# Stored data for newform 1728.3.b.a, downloaded from the LMFDB on 25 April 2024.
{"label": "1728.3.b.a", "space_label": "1728.3.b", "level": 1728, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 68769810112, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 2230736224310631468, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [36, 0, 1]], [7, [25, 0, 1]], [11, [6, 1]], [17, [-972, 0, 1]]], "qexp_display": "q+6\\zeta_{12}q^{5}-5\\zeta_{12}q^{7}-6q^{11}-\\zeta_{12}^{2}q^{13}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "b", "char_is_real": true, "Nk2": 15552, "analytic_conductor": 47.084589681459306, "hecke_ring_index": 36, "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": "0.757", "prec": 17}, "analytic_rank_proved": true, "char_values": [1728, 2, [703, 325, 1217], [1, 1, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [1567], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[2, 2], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.041", "prec": 17}, {"__RealLiteral__": 0, "data": "3.858", "prec": 17}, {"__RealLiteral__": 0, "data": "1.678", "prec": 17}, {"__RealLiteral__": 0, "data": "122.569", "prec": 24}, {"__RealLiteral__": 0, "data": "68.464", "prec": 20}, {"__RealLiteral__": 0, "data": "4888.325", "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, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -340, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -340, 0, 0, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 0, 0, -624, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 568, 0, 0, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1300, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -524, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2732, 0, 0, 0, 0, 0, 0, 0, 0, 0, 648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 340, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1300, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2156, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 540, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1772, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1540, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1780, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2500, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, -744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4036, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1620, 0, 0, 0, 0, 0, 0, 0, 0, 0, -600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1820, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2260, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1140, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 476, 0, 0, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3888, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2732, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7820, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2308, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1056, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1492, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5860, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5180, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1436, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19440, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8640, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6200, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10028, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6724, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2700, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5668, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3500, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6340, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5952, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8496, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23328, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3504, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4900, 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, 24, 8, -1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 12, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 4, "minimal_twist": "1728.3.b.a", "char_is_minimal": true, "conrey_index": 1567, "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, 0, 0, 0], [0, 0, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0], [0, -5, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-6, 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, 6], [0, 0, 0, 0], [0, 0, 0, -5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 0, 0], [-11, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -36, 0, 0], [0, 0, 0, 0], [0, 26, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [30, 0, 0, 0], [0, 0, 0, 0], [0, 0, 5, 0], [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, 0], [0, 0, 6, 0], [0, 0, 0, 0], [24, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 60, 0, 0], [0, 0, 0, 0], [0, -36, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-18, 0, 0, 0], [0, 0, 0, 0], [0, 0, 15, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 6], [0, 0, 0, 0], [0, 0, 0, -15], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [25, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 30, 0, 0], [0, 0, 0, 0], [0, -31, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-120, 0, 0, 0], [0, 0, 0, 0], [0, 0, 36, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -30], [0, 0, 0, 0], [0, 0, 0, -5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -30, 0], [0, 0, 0, 0], [-85, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}