# Stored data for newform 54.4.a.d, downloaded from the LMFDB on 14 September 2025. {"Nk2": 864, "analytic_conductor": 3.186103140309993, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [54, 1, [29], [1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[5, [-12, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798949220406, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "54.4.a.d", "level": 54, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3], "level_radical": 6, "minimal_twist": "54.4.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+2q^{2}+4q^{4}+12q^{5}-7q^{7}+8q^{8}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "54.4.a", "trace_display": [2, 0, 12, -7], "trace_hash": 590365085223258785, "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "0.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.957", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.787", "prec": 17}], "trace_zratio": 0, "traces": [0, 1, 2, 0, 4, 12, 0, -7, 8, 0, 24, 60, 0, -79, -14, 0, 16, -108, 0, 11, 48, 0, 120, -132, 0, 19, -158, 0, -28, 96, 0, 20, 32, 0, -216, -84, 0, -169, 22, 0, 96, 192, 0, 488, 240, 0, -264, 204, 0, -294, 38, 0, -316, 360, 0, 720, -56, 0, 192, 156, 0, 83, 40, 0, 64, -948, 0, 47, -432, 0, -168, 216, 0, -511, -338, 0, 44, -420, 0, -529, 192, 0, 384, -1128, 0, -1296, 976, 0, 480, 36, 0, 553, -528, 0, 408, 132, 0, 605, -588, 0, 76, 1248, 0, 965, -632, 0, 720, 1332, 0, -1942, 1440, 0, -112, 516, 0, -1584, 384, 0, 312, 756, 0, 2269, 166, 0, 80, -1272, 0, -52, 128, 0, -1896, 48, 0, -77, 94, 0, -864, 2364, 0, 173, -336, 0, 432, -4740, 0, 1152, -1022, 0, -676, -1608, 0, -997, 88, 0, -840, 240, 0, 614, -1058, 0, 384, 924, 0, 2693, 768, 0, -2256, 1164, 0, 4044, -2592, 0, 1952, -3648, 0, -133, 960, 0, 72, 1800, 0, -547, 1106, 0, -1056, -2028, 0, -6480, 816, 0, 264, 3156, 0, 1127, 1210, 0, -1176, 1116, 0, -3283, 152, 0, 2496, -672, 0, 2304, 1930, 0, -1264, 660, 0, -295, 1440, 0, 2664, 5856, 0, -140, -3884, 0, 2880, 8532, 0, -2644, -224, 0, 1032, -6024, 0, -4462, -3168, 0, 768, -1008, 0, 2448, 624, 0, 1512, -5064, 0, 6257, 4538, 0, 332, -3528, 0, -869, 160, 0, -2544, -2160, 0, -7920, -104, 0, 256, -168, 0, 1183, -3792, 0, 96, -2424, 0, 4320, -154, 0, 188, -396, 0, 1811, -1728, 0, 4728, 1140, 0, -3022, 346, 0, -672, -3072, 0, -8080, 864, 0, -9480, -1344, 0, 6751, 2304, 0, -2044, -4668, 0, 1872, -1352, 0, -3216, 10428, 0, -3416, -1994, 0, 176, 996, 0, 6752, -1680, 0, 480, 1812, 0, 6203, 1228, 0, -2116, 10968, 0, 5760, 768, 0, 1848, -1188, 0, -1501, 5386, 0, 1536, -1428, 0, 8165, -4512, 0, 2328, 564, 0, -6523, 8088, 0, -5184, 1200, 0, 4459, 3904, 0, -7296, 6168, 0, -6001, -266, 0, 1920, -552, 0, 2592, 144, 0, 3600, -5004, 0, -6738, -1094, 0, 2212, -6132, 0, -4291, -2112, 0, -4056, -2520, 0, -2833, -12960, 0, 1632, -7584, 0, -5137, 528, 0, 6312, 5088, 0, -5040, 2254, 0, 2420, 7980, 0, 14256, -2352, 0, 2232, -6348, 0, -1834, -6566, 0, 