# Stored data for newform 576.3.e.d, downloaded from the LMFDB on 16 April 2024.
{"label": "576.3.e.d", "space_label": "576.3.e", "level": 576, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13511073810350656, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 2281310102455726162, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [2, 0, 1]], [7, [0, 1]]], "qexp_display": "q+\\beta q^{5}-24q^{13}-23\\beta q^{17}+23q^{25}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 5184, "analytic_conductor": 15.694863227153101, "hecke_ring_index": 1, "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": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [576, 2, [127, 325, 65], [2, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [449], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.850", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21.841", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "288.530", "prec": 24}], "related_objects": [], "self_twist_discs": [-4], "cm_discs": [-4], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 0, 0, 0], "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 242, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 340, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 814, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1538, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -722, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -580, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -476, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 476, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1058, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 388, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 958, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2356, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -772, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4508, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -764, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1056, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1678, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 820, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -868, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 860, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1922, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3700, 0, 0, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, -4], [1, 1, 3, 2, -1, 2, 0], [1, 1, 12, 2, 1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "288.3.e.c", "char_is_minimal": false, "conrey_index": 449, "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], [0, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-24, 0], [0, 0], [0, 0], [0, 0], [0, -23], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [23, 0], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-70, 0], [0, 0], [0, 0], [0, 0], [0, -49], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-49, 0], [0, 0], [0, 0], [0, 0], [0, -73], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [22, 0], [0, 0], [0, 0], [0, 0], [0, -24], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-96, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [46, 0], [0, 0], [0, 0], [0, 0], [0, 119], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-144, 0], [0, 0], [0, 0], [0, 0]]}