064, 0, 0, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 2240, 0, 0, 0, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 2680, 0, 0, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1512, 0, 0, 0, 0, 0, 0, 0, -2232, 0, 0, 0, 0, 0, 0, 0, -5184, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 3300, 0, 0, 0, 0, 0, 0, 0, -2448, 0, 0, 0, 0, 0, 0, 0, 1224, 0, 0, 0, 0, 0, 0, 0, 832, 0, 0, 0, 0, 0, 0, 0, 1320, 0, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 0, 0, 0, 4416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, 0, 0, -3648, 0, 0, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 0, 0, 1080, 0, 0, 0, 0, 0, 0, 0, -2696, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -5564, 0, 0, 0, 0, 0, 0, 0, 2592, 0, 0, 0, 0, 0, 0, 0, 6840, 0, 0, 0, 0, 0, 0, 0, -3008, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 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, 4, 2, -1, 2, 0], [1, 1, 8, 2, 1, 2, 0], [1, 1, 8, 4, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 4, "minimal_twist": "384.3.b.a", "char_is_minimal": true, "conrey_index": 319, "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, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [-18, 0, 0, 0], [0, 0, 0, 0], [0, -12, 0, 0], [0, 0, 0, 0], [0, 0, 0, 3], [0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 0, 0], [9, 0, 0, 0], [0, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 7, 0], [0, 0, 0, 0], [12, 0, 0, 0], [0, 0, 0, 0], [0, -16, 0, 0], [0, 0, 0, 0], [0, 0, 0, -18], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [18, 0, 0, 0], [0, 0, 0, 0], [0, 36, 0, 0], [0, 0, 0, 0], [0, 0, 0, 3], [0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, -18, 0, 0], [0, 0, 0, 0], [0, 0, 0, 11], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [-36, 0, 0, 0], [0, 0, 0, 0], [0, 36, 0, 0], [0, 0, 0, 0], [0, 0, 0, -18], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -12, 0, 0], [0, 0, 0, 0], [0, 0, 0, 18], [0, 0, 0, 0], [0, 0, -6, 0], [0, 0, 0, 0], [-82, 0, 0, 0], [0, 0, 0, 0], [0, 9, 0, 0], [0, 0, 0, 0], [0, 0, 0, 12], [0, 0, 0, 0], [0, 0, -9, 0], [0, 0, 0, 0], [9, 0, 0, 0], [0, 0, 0, 0], [0, -76, 0, 0], [0, 0, 0, 0], [0, 0, 0, -18], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [126, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 21], [0, 0, 0, 0], [0, 0, -12, 0], [0, 0, 0, 0], [110, 0, 0, 0], [0, 0, 0, 0], [0, 12, 0, 0], [0, 0, 0, 0]]}