304, -1464, 0, -1580, 4992, 0, -1344, -10140, 0, -151, 4608, 0, 3860, -1092, 0, -13536, -2528, 0, 1320, -11508, 0, -6271, -590, 0, 2880, -2052, 0, -581, 5328, 0, 11712, 9468, 0, 3026, -280, 0, -7768, -1452, 0, 11180, 5760, 0, 17064, -840, 0, 432, -5288, 0, -448, 12780, 0, 11520, 2064, 0, -12048, 6636, 0, -15658, -8924, 0, -6336, -15564, 0, -4183, 1536, 0, -2016, 13932, 0, -329, 4896, 0, 1248, 29280, 0, 209, 3024, 0, -10128, -2712, 0, 13351, 12514, 0, 9076, 7260, 0, -9439, 664, 0, -7056, -11724, 0, -10368, -1738, 0, 320, -1512, 0, -11968, -5088, 0, -4320, 8892, 0, 14976, -15840, 0, -208, -6756, 0, 3577, 512, 0, -336, 11580, 0, 12240, 2366, 0, -7584, -6228, 0, 11639, 192, 0, -4848, -2160, 0, 5257, 8640, 0, -308, -15168, 0, 15984, 376, 0, -792, -17640, 0, 17705, 3622, 0, -3456, -23304, 0, 3485, 9456, 0, 2280, 1056, 0, 3703, -6044, 0, 692, -19116, 0, -38552, -1344, 0, -6144, 22368, 0, 6192, -16160, 0, 1728, 8340, 0, -14677, -18960, 0, -2688, -2508, 0, -10069, 13502, 0, 4608, 7896, 0, 21600, -4088, 0, -9336, 1572, 0, 220, 3744, 0, -2704, 1368, 0, 9072, -6432, 0, 20856, -23712, 0, -11014, -6832, 0, -3988, 27228, 0, -6415, 352, 0, 1992, -16116, 0, 15851, 13504, 0, -3360, 5772, 0, -27781, 960, 0, 3624, -252, 0, -17639, 12406, 0, 2456, 18252, 0, -29869, -4232, 0, 21936, -624, 0, 23226, 11520, 0, 1536, 3480, 0, -7432, 3696, 0, -2376, -12960, 0, 9360, -3002, 0, 10772, 23592, 0, 576, 3072, 0, -2856, 32280, 0, 22619, 16330, 0, -9024, -924, 0, -12672, 4656, 0, 1128, 4980, 0, -19861, -13046, 0, 16176, -8292, 0, -4235, -10368, 0, 2400, 19728, 0, 28368, 8918, 0, 7808, -28440, 0, 27272, -14592, 0, 12336, 2076, 0, -20736, -12002, 0, -532, -21996, 0, -1859, 3840, 0, -1104, -8736, 0, 2009, 5184, 0, 288, -2640, 0, -56880, 7200, 0, -10008, 26280, 0, -6755, -13476, 0, -2188, 1824, 0, 20900, 4424, 0, -12264, -52704, 0, -17638, -8582, 0, -4224, 2820, 0, 30080, -8112, 0, -5040, 15708, 0, -19296, -5666, 0, -25920, -9324, 0, 20423, 3264, 0, -15168, -11964, 0, -4399, -10274, 0, 1056, -20652, 0, 13594, 12624, 0, 10176, -12324, 0, 27407, -10080, 0, 4508, 5976, 0, 380, 4840, 0, 15960, 2112, 0, 12960, 28512, 0, -4704, 7368, 0, 24131, 4464, 0, -12696, -3612, 0, -6557, -3668, 0, -13132, 912, 0, -22032, 608, 0, -2928, -30660, 0, 11088, -3160, 0, 9984, -12888, 0, -6856, -2688, 0, -20280, 32316, 0, 5368, -302, 0, 9216, 636, 0, 39827, 7720, 0, -2184, 38124, 0, 18965, -27072, 0, -5056, 31752, 0, 13968, 2640, 0, -23016, 27816, 0, -15173, -12542, 0, -1180, 48528, 0, -15883, 5760, 0, -4104, 22308, 0, -12337, -1162, 0, 10656, -11352, 0, -2527, 23424, 0, 18936, -26388, 0, -43776, 6052, 0, -560, -31740, 0, -3713, -15536, 0, -2904, 8904, 0, 6383, 22360, 0, 11520, 28908, 0, 36893, 34128, 0, -1680, -45528, 0, 364, 864, 0, -10576, 2244, 0, 21600, -896, 0, 25560, 1920, 0, -38880, 23040, 0, 4128, -6564, 0, -31201, -24096, 0, 13272, 23856, 0, -67680, -31316, 0, -17848, -336, 0, 23492, -12672, 