# Stored data for newform 144.3.q.e, downloaded from the LMFDB on 12 May 2024. {"label": "144.3.q.e", "space_label": "144.3.q", "level": 144, "weight": 3, "hecke_orbit": 5, "hecke_orbit_code": 18015498071441552, "dim": 8, "is_polredabs": true, "nf_label": "8.0.19269881856.9", "trace_hash": 201646746254634725, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [16, 528, 5612, -6468, 2661, -294, -37, 6, 1]]], "qexp_display": "q+(-1+\\beta _{2}-\\beta _{3})q^{3}+(-1+\\beta _{1}-\\beta _{2}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "q", "char_is_real": false, "Nk2": 1296, "analytic_conductor": 3.9237158067882754, "hecke_ring_index": 12, "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": "0.173", "prec": 17}, "analytic_rank_proved": true, "char_values": [144, 6, [127, 37, 65], [6, 6, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [65, 113], "field_disc": 19269881856, "field_disc_factorization": [[2, 12], [3, 4], [241, 2]], "field_poly": [144, 144, 276, -84, 133, -2, 15, -2, 1], "hecke_ring_index_factorization": [[2, 2], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.633", "prec": 17}, {"__RealLiteral__": 0, "data": "0.155", "prec": 17}, {"__RealLiteral__": 0, "data": "213.487", "prec": 24}, {"__RealLiteral__": 0, "data": "59.392", "prec": 20}, {"__RealLiteral__": 0, "data": "9175.305", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, -10, -6, -6], "traces": [0, 8, 0, -10, 0, -6, 0, -6, 0, -22, 0, -36, 0, 14, 0, -10, 0, 0, 0, -4, 0, -54, 0, 102, 0, 10, 0, 20, 0, -114, 0, 50, 0, -104, 0, 0, 0, 120, 0, -82, 0, 264, 0, 28, 0, 206, 0, -150, 0, 94, 0, -170, 0, 0, 0, 244, 0, -178, 0, 108, 0, 14, 0, 210, 0, -198, 0, 20, 0, -14, 0, 0, 0, -76, 0, -326, 0, 66, 0, -26, 0, 194, 0, -246, 0, -224, 0, 18, 0, 0, 0, -108, 0, -130, 0, 456, 0, -236, 0, 634, 0, -342, 0, -146, 0, -180, 0, 0, 0, -304, 0, -204, 0, 510, 0, -50, 0, 602, 0, -624, 0, 124, 0, -318, 0, 0, 0, -632, 0, -332, 0, -30, 0, 456, 0, 38, 0, -132, 0, -72, 0, 162, 0, 0, 0, 228, 0, 328, 0, -174, 0, 50, 0, 538, 0, 558, 0, -166, 0, 680, 0, 0, 0, -48, 0, 172, 0, 630, 0, -222, 0, 1022, 0, -438, 0, -24, 0, -410, 0, 0, 0, -240, 0, -406, 0, 600, 0, 146, 0, 150, 0, -714, 0, -8, 0, -538, 0, 0, 0, 472, 0, -550, 0, -378, 0, 54, 0, -470, 0, 498, 0, 46, 0, 404, 0, 0, 0, -252, 0, 134, 0, -396, 0, -266, 0, -608, 0, 612, 0, 62, 0, 174, 0, 0, 0, -108, 0, 766, 0, 798, 0, -60, 0, -250, 0, -312, 0, -76, 0, 146, 0, 0, 0, 788, 0, -692, 0, 156, 0, -48, 0, -42, 0, -1566, 0, 140, 0, -1464, 0, 0, 0, -232, 0, 24, 0, -1842, 0, -526, 0, -994, 0, 402, 0, 674, 0, -988, 0, 0, 0, -596, 0, 568, 0, -174, 0, 790, 0, -896, 0, 1866, 0, 102, 0, 1902, 0, 0, 0, 2388, 0, -758, 0, 522, 0, 516, 0, 120, 0, -246, 0, 342, 0, 174, 0, 0, 0, 616, 0, 56, 0, -918, 0, -826, 0, -588, 0, 810, 0, 744, 0, -1506, 0, 0, 0, 228, 0, 502, 0, -984, 0, 378, 0, -2374, 0, -12, 0, -988, 0, 1056, 0, 0, 0, 1836, 0, 1336, 0, 372, 0, -458, 0, -672, 0, 1164, 0, -458, 0, 2772, 0, 0, 0, -2956, 0, 544, 0, 1134, 0, -474, 0, -146, 0, 3210, 0, 884, 0, 662, 0, 0, 0, -776, 0, 672, 0, -1404, 0, 1298, 