# Stored data for newform 900.3.u.b, downloaded from the LMFDB on 24 April 2024. {"label": "900.3.u.b", "space_label": "900.3.u", "level": 900, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504974067237764, "dim": 8, "is_polredabs": true, "nf_label": "8.0.12960000.1", "trace_hash": 254018104898471734, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [3748096, 0, -294272, 0, 21168, 0, -152, 0, 1]]], "qexp_display": "q+3\\beta _{1}q^{3}+(4\\beta _{1}+\\beta _{6})q^{7}-9\\beta _{2}q^{9}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 45, "char_orbit_label": "u", "char_is_real": false, "Nk2": 8100, "analytic_conductor": 24.52322379242672, "hecke_ring_index": 2304, "level_radical": 30, "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": "0.593", "prec": 17}, "analytic_rank_proved": true, "char_values": [900, 6, [451, 101, 577], [6, 5, 3]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 4, "level_primes": [2, 3, 5], "conrey_indexes": [149, 749], "field_disc": 12960000, "field_disc_factorization": [[2, 8], [3, 4], [5, 4]], "field_poly": [1, 0, -3, 0, 8, 0, -3, 0, 1], "hecke_ring_index_factorization": [[2, 8], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.056", "prec": 17}, {"__RealLiteral__": 0, "data": "7.559", "prec": 17}, {"__RealLiteral__": 0, "data": "6.515", "prec": 17}, {"__RealLiteral__": 0, "data": "428.823", "prec": 24}, {"__RealLiteral__": 0, "data": "655.134", "prec": 24}, {"__RealLiteral__": 0, "data": "38423.249", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 36, 0, 12, 0, 0, 0, 0, 0, 0, 0, 152, 0, 48, 0, 0, 0, 0, 0, 0, 0, 120, 0, -8, 0, 0, 0, 0, 0, 0, 0, 240, 0, -180, 0, 0, 0, 0, 0, 0, 0, 108, 0, -36, 0, 0, 0, 0, 0, 0, 0, 348, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 320, 0, -324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 800, 0, 0, 0, 0, 0, 0, 0, 0, 0, -888, 0, 0, 0, 0, 0, 0, 0, 800, 0, -168, 0, 0, 0, 0, 0, 0, 0, -768, 0, 248, 0, 0, 0, 0, 0, 0, 0, 132, 0, -96, 0, 0, 0, 0, 0, 0, 0, -148, 0, -1224, 0, 0, 0, 0, 0, 0, 0, 504, 0, 544, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 684, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1648, 0, 0, 0, 0, 0, 0, 0, -432, 0, -912, 0, 0, 0, 0, 0, 0, 0, 512, 0, -168, 0, 0, 0, 0, 0, 0, 0, -492, 0, 664, 0, 0, 0, 0, 0, 0, 0, -444, 0, -840, 0, 0, 0, 0, 0, 0, 0, 848, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1104, 0, 820, 0, 0, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2944, 0, 0, 0, 0, 0, 0, 0, 72, 0, -1248, 0, 0, 0, 0, 0, 0, 0, -848, 0, 12, 0, 0, 0, 0, 0, 0, 0, -1920, 0, -784, 0, 0, 0, 0, 0, 0, 0, -2064, 0, -1752, 0, 0, 0, 0, 0, 0, 0, -1320, 0, -1764, 0, 0, 0, 0, 0, 0, 0, -2352, 0, 376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 368, 0, 1080, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, -1620, 0, 1392, 0, 0, 0, 0, 0, 0, 0, -2344, 0, 480, 0, 0, 0, 0, 0, 0, 0, -240, 0, 1488, 0, 0, 0, 0, 0, 0, 0, 192, 0, -1836, 0, 0, 0, 0, 0, 0, 0, 212, 0, -2916, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 928, 0, 0, 0, 0, 0, 0, 0, 2520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 344, 0, -972, 0, 0, 0, 0, 0, 0, 0, 0, 0, -360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2232, 0, 0, 0, 0, 0, 0, 0, 5536, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 1992, 0, 560, 0, 0, 0, 0, 0, 0, 0, -1128, 0, -1812, 0, 0, 0, 0, 0, 0, 0, 956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5184, 0, -1312, 0, 0, 0, 0, 0, 0, 0, 1656, 0, 0, 0, 0, 0, 0, 0, 0, 0, -956, 0, 3132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 976, 0, 0, 0, 0, 0, 0, 0, 1584, 0, 3720, 0, 0, 0, 0, 0, 0, 0, -1040, 0, -2196, 0, 0, 0, 0, 0, 0, 0, 1572, 0, -2732, 0, 0, 0, 0, 0, 0, 0, 4200, 0, -2496, 0, 0, 0, 0, 0, 0, 0, 1528, 0, -1584, 0, 0, 0, 0, 0, 0, 0, 2664, 0, -1604, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1196, 0, 1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4736, 0, 0, 0, 0, 0, 0, 0, 3888, 0, 5076, 0, 0, 0, 0, 0, 0, 0, 2136, 0, 5136, 0, 0, 0, 0, 0, 0, 0, 1776, 0, 760, 0, 0, 