0, -31128, -17064, 0, -3211, -8366, 0, 3072, -15096, 0, -3234, -4032, 0, 27864, -77760, 0, -14965, -658, 0, 9792, 19524, 0, -25344, 2496, 0, 58560, 11076, 0, 40369, 418, 0, 6048, -44748, 0, 37872, -20256, 0, -5424, -16548, 0, -29391, 26702, 0, 25028, 13524, 0, 41519, 18152, 0, 14520, 28404, 0, -1211, -18878, 0, 1328, 43032, 0, 2160, -14112, 0, -23448, 18132, 0, 13392, -20736, 0, -3476, -64416, 0, -44467, 640, 0, -3024, -39396, 0, 19550, -23936, 0, -10176], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 2, 0, 4, 12, 0, -7, 8, 0, 24, 60, 0, -79, -14, 0, 16, -108, 0, 11, 48, 0, 120, -132, 0, 19, -158, 0, -28, 96, 0, 20, 32, 0, -216, -84, 0, -169, 22, 0, 96, 192, 0, 488, 240, 0, -264, 204, 0, -294, 38, 0, -316, 360, 0, 720, -56, 0, 192, 156, 0, 83, 40, 0, 64, -948, 0, 47, -432, 0, -168, 216, 0, -511, -338, 0, 44, -420, 0, -529, 192, 0, 384, -1128, 0, -1296, 976, 0, 480, 36, 0, 553, -528, 0, 408, 132, 0, 605, -588, 0, 76, 1248, 0, 965, -632, 0, 720, 1332, 0, -1942, 1440, 0, -112, 516, 0, -1584, 384, 0, 312, 756, 0, 2269, 166, 0, 80, -1272, 0, -52, 128, 0, -1896, 48, 0, -77, 94, 0, -864, 2364, 0, 173, -336, 0, 432, -4740, 0, 1152, -1022, 0, -676, -1608, 0, -997, 88, 0, -840, 240, 0, 614, -1058, 0, 384, 924, 0, 2693, 768, 0, -2256, 1164, 0, 4044, -2592, 0, 1952, -3648, 0, -133, 960, 0, 72, 1800, 0, -547, 1106, 0, -1056, -2028, 0, -6480, 816, 0, 264, 3156, 0, 1127, 1210, 0, -1176, 1116, 0, -3283, 152, 0, 2496, -672, 0, 2304, 1930, 0, -1264, 660, 0, -295, 1440, 0, 2664, 5856, 0, -140, -3884, 0, 2880, 8532, 0, -2644, -224, 0, 1032, -6024, 0, -4462, -3168, 0, 768, -1008, 0, 2448, 624, 0, 1512, -5064, 0, 6257, 4538, 0, 332, -3528, 0, -869, 160, 0, -2544, -2160, 0, -7920, -104, 0, 256, -168, 0, 1183, -3792, 0, 96, -2424, 0, 4320, -154, 0, 188, -396, 0, 1811, -1728, 0, 4728, 1140, 0, -3022, 346, 0, -672, -3072, 0, -8080, 864, 0, -9480, -1344, 0, 6751, 2304, 0, -2044, -4668, 0, 1872, -1352, 0, -3216, 10428, 0, -3416, -1994, 0, 176, 996, 0, 6752, -1680, 0, 480, 1812, 0, 6203, 1228, 0, -2116, 10968, 0, 5760, 768, 0, 1848, -1188, 0, -1501, 5386, 0, 1536, -1428, 0, 8165, -4512, 0, 2328, 564, 0, -6523, 8088, 0, -5184, 1200, 0, 4459, 3904, 0, -7296, 6168, 0, -6001, -266, 0, 1920, -552, 0, 2592, 144, 0, 3600, -5004, 0, -6738, -1094, 0, 2212, -6132, 0, -4291, -2112, 0, -4056, -2520, 0, -2833, -12960, 0, 1632, -7584, 0, -5137, 528, 0, 6312, 5088, 0, -5040, 2254, 0, 2420, 7980, 0, 14256, -2352, 0, 2232, -6348, 0, -1834, -6566, 0, 304, -1464, 0, -1580, 4992, 0, -1344, -10140, 0, -151, 4608, 0, 3860, -1092, 0, -13536, -2528, 0, 1320, -11508, 0, -6271, -590, 0, 2880, -2052, 0, -581, 5328, 0, 11712, 9468, 0, 3026, -280, 0, -7768, -1452, 0, 11180, 5760, 0, 17064, -840, 0, 432, -5288, 0, -448, 12780, 0, 11520, 2064, 0, -12048, 6636, 0, -15658, -8924, 0, -6336, -15564, 0, -4183, 1536, 0, -2016, 13932, 0, -329, 4896, 0, 1248, 29280, 0, 209, 3024, 0, -10128, -2712, 0, 13351, 12514, 