# Stored data for newform 384.3.h.d, downloaded from the LMFDB on 25 April 2024.
{"label": "384.3.h.d", "space_label": "384.3.h", "level": 384, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13511279968780672, "dim": 2, "is_polredabs": true, "nf_label": "2.2.24.1", "trace_hash": 1435954879408079578, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-96, 0, 1]], [11, [-10, 1]]], "qexp_display": "q+3q^{3}+\\beta q^{5}-\\beta q^{7}+9q^{9}+10q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 24, "char_orbit_label": "h", "char_is_real": true, "Nk2": 3456, "analytic_conductor": 10.4632421514354, "hecke_ring_index": 4, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.756", "prec": 17}, "analytic_rank_proved": true, "char_values": [384, 2, [127, 133, 257], [2, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [65], "field_disc": 24, "field_disc_factorization": [[2, 3], [3, 1]], "field_poly": [-6, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.865", "prec": 17}, {"__RealLiteral__": 0, "data": "0.145", "prec": 17}, {"__RealLiteral__": 0, "data": "21.806", "prec": 20}, {"__RealLiteral__": 0, "data": "3.491", "prec": 17}, {"__RealLiteral__": 0, "data": "285.241", "prec": 24}], "related_objects": [], "self_twist_discs": [-24], "cm_discs": [-24], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 6, 0, 0], "traces": [0, 2, 0, 6, 0, 0, 0, 0, 0, 18, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 142, 0, 54, 0, 0, 0, 0, 0, 60, 0, -192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 426, 0, 0, 0, 0, 0, 162, 0, -268, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -380, 0, 180, 0, 0, 0, 0, 0, -576, 0, 172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 0, 0, 0, -500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 282, 0, 0, 0, 0, 0, 0, 0, -960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 338, 0, 0, 0, 0, 0, 0, 0, -60, 0, 460, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -580, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 960, 0, -300, 0, 0, 0, 0, 0, 1278, 0, 692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 764, 0, 486, 0, 0, 0, 0, 0, -804, 0, -940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1420, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 578, 0, -1140, 0, 0, 0, 0, 0, 540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1060, 0, -1728, 0, 0, 0, 0, 0, 516, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380, 0, 0, 0, 0, 0, 0, 0, 0, 0, 212, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 722, 0, -126, 0, 0, 0, 0, 0, 0, 0, -960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1920, 0, 0, 0, 0, 0, 0, 0, -1500, 0, 2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1436, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1460, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1340, 0, -1728, 0, 0, 0, 0, 0, 846, 0, -172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1060, 0, 0, 0, 0, 0, 0, 0, -2880, 0, 1268, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1344, 0, 1014, 0, 0, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1058, 0, -180, 0, 0, 0, 0, 0, 1380, 0, 940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -652, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -580, 0, -1740, 0, 0, 0, 0, 0, 0, 0, -1748, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2396, 0, 0, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5282, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -200, 0, 2880, 0, 0, 0, 0, 0, -900, 0, -1460, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -380, 0, 3834, 0, 0, 0, 0, 0, 2076, 0, -2668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4032, 0, 2292, 0, 0, 0, 0, 0, 1458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1344, 0, -2412, 0, 0, 0, 0, 0, -2820, 0, -960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1724, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 0, 0, -1000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4260, 0, -3092, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6720, 0, 1734, 0, 0, 0, 0, 0, -3420, 0, -8832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2112, 0, 1620, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2980, 0, -3180, 0, 0, 0, 0, 0, -5184, 0, -2612, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2878, 0, 1548, 0, 0, 0, 0, 0, 0, 0, 3860, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6720, 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, 24, 8, -1, 2, -24], [1, 1, 8, 4, -1, 2, 0], [1, 1, 12, 2, 1, 2, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "384.3.h.a", "char_is_minimal": true, "conrey_index": 65, "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], [3, 0], [0, 0], [0, 1], [0, 0], [0, -1], [0, 0], [9, 0], [0, 0], [10, 0], [0, 0], [0, 0], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -3], [0, 0], [0, 0], [0, 0], [71, 0], [0, 0], [27, 0], [0, 0], [0, -3], [0, 0], [0, -5], [0, 0], [30, 0], [0, 0], [-96, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 9], [0, 0], [0, 0], [0, 0], [47, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [0, 10], [0, 0], [0, 0], [0, 0], [-10, 0], [0, 0], [0, 0], [0, 0], [0, -9], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-50, 0], [0, 0], [213, 0], [0, 0], [0, -10], [0, 0], [0, 15], [0, 0], [81, 0], [0, 0], [-134, 0], [0, 0], [0, 0], [0, 0], [0, -9], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -15], [0, 0], [0, 0], [0, 0], [-190, 0], [0, 0], [90, 0], [0, 0]]}