# Stored data for newform 576.2.i.n, downloaded from the LMFDB on 18 April 2024.
{"label": "576.2.i.n", "space_label": "576.2.i", "level": 576, "weight": 2, "hecke_orbit": 14, "hecke_orbit_code": 58547344945185344, "dim": 8, "is_polredabs": true, "nf_label": "8.0.170772624.1", "trace_hash": 463084763778274688, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [64, -8, 9, 1, 1]], [7, [11664, 0, 2916, 0, 621, 0, 27, 0, 1]]], "qexp_display": "q+(-\\beta _{1}+\\beta _{5})q^{3}+(-1+\\beta _{4}-\\beta _{7})q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "i", "char_is_real": false, "Nk2": 2304, "analytic_conductor": 4.59938315642575, "hecke_ring_index": 36, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [576, 3, [127, 325, 65], [3, 3, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [193, 385], "field_disc": 170772624, "field_disc_factorization": [[2, 4], [3, 6], [11, 4]], "field_poly": [16, -24, 20, -12, 6, -6, 5, -3, 1], "hecke_ring_index_factorization": [[2, 2], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.043", "prec": 17}, {"__RealLiteral__": 0, "data": "7.365", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "435.539", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "46685.926", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, -2, 0], "traces": [0, 8, 0, 0, 0, -2, 0, 0, 0, -6, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, -30, 0, 0, 0, -14, 0, 0, 0, -10, 0, 0, 0, 12, 0, 0, 0, -32, 0, 0, 0, -4, 0, 0, 0, 66, 0, 0, 0, -26, 0, 0, 0, 32, 0, 0, 0, 6, 0, 0, 0, 26, 0, 0, 0, -30, 0, 0, 0, 6, 0, 0, 0, 60, 0, 0, 0, -18, 0, 0, 0, -30, 0, 0, 0, 32, 0, 0, 0, 56, 0, 0, 0, -90, 0, 0, 0, -36, 0, 0, 0, -26, 0, 0, 0, 12, 0, 0, 0, -48, 0, 0, 0, -58, 0, 0, 0, 66, 0, 0, 0, -28, 0, 0, 0, 60, 0, 0, 0, -12, 0, 0, 0, 36, 0, 0, 0, 4, 0, 0, 0, -30, 0, 0, 0, 76, 0, 0, 0, -58, 0, 0, 0, 30, 0, 0, 0, 22, 0, 0, 0, 108, 0, 0, 0, -84, 0, 0, 0, 10, 0, 0, 0, 10, 0, 0, 0, 30, 0, 0, 0, -72, 0, 0, 0, 8, 0, 0, 0, 126, 0, 0, 0, -4, 0, 0, 0, 40, 0, 0, 0, -30, 0, 0, 0, -2, 0, 0, 0, -54, 0, 0, 0, 48, 0, 0, 0, -36, 0, 0, 0, 36, 0, 0, 0, -12, 0, 0, 0, -6, 0, 0, 0, -92, 0, 0, 0, -54, 0, 0, 0, -24, 0, 0, 0, -112, 0, 0, 0, -6, 0, 0, 0, 36, 0, 0, 0, -20, 0, 0, 0, -18, 0, 0, 0, -8, 0, 0, 0, 16, 0, 0, 0, -36, 0, 0, 0, 18, 0, 0, 0, -46, 0, 0, 0, -24, 0, 0, 0, -68, 0, 0, 0, -70, 0, 0, 0, 108, 0, 0, 0, 18, 0, 0, 0, 172, 0, 0, 0, -6, 0, 0, 0, -8, 0, 0, 0, 22, 0, 0, 0, 6, 0, 0, 0, 24, 0, 0, 0, -54, 0, 0, 0, 24, 0, 0, 0, 36, 0, 0, 0, 252, 0, 0, 0, -114, 0, 0, 0, -58, 0, 0, 0, 8, 0, 0, 0, 84, 0, 0, 0, 28, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 36, 0, 0, 0, 12, 0, 0, 0, 90, 0, 0, 0, 26, 0, 0, 0, -90, 0, 0, 0, 32, 0, 0, 0, -20, 0, 0, 0, -114, 0, 0, 0, 96, 0, 0, 0, -252, 0, 0, 0, -66, 0, 0, 0, -78, 0, 0, 0, 26, 0, 0, 0, -144, 0, 0, 0, -76, 0, 0, 0, 36, 0, 0, 0, 198, 0, 0, 0, -80, 0, 0, 0, -76, 0, 0, 0, 30, 0, 0, 0, 12, 0, 0, 0, -82, 0, 0, 0, 126, 0, 0, 0, 252, 0, 0, 0, 72, 0, 0, 0, -24, 0, 0, 0, -24, 0, 0, 0, 36, 0, 0, 0, -96, 0, 0, 0, 28, 0, 0, 0, -108, 0, 0, 0, 90, 0, 0, 0, -172, 0, 0, 0, 50, 0, 0, 0, 72, 0, 0, 0, -18, 0, 0, 0, 76, 0, 0, 0, 120, 0, 0, 0, 38, 0, 0, 0, 6, 0, 0, 0, -96, 0, 0, 0, -24, 0, 0, 0, -120, 0, 0, 0, -138, 0, 0, 0, -18, 0, 0, 0, 104, 0, 0, 0, 6, 0, 0, 0, -62, 0, 0, 0, 136, 0, 0, 0, 138, 0, 0, 0, 76, 0, 0, 0, -90, 0, 0, 0, 78, 0, 0, 