0, 9076, 7260, 0, -9439, 664, 0, -7056, -11724, 0, -10368, -1738, 0, 320, -1512, 0, -11968, -5088, 0, -4320, 8892, 0, 14976, -15840, 0, -208, -6756, 0, 3577, 512, 0, -336, 11580, 0, 12240, 2366, 0, -7584, -6228, 0, 11639, 192, 0, -4848, -2160, 0, 5257, 8640, 0, -308, -15168, 0, 15984, 376, 0, -792, -17640, 0, 17705, 3622, 0, -3456, -23304, 0, 3485, 9456, 0, 2280, 1056, 0, 3703, -6044, 0, 692, -19116, 0, -38552, -1344, 0, -6144, 22368, 0, 6192, -16160, 0, 1728, 8340, 0, -14677, -18960, 0, -2688, -2508, 0, -10069, 13502, 0, 4608, 7896, 0, 21600, -4088, 0, -9336, 1572, 0, 220, 3744, 0, -2704, 1368, 0, 9072, -6432, 0, 20856, -23712, 0, -11014, -6832, 0, -3988, 27228, 0, -6415, 352, 0, 1992, -16116, 0, 15851, 13504, 0, -3360, 5772, 0, -27781, 960, 0, 3624, -252, 0, -17639, 12406, 0, 2456, 18252, 0, -29869, -4232, 0, 21936, -624, 0, 23226, 11520, 0, 1536, 3480, 0, -7432, 3696, 0, -2376, -12960, 0, 9360, -3002, 0, 10772, 23592, 0, 576, 3072, 0, -2856, 32280, 0, 22619, 16330, 0, -9024, -924, 0, -12672, 4656, 0, 1128, 4980, 0, -19861, -13046, 0, 16176, -8292, 0, -4235, -10368, 0, 2400, 19728, 0, 28368, 8918, 0, 7808, -28440, 0, 27272, -14592, 0, 12336, 2076, 0, -20736, -12002, 0, -532, -21996, 0, -1859, 3840, 0, -1104, -8736, 0, 2009, 5184, 0, 288, -2640, 0, -56880, 7200, 0, -10008, 26280, 0, -6755, -13476, 0, -2188, 1824, 0, 20900, 4424, 0, -12264, -52704, 0, -17638, -8582, 0, -4224, 2820, 0, 30080, -8112, 0, -5040, 15708, 0, -19296, -5666, 0, -25920, -9324, 0, 20423, 3264, 0, -15168, -11964, 0, -4399, -10274, 0, 1056, -20652, 0, 13594, 12624, 0, 10176, -12324, 0, 27407, -10080, 0, 4508, 5976, 0, 380, 4840, 0, 15960, 2112, 0, 12960, 28512, 0, -4704, 7368, 0, 24131, 4464, 0, -12696, -3612, 0, -6557, -3668, 0, -13132, 912, 0, -22032, 608, 0, -2928, -30660, 0, 11088, -3160, 0, 9984, -12888, 0, -6856, -2688, 0, -20280, 32316, 0, 5368, -302, 0, 9216, 636, 0, 39827, 7720, 0, -2184, 38124, 0, 18965, -27072, 0, -5056, 31752, 0, 13968, 2640, 0, -23016, 27816, 0, -15173, -12542, 0, -1180, 48528, 0, -15883, 5760, 0, -4104, 22308, 0, -12337, -1162, 0, 10656, -11352, 0, -2527, 23424, 0, 18936, -26388, 0, -43776, 6052, 0, -560, -31740, 0, -3713, -15536, 0, -2904, 8904, 0, 6383, 22360, 0, 11520, 28908, 0, 36893, 34128, 0, -1680, -45528, 0, 364, 864, 0, -10576, 2244, 0, 21600, -896, 0, 25560, 1920, 0, -38880, 23040, 0, 4128, -6564, 0, -31201, -24096, 0, 13272, 23856, 0, -67680, -31316, 0, -17848, -336, 0, 23492, -12672, 0, -31128, -17064, 0, -3211, -8366, 0, 3072, -15096, 0, -3234, -4032, 0, 27864, -77760, 0, -14965, -658, 0, 9792, 19524, 0, -25344, 2496, 0, 58560, 11076, 0, 40369, 418, 0, 6048, -44748, 0, 37872, -20256, 0, -5424, -16548, 0, -29391, 26702, 0, 25028, 13524, 0, 41519, 18152, 0, 14520, 28404, 0, -1211, -18878, 0, 1328, 43032, 0, 2160, -14112, 0, -23448, 18132, 0, 13392, -20736, 0, -3476, -64416, 0, -44467, 640, 0, -3024, -39396, 0, 19550, -23936, 0, -10176]}