# Stored data for newform 525.4.d.n, downloaded from the LMFDB on 24 April 2024.
{"label": "525.4.d.n", "space_label": "525.4.d", "level": 525, "weight": 4, "hecke_orbit": 14, "hecke_orbit_code": 58547001381356045, "dim": 8, "is_polredabs": true, "trace_hash": 899706895036548724, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [2116, 0, 2217, 0, 668, 0, 48, 0, 1]], [11, [-304010, 61617, -2643, -21, 1]]], "qexp_display": "q+\\beta _{1}q^{2}-3\\beta _{3}q^{3}+(-4+\\beta _{2})q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "d", "char_is_real": true, "Nk2": 8400, "analytic_conductor": 30.976002753013823, "hecke_ring_index": 1, "level_radical": 105, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [525, 2, [176, 127, 451], [2, 1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [274], "field_disc": 3220525818109851904, "field_disc_factorization": [[2, 8], [112161397, 2]], "field_poly": [2116, 0, 2217, 0, 668, 0, 48, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "7.776", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "336.112", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "20865.320", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, -32, 0, 0, 0, 0, -72, 0, 42, 0, 0, 0, 0, 144, 0, 0, -144, 0, 168, 0, 0, -54, 0, 258, 0, 0, 480, 0, 702, 0, 0, 570, 0, 288, 0, 0, -30, 0, 762, 0, 0, 1950, 0, 1100, 0, 0, -392, 0, 594, 0, 0, 0, 0, 126, 0, 0, 1710, 0, 1374, 0, 0, 2570, 0, 1326, 0, 0, -612, 0, -1362, 0, 0, 6738, 0, 3820, 0, 0, -690, 0, 648, 0, 0, -672, 0, -1080, 0, 0, 396, 0, 70, 0, 0, 3464, 0, 432, 0, 0, -378, 0, -804, 0, 0, 7818, 0, 1338, 0, 0, -326, 0, 2394, 0, 0, -1944, 0, -1956, 0, 0, -1386, 0, 806, 0, 0, -3702, 0, 0, 0, 0, -2760, 0, -4020, 0, 0, 10206, 0, 7550, 0, 0, -5396, 0, 360, 0, 0, -1296, 0, 14520, 0, 0, -5532, 0, -7146, 0, 0, -3094, 0, 1338, 0, 0, -5238, 0, 1428, 0, 0, 9270, 0, -3838, 0, 0, -10234, 0, 1296, 0, 0, -8448, 0, 2082, 0, 0, 11412, 0, 9336, 0, 0, -11926, 0, -2862, 0, 0, -1512, 0, -19038, 0, 0, 15048, 0, 1568, 0, 0, -8896, 0, -3018, 0, 0, -10350, 0, 2694, 0, 0, 5064, 0, -11178, 0, 0, 6964, 0, 486, 0, 0, -7368, 0, -26958, 0, 0, -1008, 0, -11962, 0, 0, -23016, 0, 882, 0, 0, -2322, 0, -25506, 0, 0, 14880, 0, 1844, 0, 0, -11574, 0, -2970, 0, 0, -9054, 0, -7002, 0, 0, 7986, 0, -34352, 0, 0, -5586, 0, -4320, 0, 0, -13596, 0, 4536, 0, 0, -17976, 0, -23144, 0, 0, -38916, 0, 17964, 0, 0, -6318, 0, -7158, 0, 0, 24594, 0, 26180, 0, 0, -5714, 0, -2232, 0, 0, 0, 0, -18492, 0, 0, 12474, 0, 6440, 0, 0, -4536, 0, -5130, 0, 0, -20994, 0, -27096, 0, 0, 16164, 0, 28582, 0, 0, -62, 0, 21132, 0, 0, -2592, 0, -42810, 0, 0, -840, 0, -3744, 0, 0, 23876, 0, 3024, 0, 0, 990, 0, -30672, 0, 0, 6378, 0, 74464, 0, 0, -17466, 0, 270, 0, 0, -222, 0, 55032, 0, 0, 27240, 0, -35416, 0, 0, -3122, 0, 25938, 0, 0, -6858, 0, 12222, 0, 0, -16968, 0, -7164, 0, 0, 276, 0, 24810, 0, 0, 2340, 0, 75834, 0, 0, 28338, 0, 34066, 0, 0, 52784, 0, -17550, 0, 0, -3024, 0, -39654, 0, 0, 64872, 0, 19712, 0, 0, -53068, 0, 612, 0, 0, -9900, 0, 68766, 0, 