# Stored data for newform 288.2.r.b, downloaded from the LMFDB on 23 April 2024.
{"label": "288.2.r.b", "space_label": "288.2.r", "level": 288, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504767892029728, "dim": 16, "is_polredabs": true, "trace_hash": 2219250025650231274, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [4096, 0, -11712, 0, 26129, 0, -18357, 0, 9318, 0, -2049, 0, 326, 0, -21, 0, 1]]], "qexp_display": "q-\\beta _{12}q^{3}+(-\\beta _{4}-\\beta _{7}+\\beta _{8}-\\beta _{11}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 72, "char_orbit_label": "r", "char_is_real": false, "Nk2": 1152, "analytic_conductor": 2.299691578212875, "hecke_ring_index": 2304, "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": "0.511", "prec": 17}, "analytic_rank_proved": true, "char_values": [288, 6, [127, 37, 65], [6, 3, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [49, 241], "field_disc": 988177457384100000000, "field_disc_factorization": [[2, 8], [3, 8], [5, 8], [197, 4]], "field_poly": [256, -128, 64, 0, 32, -32, 0, -16, 4, -8, 0, -4, 2, 0, 1, -1, 1], "hecke_ring_index_factorization": [[2, 8], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.062", "prec": 17}, {"__RealLiteral__": 0, "data": "13.863", "prec": 20}, {"__RealLiteral__": 0, "data": "14.524", "prec": 20}, {"__RealLiteral__": 0, "data": "1530.525", "prec": 27}, {"__RealLiteral__": 0, "data": "4215.100", "prec": 27}, {"__RealLiteral__": 0, "data": "307081.260", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, -6], "traces": [0, 16, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 10, 0, -28, 0, 0, 0, 0, 0, 10, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, -6, 0, 18, 0, 0, 0, 0, 0, 4, 0, 10, 0, 0, 0, 0, 0, -2, 0, -14, 0, 0, 0, 0, 0, -72, 0, -44, 0, 0, 0, 0, 0, 30, 0, 10, 0, 0, 0, 0, 0, -42, 0, 64, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 14, 0, -28, 0, 0, 0, 0, 0, -8, 0, 18, 0, 0, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 86, 0, 0, 0, 0, 0, 0, 0, 156, 0, -28, 0, 0, 0, 0, 0, -10, 0, 26, 0, 0, 0, 0, 0, 96, 0, 20, 0, 0, 0, 0, 0, 62, 0, 2, 0, 0, 0, 0, 0, -44, 0, 58, 0, 0, 0, 0, 0, -66, 0, -8, 0, 0, 0, 0, 0, -38, 0, -32, 0, 0, 0, 0, 0, -72, 0, -6, 0, 0, 0, 0, 0, -170, 0, 66, 0, 0, 0, 0, 0, -52, 0, 84, 0, 0, 0, 0, 0, -38, 0, -16, 0, 0, 0, 0, 0, -126, 0, -92, 0, 0, 0, 0, 0, -30, 0, 32, 0, 0, 0, 0, 0, -20, 0, -14, 0, 0, 0, 0, 0, 88, 0, -24, 0, 0, 0, 0, 0, 110, 0, 8, 0, 0, 0, 0, 0, -16, 0, -4, 0, 0, 0, 0, 0, 182, 0, -30, 0, 0, 0, 0, 0, 92, 0, -60, 0, 0, 0, 0, 0, 26, 0, -48, 0, 0, 0, 0, 0, 82, 0, -12, 0, 0, 0, 0, 0, 82, 0, 8, 0, 0, 0, 0, 0, 46, 0, -78, 0, 0, 0, 0, 0, 32, 0, 18, 0, 0, 0, 0, 0, -114, 0, 0, 0, 0, 0, 0, 0, 12, 0, 50, 0, 0, 0, 0, 0, -166, 0, -24, 0, 0, 0, 0, 0, -272, 0, -28, 0, 0, 0, 0, 0, 14, 0, -32, 0, 0, 0, 0, 0, -144, 0, 36, 0, 0, 0, 0, 0, -162, 0, -62, 0, 0, 0, 0, 0, 40, 0, 46, 0, 0, 0, 0, 0, 20, 0, 72, 0, 0, 0, 0, 0, 84, 0, 72, 0, 0, 0, 0, 0, 92, 0, 130, 0, 0, 0, 0, 0, 150, 0, -22, 0, 0, 0, 0, 0, 144, 0, 20, 0, 0, 0, 0, 0, 62, 0, 66, 0, 0, 0, 0, 0, 198, 0, 132, 0, 0, 0, 0, 0, 62, 0, -40, 0, 0, 0, 0, 0, 18, 0, 82, 0, 0, 0, 0, 0, -62, 0, 0, 0, 0, 0, 0, 0, -202, 0, -8, 0, 0, 0, 0, 0, 208, 0, -148, 0, 0, 0, 0, 0, -204, 0, 0, 0, 0, 0, 0, 0, -168, 0, 84, 0, 0, 0, 0, 0, -56, 0, 116, 0, 0, 0, 0, 0, -78, 0, -156, 0, 0, 0, 0, 0, -64, 0, -6, 0, 0, 0, 0, 0, -44, 0, 52, 0, 0, 0, 0, 0, -64, 0, -160, 0, 0, 0, 0, 0, 132, 0, -62, 0, 0, 0, 0, 0, -28, 0, -174, 0, 0, 0, 0, 0, 242, 0, 48, 0, 0, 0, 0, 0, 280, 0, 148, 0, 0, 0, 0, 0, -116, 0, -110, 0, 0, 0, 0, 0, 152, 0, -192, 0, 0, 0, 0, 0, 94, 0, 32, 0, 0, 0, 0, 0, -42, 0, -222, 0, 0, 0, 0, 0, 14, 0, 8, 0, 0, 0, 0, 0, -40, 0, 8, 0, 0, 0, 0, 0, -48, 0, 110, 0, 0, 0, 0, 0, -192, 0, -184, 0, 0, 0, 0, 0, -192, 0, -64, 0, 0, 0, 0, 0, -46, 0, -78, 0, 0, 0, 0, 0, -176, 0, 152, 0, 0, 0, 0, 0, -42, 0, 50, 0, 0, 0, 0, 0, -94, 0, 56, 0, 0, 0, 0, 0, 98, 0, 96, 0, 0, 0, 0, 0, 130, 0, -86, 