0, -2146, 0, -1236, 0, -792, 0, -612, 0, 0, 0, 788, 0, 2934, 0, -2778, 0, -86, 0, -834, 0, 966, 0, -786, 0, -92, 0, 0, 0, -316, 0, 936, 0, -1548, 0, -774, 0, -74, 0, 2100, 0, 1140, 0, 610, 0, 0, 0, -480, 0, -502, 0, 6, 0, 844, 0, 520, 0, 1098, 0, -946, 0, 638, 0, 0, 0, -180, 0, -166, 0, -3912, 0, -650, 0, -1408, 0, 1482, 0, -1296, 0, -1428, 0, 0, 0, -512, 0, -228, 0, -2640, 0, -984, 0, -1928, 0, -1716, 0, 1560, 0, -330, 0, 0, 0, -3300, 0, 1818, 0, 810, 0, 948, 0, -604, 0, 1746, 0, -114, 0, 2766, 0, 0, 0, 1480, 0, 2004, 0, 252, 0, 454, 0, 1108, 0, 1374, 0, -516, 0, 1272, 0, 0, 0, -2496, 0, -48, 0, 1536, 0, 296, 0, 1082, 0, -2400, 0, 414, 0, -1464, 0, 0, 0, -4028, 0, 1058, 0, -2976, 0, 30, 0, -2358, 0, 2916, 0, -1284, 0, -138, 0, 0, 0, 2980, 0, -38, 0, 762, 0, 844, 0, 2846, 0, 3312, 0, -148, 0, 1584, 0, 0, 0, -216, 0, -1052, 0, 966, 0, -604, 0, 800, 0, -1536, 0, 422, 0, 282, 0, 0, 0, 568, 0, -102, 0, -876, 0, -884, 0, -794, 0, -1116, 0, -2588, 0, -1082, 0, 0, 0, 5104, 0, -1778, 0, 1836, 0, -788, 0, 356, 0, -2592, 0, 0, 0, 1336, 0, 0, 0, -832, 0, -48, 0, 2178, 0, -2350, 0, -418, 0, -234, 0, 2950, 0, 1156, 0, 0, 0, -492, 0, -602, 0, 3138, 0, 2714, 0, 2290, 0, -690, 0, -654, 0, -384, 0, 0, 0, 5004, 0, -1270, 0, 1596, 0, 1514, 0, -1242, 0, -5106, 0, 414, 0, -874, 0, 0, 0, 600, 0, 1512, 0, 2034, 0, -1886, 0, 766, 0, -150, 0, 2962, 0, -3718, 0, 0, 0, -180, 0, -1608, 0, -2472, 0, 2418, 0, -16, 0, 1002, 0, -1142, 0, -2240, 0, 0, 0, 2252, 0, -3532, 0, 822, 0, -998, 0, 926, 0, -324, 0, -606, 0, -2962, 0, 0, 0, -2384, 0, -3088, 0, -1710, 0, -1704, 0, 1576, 0, -3090, 0, 2686, 0, -698, 0, 0, 0, -4280, 0, -2472, 0, -654, 0, 3184, 0, 2382, 0, -3306, 0, -542, 0, 490, 0, 0, 0, 4916, 0, -220, 0, 6414, 0, -2340, 0, 1488, 0, -3546, 0, -30, 0, -2432, 0, 0, 0, -2516, 0, 344, 0, 3924, 0, -1262, 0, 1260, 0, -546, 0, 1142, 0, 2900, 0, 0, 0, -2824, 0, -1378, 0, 2982, 0, 858, 0, 5498, 0, 1266, 0, -838, 0, -2354, 0, 0, 0, 1968, 0, -646, 0, -312, 0, -458, 0, -1288, 0, -1566, 0, -1824, 0, -3144, 0, 0, 0, -3828, 0, 580, 0, 1302, 0, -550, 0, 1870, 0, -234, 0, 342, 0, 2718, 0, 0, 0, 1628, 0, -4106, 0, 1146, 0, 468, 0, 1696, 0, -5676, 0, 912, 0, -4286, 0, 0, 0, 5296, 0, -750, 0, 696, 0, 2308, 0, -1014, 0, 198, 0, 958, 0, 356, 0, 0, 0, 3784, 0, -2526, 0, 204, 0, -2076, 0, 466, 0, -1710, 0, 2410, 0, 1794, 0, 0, 0, -3144, 0, -3144, 0, 3198, 0, 3306, 0, 780, 0, -5388, 0, -3328, 0, -810, 0, 0, 0, 3060, 0, 5142, 0, 1674, 0, -42, 0, 1626, 0, 2310, 0, 422, 0, 2326, 0, 0, 0, -204, 0, 2584, 0, 4944, 0, -2796, 0, 2120, 0, 1170, 0, 2256, 0, 426, 0, 0, 0, -3608, 0, 1886, 0, 3768, 0, 3314, 0, 4392, 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]], "char_orbit_index": 17, "prim_orbit_index": 4, "minimal_twist": "72.3.m.b", "char_is_minimal": false, "conrey_index": 65, "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], [-1, 0, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 1, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -3, 1, -1, 1, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 1, -2, -2, 2, 4, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 3, 6, 2, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, 1, 7, 4, -2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [1, 5, 4, -1, 1, -3, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -2, 1, 0, -3, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [-5, -2, -1, -2, 3, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [14, 1, -7, -5, 0, 6, -4, 2], [0, 0, 0, 0, 0, 0, 0, 0], [2, -6, 9, -7, -3, 1, -6, 1], [0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 0, 3, 2, -2, 10, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-11, 2, 1, -10, -3, 3, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 13, -12, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-20, -1, -6, 20, -7, -3, 1, 4], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 2, -12, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, 0, 0, -6, -2, 6, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-6, -5, 1, -3, -12, -6, -12, 10], [0, 0, 0, 0, 0, 0, 0, 0], [42, 2, -6, -19, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, -7, 14, -14, 6, 0, 12, 0], [0, 0, 0, 0, 0, 0, 0, 0], [29, -7, 5, -3, -4, -6, -11, 7], [0, 0, 0, 0, 0, 0, 0, 0], [-13, 3, 5, -15, -6, 1, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [1, -5, -5, 26, 6, -2, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-30, -8, -1, 19, 8, -1, -8, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-6, -8, -12, 16, -4, 2, -4, 6], [0, 0, 0, 0, 0, 0, 0, 0], [33, -6, 12, -6, 12, -5, -12, 13], [0, 0, 0, 0, 0, 0, 0, 0], [-8, -4, -1, -29, 15, 1, 18, 11], [0, 0, 0, 0, 0, 0, 0, 0], [21, 6, 0, -9, 0, -6, 14, -9], [0, 0, 0, 0, 0, 0, 0, 0], [7, 12, -3, -2, -9, -7, -18, -7], [0, 0, 0, 0, 0, 0, 0, 0], [31, -5, -7, -11, -6, 5, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0], [-27, 6, -9, -12, 7, 21, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 5, 0, 10, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-25, -3, 19, 39, -10, -2, 7, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-30, 12, 0, 72, -4, -12, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, -7, 14, -7, -9, -25, 9, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-13, 1, -19, -58, -18, 12, -6, -17], [0, 0, 0, 0, 0, 0, 0, 0], [7, -3, -5, -3, 0, 8, -9, 7], [0, 0, 0, 0, 0, 0, 0, 0], [-7, 5, -13, 13, 12, 1, 24, 1], [0, 0, 0, 0, 0, 0, 0, 0], [24, 15, 5, -2, 8, 0, -11, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-21, -1, -3, -19, -2, 1, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 4, 4, -58, 0, 12, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [-29, 7, -19, 67, 0, 5, -6, -11], [0, 0, 0, 0, 0, 0, 0, 0], [-22, -4, 20, 20, 0, 14, 0, -10], [0, 0, 0, 0, 0, 0, 0, 0], [-19, 4, -8, 4, 6, 11, -6, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 13, 13, -21, 18, -12, 21, -23], [0, 0, 0, 0, 0, 0, 0, 0], [82, -4, 16, -46, 0, -12, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-57, 10, -8, 63, 0, -4, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [80, 14, 9, 10, 22, -16, 14, -9], [0, 0, 0, 0, 0, 0, 0, 0]]}