0, 23070, 0, 53590, 0, 0, 36202, 0, -14718, 0, 0, 26244, 0, -59670, 0, 0, 6678, 0, 8798, 0, 0, 36918, 0, 3528, 0, 0, 14022, 0, 44298, 0, 0, -8646, 0, 24668, 0, 0, -16106, 0, 10764, 0, 0, -5346, 0, 3576, 0, 0, 192, 0, -81498, 0, 0, 7042, 0, -3132, 0, 0, 42210, 0, 24150, 0, 0, -45192, 0, -47076, 0, 0, -118, 0, 0, 0, 0, -22698, 0, 68202, 0, 0, 19344, 0, 9774, 0, 0, 19118, 0, -3564, 0, 0, -1134, 0, 16818, 0, 0, 12696, 0, 17192, 0, 0, 74650, 0, -55140, 0, 0, 20952, 0, -2574, 0, 0, -79392, 0, -13248, 0, 0, 35968, 0, -15390, 0, 0, 36780, 0, -123900, 0, 0, -2058, 0, -12430, 0, 0, 55558, 0, 5418, 0, 0, -12366, 0, 8112, 0, 0, -34944, 0, 57216, 0, 0, 11766, 0, -1200, 0, 0, 83124, 0, 141276, 0, 0, -18414, 0, -29316, 0, 0, 6930, 0, -23130, 0, 0, -5142, 0, 21126, 0, 0, -92664, 0, -142808, 0, 0, -10488, 0, 42696, 0, 0, -11934, 0, 128088, 0, 0, -46356, 0, 34960, 0, 0, 73846, 0, -79956, 0, 0, 10080, 0, -57696, 0, 0, 21576, 0, 31724, 0, 0, 4204, 0, 5508, 0, 0, -2862, 0, 79020, 0, 0, -63312, 0, 42930, 0, 0, 49808, 0, 8334, 0, 0, 12258, 0, -96930, 0, 0, -41916, 0, 41024, 0, 0, -94916, 0, 14742, 0, 0, 101286, 0, 10746, 0, 0, 22932, 0, 47116, 0, 0, -82998, 0, -60642, 0, 0, 38466, 0, 79356, 0, 0, -230382, 0, -217870, 0, 0, 5208, 0, 49014, 0, 0, -34380, 0, 0, 0, 0, -138438, 0, 38420, 0, 0, 16346, 0, -4266, 0, 0, 28854, 0, -23622, 0, 0, -97248, 0, -38720, 0, 0, 5484, 0, 6210, 0, 0, 11970, 0, 8868, 0, 0, 19332, 0, 48986, 0, 0, 2452, 0, -98118, 0, 0, -5832, 0, -48234, 0, 0, -185514, 0, -52748, 0, 0, 56176, 0, 10056, 0, 0, 87426, 0, -108858, 0, 0, -49308, 0, -21888, 0, 0, 7050, 0, 6048, 0, 0, 5634, 0, -72948, 0, 0, -47298, 0, -101384, 0, 0, -23048, 0, 61434, 0, 0, 9720, 0, 48252, 0, 0, 41496, 0, -17266, 0, 0, -7056, 0, -59724, 0, 0, -33192, 0, -2310, 0, 0, -61122, 0, -107584, 0, 0, 38080, 0, -3564, 0, 0, -10578, 0, -18990, 0, 0, -62574, 0, -13352, 0, 0, -74586, 0, 5562, 0, 0, -630, 0, -179256, 0, 0, -40962, 0, 518, 0, 0, -174, 0, -12216, 0, 0, -9108, 0, 1188, 0, 0, 104628, 0, -35408, 0, 0, 83634, 0, -31176, 0, 0, 15132, 0, -80898, 0, 0, -60522, 0, -151188, 0, 0, -45492, 0, 16002, 0, 0, -3888, 0, 182628, 0, 0, 150378, 0, 218112, 0, 0, -130824, 0, -116532, 0, 0, 77184, 0, -99978, 0, 0, -195690, 0, -111168, 0, 0, -57890, 0, 3402, 0, 0, -75516, 0, -5460, 0, 0, -36882, 0, -115218, 0, 0, -5736, 0, -25182, 0, 0, 7236, 0, 90936, 0, 0, -65616, 0, 192304, 0, 0, 246954, 0, 111600, 0, 0, 40950, 0, 40728, 0, 0, 94842, 0, 7056, 0, 0, 5878, 0, -70362, 0, 0, 45756, 0, -37788, 0, 0, 30558, 0, -115886, 0, 0, 89212, 0, 77760, 0, 0, -12042, 0, -108432, 0, 0, -1428, 0, 76690, 0, 0, -29488, 0, 23100, 0, 0, -32328, 0, 219432, 0, 0, -150882, 0, 50670, 0, 0, 266536, 0, 2934, 0, 0, 40746, 0, 142818, 0, 0, 127956, 0, 256318, 0, 0, 34342, 0, 123606, 0, 0, -21546, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "525.4.a.t", "char_is_minimal": false, "conrey_index": 274, "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], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 0, 0, 