# Stored data for newform 1728.3.b.e, downloaded from the LMFDB on 18 May 2022.
{"level_primes": [2, 3], "is_polredabs": true, "sato_tate_group": "2.2.3.c2", "rm_discs": [], "conrey_indexes": [1567], "cm_discs": [], "trace_hash": 360575493935618955, "level_radical": 6, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 4, "is_cm": false, "hecke_orbit": 5, "analytic_conductor": 47.084589681459306, "inner_twist_count": 4, "field_disc_factorization": [[2, 4], [3, 2]], "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": -1, "label": "1728.3.b.e", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "1728.3.b.b", "field_poly_is_cyclotomic": true, "dim": 4, "trace_zratio": {"__RealLiteral__": 0, "data": "0.759", "prec": 17}, "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, 428, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 0, 0, 716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -888, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, 908, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1104, 0, 0, 0, 0, 0, 0, 0, 532, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 0, 0, -1012, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 0, 0, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 0, 0, 0, 0, 0, 236, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -1432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1008, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 312, 0, 0, 0, 0, 0, 0, 0, -1976, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1464, 0, 0, 0, 0, 0, 0, 0, -1592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, -2208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2904, 0, 0, 0, 0, 0, 0, 0, -1484, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2592, 0, 0, 0, 0, 0, 0, 0, -332, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3384, 0, 0, 0, 0, 0, 0, 0, -3164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3072, 0, 0, 0, 0, 0, 0, 0, -712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 648, 0, 0, 0, 0, 0, 0, 0, -524, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2880, 0, 0, 0, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -1292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1680, 0, 0, 0, 0, 0, 0, 0, -380, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4200, 0, 0, 0, 0, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5832, 0, 0, 0, 0, 0, 0, 0, 188, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, -300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, 1636, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 2496, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4056, 0, 0, 0, 0, 0, 0, 0, -760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2280, 0, 0, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4464, 0, 0, 0, 0, 0, 0, 0, -1100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6024, 0, 0, 0, 0, 0, 0, 0, 3060, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3360, 0, 0, 0, 0, 0, 0, 0, 3216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 2108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2496, 0, 0, 0, 0, 0, 0, 0, 4220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2784, 0, 0, 0, 0, 0, 0, 0, -436, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1584, 0, 0, 0, 0, 0, 0, 0, 7920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1608, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 0, 0, 0, 0, -1972, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4608, 0, 0, 0, 0, 0, 0, 0, 3604, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -936, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 648, 0, 0, 0, 0, 0, 0, 0, 5860, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1896, 0, 0, 0, 0, 0, 0, 0, 2496, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1176, 0, 0, 0, 0, 0, 0, 0, 3308, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7200, 0, 0, 0, 0, 0, 0, 0, 420, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 936, 0, 0, 0, 0, 0, 0, 0, 2396, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1104, 0, 0, 0, 0, 0, 0, 0, 6476, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 792, 0, 0, 0, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3000, 0, 0, 0, 0, 0, 0, 0, 4024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4320, 0, 0, 0, 0, 0, 0, 0, -956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7440, 0, 0, 0, 0, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10008, 0, 0, 0, 0, 0, 0, 0, 3360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3696, 0, 0, 0, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5112, 0, 0, 0, 0, 0, 0, 0, -2500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11400, 0, 0, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1368, 0, 0, 0, 0, 0, 0, 0, -520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 3648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4680, 0, 0, 0, 0, 0, 0, 0, -1588, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 912, 0, 0, 0, 0, 0, 0, 0, -5760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2568, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 816, 0, 0, 0, 0, 0, 0, 0, 2492, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2976, 0, 0, 0, 0, 0, 0, 0, -3360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1728, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2568, 0, 0, 0, 0, 0, 0, 0, -10936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 0, 0, 0, 0, -13304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5880, 0, 0, 0, 0, 0, 0, 0, -4360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9960, 0, 0, 0, 0, 0, 0, 0, 2548, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, -5668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10104, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1752, 0, 0, 0, 0, 0, 0, 0, -1060, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6480, 0, 0, 0, 0, 0, 0, 0, 3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -672, 0, 0, 0, 0, 0, 0, 0, 7536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3696, 0, 0, 0, 0, 0, 0, 0, -13440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9504, 0, 0, 0, 0, 0, 0, 0, -7004, 0, 0, 0, 0, 0, 0, 0], "hecke_ring_index_factorization": [[2, 2]], "nf_label": "4.0.144.1", "field_poly": [1, 0, -1, 0, 1], "has_non_self_twist": 1, "char_values": [1728, 2, [703, 325, 1217], [1, 1, 2]], "Nk2": 15552, "field_poly_root_of_unity": 12, "analytic_rank": 0, "char_orbit_label": "b", "weight": 3, "trace_display": [0, 0, 0, 0], "analytic_rank_proved": true, "char_parity": -1, "level_is_squarefree": false, "hecke_ring_index": 4, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-2\\zeta_{12}^{2}q^{5}-\\zeta_{12}q^{7}+10\\zeta_{12}^{3}q^{11}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 144, "level_is_prime_power": false, "relative_dim": 4, "hecke_cutters": [[5, [12, 0, 1]], [7, [1, 0, 1]], [11, [-300, 0, 1]], [17, [-6, 1]]], "space_label": "1728.3.b", "level": 1728, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0]], "char_degree": 1, "char_conductor": 8, "char_orbit_index": 2, "hecke_ring_generator_nbound": 13, "hecke_orbit_code": 18014467279292096, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.883", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "123.690", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4911.713", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 10], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 30, 0, 0], [0, 0, 0, 0], [13, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 12, 0], [0, 0, 0, 0], [0, -14, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 11, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-48, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -66, 0, 0], [0, 0, 0, 0], [48, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 28, 0], [0, 0, 0, 0], [0, -60, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -18], [0, 0, 0, 0], [0, 0, 25, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 35], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 48, 0, 0], [0, 0, 0, 0], [49, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -10, 0], [0, 0, 0, 0], [0, -83, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 8], [0, 0, 0, 0], [0, 0, -12, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [66, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -6, 0, 0], [0, 0, 0, 0], [107, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}