0, 0, 0, 0, 0, -320, 0, 252, 0, 0, 0, 0, 0, 106, 0, 130, 0, 0, 0, 0, 0, 208, 0, 116, 0, 0, 0, 0, 0, -10, 0, -40, 0, 0, 0, 0, 0, 120, 0, 144, 0, 0, 0, 0, 0, 230, 0, 26, 0, 0, 0, 0, 0, 46, 0, 234, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -74, 0, 90, 0, 0, 0, 0, 0, -88, 0, 8, 0, 0, 0, 0, 0, -246, 0, 154, 0, 0, 0, 0, 0, -252, 0, -204, 0, 0, 0, 0, 0, 168, 0, -116, 0, 0, 0, 0, 0, -312, 0, 36, 0, 0, 0, 0, 0, -172, 0, 2, 0, 0, 0, 0, 0, 106, 0, -168, 0, 0, 0, 0, 0, 50, 0, -102, 0, 0, 0, 0, 0, 170, 0, -14, 0, 0, 0, 0, 0, 200, 0, -130, 0, 0, 0, 0, 0, 292, 0, -30, 0, 0, 0, 0, 0, 336, 0, -268, 0, 0, 0, 0, 0, 162, 0, 122, 0, 0, 0, 0, 0, 282, 0, -176, 0, 0, 0, 0, 0, 66, 0, -80, 0, 0, 0, 0, 0, -4, 0, -310, 0, 0, 0, 0, 0, -2, 0, 152, 0, 0, 0, 0, 0, -162, 0, -58, 0, 0, 0, 0, 0, 80, 0, 42, 0, 0, 0, 0, 0, -318, 0, -94, 0, 0, 0, 0, 0, -240, 0, -16, 0, 0, 0, 0, 0, -70, 0, 76, 0, 0, 0, 0, 0, -122, 0, 180, 0, 0, 0, 0, 0, -150, 0, -6, 0, 0, 0, 0, 0, -86, 0, 142, 0, 0, 0, 0, 0, 88, 0, 176, 0, 0, 0, 0, 0, 86, 0, 16, 0, 0, 0, 0, 0, 304, 0, 194, 0, 0, 0, 0, 0, 152, 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, 9, 3, 1, 3, 0], [1, 1, 72, 14, 1, 6, 0]], "char_orbit_index": 18, "prim_orbit_index": 14, "minimal_twist": "72.2.n.b", "char_is_minimal": false, "conrey_index": 49, "id": null, "nf_label": 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, 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, 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, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0, -1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, 0, -1, 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, 1, 0, 0, 0, 0, -1, 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, -1, 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, -1, 0, 1, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 1, -1, 0, 0, 1, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 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, 0, 0, 0], [-1, 2, -1, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -2, -1, 0, 0, 0, 2, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, -2, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 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, 0, 0, 0], [0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, -2, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -1, -2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0, -1, 0, -1, 3, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 2, 1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, -1, 0, 2, 0, -1, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 1, -2, 0, 0, -1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -4, 1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 2, -1, 2, 0, 0, -2, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 2, -2, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, -1, 1, 0, 2, 0, 0, 0, 1, 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, 2, 0, 0, 2, -4, 0, 1, 4, 2, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, 2, 3, 0, 0, -1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 1, 3, -4, 0, -1, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, -2, 3, -1, 0, 0, 1, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 0, -2, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, -2, -4, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, -1, 2, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 2, 1, -2, 0, -1, 2, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, 1, -1, 5, 0, -3, 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, 0], [4, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, -3, 1, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, -1, -4, -1, 0, 2, -1, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 2, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0, 2, 2, -4, 0, -1, 2, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}