0], [-4, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 7, 0, 0, 0, 0], [0, -4, 0, -2, 0, 1, 0, 0], [-9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 3, 0, 5, 0, 0, -1], [0, 0, 0, 12, 0, 0, -3, 0], [0, -3, 0, -2, 0, -3, 1, 0], [0, 0, 0, 0, -7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [18, 0, 0, 0, 3, 0, 0, 0], [0, -7, 0, 24, 0, -3, -3, 0], [0, -9, 0, 0, 0, 0, 0, 0], [-18, 0, 4, 0, -6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [21, 0, 0, 0, 0, 0, 0, 0], [0, -18, 0, 56, 0, 3, -9, 0], [0, -10, 0, -25, 0, 2, 6, 0], [-6, 0, 0, 0, -12, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [32, 0, 9, 0, 7, 0, 0, -1], [0, 0, 0, 27, 0, 0, 0, 0], [0, 0, 0, -28, 0, 0, 7, 0], [59, 0, 0, 0, -30, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [90, 0, -3, 0, -9, 0, 0, 9], [0, -14, 0, 20, 0, 8, -3, 0], [0, -15, 0, -15, 0, 3, -9, 0], [72, 0, 5, 0, -51, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [36, 0, -9, 0, 0, 0, 0, 0], [0, -69, 0, 99, 0, -3, 9, 0], [0, -50, 0, -80, 0, 4, 6, 0], [-6, 0, 3, 0, -9, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0], [96, 0, 15, 0, -7, 0, 0, 3], [0, 21, 0, 0, 0, 0, 0, 0], [0, 6, 0, -115, 0, 0, -28, 0], [244, 0, -6, 0, -85, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [136, 0, -18, 0, 75, 0, 0, -6], [0, -30, 0, 14, 0, -4, 36, 0], [0, -9, 0, -54, 0, 0, 0, 0], [-49, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [72, 0, -9, 0, -21, 0, 0, -9], [0, -63, 0, 52, 0, -15, -3, 0], [0, -17, 0, -222, 0, -15, -3, 0], [0, 0, 0, 0, -27, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [14, 0, 0, 0, 28, 0, 0, -7], [0, 18, 0, 54, 0, 0, -12, 0], [0, 63, 0, -352, 0, 0, 14, 0], [218, 0, -27, 0, -3, 0, 0, 17], [0, 0, 0, 0, 0, 0, 0, 0], [168, 0, -3, 0, 87, 0, 0, -15], [0, 105, 0, -120, 0, -3, 45, 0], [0, 0, 0, -63, 0, 0, 0, 0], [322, 0, -46, 0, -12, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [168, 0, -27, 0, -54, 0, 0, 9], [0, -105, 0, -119, 0, 27, -17, 0], [0, -27, 0, -436, 0, -19, 39, 0], [-75, 0, 18, 0, -30, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0], [-167, 0, 21, 0, -45, 0, 0, 13], [0, 36, 0, 18, 0, -9, 0, 0], [0, -162, 0, -304, 0, 12, -68, 0], [840, 0, -57, 0, -30, 0, 0, -9], [0, 0, 0, 0, 0, 0, 0, 0], [476, 0, -34, 0, 84, 0, 0, -6], [0, 35, 0, 35, 0, -7, 21, 0], [0, -21, 0, -96, 0, 3, -27, 0], [-87, 0, 37, 0, 153, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [81, 0, 0, 0, 0, 0, 0, 0], [0, -27, 0, -120, 0, 15, 19, 0], [0, 51, 0, -370, 0, 29, 33, 0], [-84, 0, 21, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-128, 0, 6, 0, -109, 0, 0, 28], [0, 90, 0, -177, 0, 12, 0, 0], [0, 147, 0, -562, 0, 18, 17, 0], [46, 0, 78, 0, 140, 0, 0, -14], [0, 0, 0, 0, 0, 0, 0, 0], [14, 0, -7, 0, 21, 0, 0, 21], [0, 206, 0, 748, 0, -2, -51, 0], [0, 27, 0, -270, 0, -27, 9, 0], [424, 0, -14, 0, 270, 0, 0, -36], [0, 0, 0, 0, 0, 0, 0, 0], [60, 0, -9, 0, -42, 0, 0, 24], [0, -168, 0, -102, 0, -36, -28, 0], [0, -49, 0, 0, 0, 0, 0, 0], [-45, 0, -27, 0, -45, 0, 0, 9], [0, 0, 0, 0, 0, 0, 0, 0]]}