0, 0, 0, 0, 0, -192, 0, -1896, 0, 0, 0, 0, 0, 0, 0, -3104, 0, -5724, 0, 0, 0, 0, 0, 0, 0, 2400, 0, -920, 0, 0, 0, 0, 0, 0, 0, 1620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 440, 0, 5760, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7072, 0, 0, 0, 0, 0, 0, 0, -5832, 0, 2748, 0, 0, 0, 0, 0, 0, 0, -3160, 0, 3120, 0, 0, 0, 0, 0, 0, 0, -2352, 0, -2888, 0, 0, 0, 0, 0, 0, 0, 4464, 0, 1056, 0, 0, 0, 0, 0, 0, 0, 2120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3420, 0, -1728, 0, 0, 0, 0, 0, 0, 0, -3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1128, 0, 2592, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7544, 0, 0, 0, 0, 0, 0, 0, 3600, 0, 4656, 0, 0, 0, 0, 0, 0, 0, -3520, 0, -3984, 0, 0, 0, 0, 0, 0, 0, -216, 0, 716, 0, 0, 0, 0, 0, 0, 0, -4944, 0, 672, 0, 0, 0, 0, 0, 0, 0, -3964, 0, -2160, 0, 0, 0, 0, 0, 0, 0, 3120, 0, 2600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5120, 0, -972, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6984, 0, 0, 0, 0, 0, 0, 0, -5824, 0, 4836, 0, 0, 0, 0, 0, 0, 0, 4080, 0, 132, 0, 0, 0, 0, 0, 0, 0, 1788, 0, -816, 0, 0, 0, 0, 0, 0, 0, 2200, 0, -1224, 0, 0, 0, 0, 0, 0, 0, -288, 0, -7932, 0, 0, 0, 0, 0, 0, 0, 1476, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2592, 0, 3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5600, 0, 0, 0, 0, 0, 0, 0, -3024, 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, 9, 4, -1, 6, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 45, 8, -1, 6, 0]], "char_orbit_index": 21, "prim_orbit_index": 8, "minimal_twist": "180.3.o.a", "char_is_minimal": false, "conrey_index": 149, "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, 3, 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, 4, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 10, 0, 10, -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, -1, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [19, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -12, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 4, -2, 0, -4, 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, -27, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10, 0, -10, 0, 0, 2, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, -3, 3, 0, 6, 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, -14, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [30, 0, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-30, 0, -15, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 11, 0, 0, 0, 0, -4, 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, -34, 0, -68, 2, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -27, 0, 0, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 3, 0, 0, 3, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 28, 0, 14, -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, 57, 0, 0, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [58, 0, 29, 0, 0, -2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [22, 0, 22, 0, 0, 3, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -36, 9, 0, 9, 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, -7, 0, -7, -12, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [12, 0, 24, 0, 0, -6, 0, 12], [0, 0, 0, 0, 0, 0, 0, 0], [36, 0, 72, 0, 0, 3, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -37, 3, 0, 3, 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, 64, 0, -64, 5, 0, 10, 0], [0, 0, 0, 0, 0, 0, 0, 0], [80, 0, 80, 0, 0, -3, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-81, 0, -81, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -52, 0, -104, 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, 30, 0, -30, -6, 0, -12, 0], [0, 0, 0, 0, 0, 0, 0, 0], [24, 0, 48, 0, 0, 4, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [100, 0, 0, 0, 0, -14, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, -21, 0, -21, 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, -13, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, -18, 0, 0, 9, 0, -18], [0, 0, 0, 0, 0, 0, 0, 0]]}