0, -144, 0, 0, 0, 88, 0, 0, 0, 156, 0, 0, 0, 80, 0, 0, 0, 184, 0, 0, 0, 114, 0, 0, 0, -16, 0, 0, 0, 128, 0, 0, 0, -18, 0, 0, 0, 88, 0, 0, 0, -16, 0, 0, 0, -102, 0, 0, 0, -60, 0, 0, 0, -32, 0, 0, 0, 84, 0, 0, 0, -216, 0, 0, 0, 130, 0, 0, 0, -78, 0, 0, 0, 22, 0, 0, 0, -432, 0, 0, 0, -30, 0, 0, 0, 10, 0, 0, 0, -98, 0, 0, 0, -156, 0, 0, 0, 260, 0, 0, 0, 24, 0, 0, 0, -198, 0, 0, 0, -2, 0, 0, 0, -232, 0, 0, 0, 12, 0, 0, 0, 30, 0, 0, 0, 18, 0, 0, 0, -186, 0, 0, 0, -108, 0, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 126, 0, 0, 0, 216, 0, 0, 0, 72, 0, 0, 0, -62, 0, 0, 0, 36, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, 94, 0, 0, 0, 104, 0, 0, 0, 120, 0, 0, 0, -36, 0, 0, 0, 110, 0, 0, 0, -138, 0, 0, 0, 276, 0, 0, 0, 58, 0, 0, 0, -108, 0, 0, 0, -126, 0, 0, 0, -124, 0, 0, 0, 24, 0, 0, 0, 54, 0, 0, 0, 22, 0, 0, 0, -48, 0, 0, 0, -72, 0, 0, 0, 86, 0, 0, 0, -126, 0, 0, 0, 58, 0, 0, 0, -208, 0, 0, 0, 102, 0, 0, 0, -50, 0, 0, 0, 50, 0, 0, 0, 24, 0, 0, 0, -76, 0, 0, 0, 126, 0, 0, 0, 54, 0, 0, 0, 50, 0, 0, 0, -104, 0, 0, 0, 222, 0, 0, 0, 72, 0, 0, 0, 36, 0, 0, 0, -54, 0, 0, 0, 16, 0, 0, 0, 216, 0, 0, 0, 138, 0, 0, 0, -162, 0, 0, 0, -36, 0, 0, 0, 210, 0, 0, 0, 56, 0, 0, 0, -134, 0, 0, 0, 198, 0, 0, 0, -40, 0, 0, 0, -58, 0, 0, 0, -252, 0, 0, 0, 12, 0, 0, 0, -92, 0, 0, 0, -6, 0, 0, 0, -146, 0, 0, 0, -2, 0, 0, 0, 102, 0, 0, 0, -396, 0, 0, 0, -112, 0, 0, 0, -96, 0, 0, 0, -76, 0, 0, 0, -36, 0, 0, 0, 102, 0, 0, 0, 62, 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, 0], [1, 1, 9, 3, 1, 3, 0], [1, 1, 36, 6, -1, 6, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "288.2.i.f", "char_is_minimal": false, "conrey_index": 193, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -2, -1, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -4, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -3, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 2, 1, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, -5, 0, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, -1, 2, 0, -2, 0, 0], [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, -2, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, -1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 0, 8, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -2, 0, -1, 0, 0], [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, 3, 2, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 8, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 2, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 5, 0, 3, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 6, -3, -3, 0, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, -7, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -2, 0, -4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 5, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 3, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 1, -1, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, 8, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 1, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [8, 0, 0, 0, -8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 2, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, -3, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 4, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, -3, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}