# Stored data for newform 162.5.d.c, downloaded from the LMFDB on 03 May 2024.
{"label": "162.5.d.c", "space_label": "162.5.d", "level": 162, "weight": 5, "hecke_orbit": 3, "hecke_orbit_code": 9007405497057442, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 1035731582379887313, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [186320859201, 0, -691501698, 0, 2134755, 0, -1602, 0, 1]]], "qexp_display": "q-\\zeta_{24}^{5}q^{2}+8\\zeta_{24}^{2}q^{4}+(\\zeta_{24}-\\zeta_{24}^{3}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "d", "char_is_real": false, "Nk2": 4050, "analytic_conductor": 16.74593401958278, "hecke_ring_index": 34012224, "level_radical": 6, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [162, 6, [83], [5]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [53, 107], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 6], [3, 12]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.765", "prec": 17}, {"__RealLiteral__": 0, "data": "5.654", "prec": 17}, {"__RealLiteral__": 0, "data": "475.538", "prec": 24}, {"__RealLiteral__": 0, "data": "1335.398", "prec": 27}, {"__RealLiteral__": 0, "data": "49602.028", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "4.2.3.c6", "trace_display": [0, 0, 0, -68], "traces": [0, 8, 0, 0, 32, 0, 0, -68, 0, 0, 192, 0, 0, 520, 0, 0, -256, 0, 0, 2176, 0, 0, 960, 0, 0, 704, 0, 0, -1088, 0, 0, -812, 0, 0, -3456, 0, 0, -2144, 0, 0, 768, 0, 0, 7096, 0, 0, -7296, 0, 0, -14880, 0, 0, -4160, 0, 0, -72, 0, 0, 8448, 0, 0, 13936, 0, 0, -4096, 0, 0, -3224, 0, 0, -24960, 0, 0, 17224, 0, 0, 8704, 0, 0, 11560, 0, 0, -21120, 0, 0, 16200, 0, 0, -7680, 0, 0, 75632, 0, 0, 25728, 0, 0, -1580, 0, 0, 11264, 0, 0, -19784, 0, 0, -17568, 0, 0, -81632, 0, 0, -4352, 0, 0, 47376, 0, 0, 14592, 0, 0, -26848, 0, 0, 6496, 0, 0, 10744, 0, 0, -34176, 0, 0, -65152, 0, 0, -55296, 0, 0, 22768, 0, 0, 63936, 0, 0, -77616, 0, 0, -8576, 0, 0, 3100, 0, 0, 14016, 0, 0, -59312, 0, 0, -6144, 0, 0, -272, 0, 0, -54336, 0, 0, -46668, 0, 0, 113536, 0, 0, 151936, 0, 0, 90432, 0, 0, -166016, 0, 0, -29184, 0, 0, -97848, 0, 0, 145536, 0, 0, 140452, 0, 0, 119040, 0, 0, 541672, 0, 0, -13728, 0, 0, -229968, 0, 0, -66560, 0, 0, 79216, 0, 0, 57600, 0, 0, -672232, 0, 0, -288, 0, 0, 65128, 0, 0, 48000, 0, 0, -55064, 0, 0, -67584, 0, 0, 329328, 0, 0, -105408, 0, 0, -88376, 0, 0, 222976, 0, 0, 48128, 0, 0, 96864, 0, 0, -335520, 0, 0, -16384, 0, 0, 344816, 0, 0, -317184, 0, 0, -294300, 0, 0, 25792, 0, 0, 155320, 0, 0, -27840, 0, 0, -221936, 0, 0, -399360, 0, 0, -190496, 0, 0, -171456, 0, 0, -101656, 0, 0, 68896, 0, 0, 307656, 0, 0, 293952, 0, 0, -19336, 0, 0, -69632, 0, 0, 77200, 0, 0, 330432, 0, 0, 7996, 0, 0, 184960, 0, 0, 317592, 0, 0, -404544, 0, 0, -376832, 0, 0, -84480, 0, 0, 52024, 0, 0, -211200, 0, 0, -275672, 0, 0, -129600, 0, 0, 1765688, 0, 0, 377952, 0, 0, 470848, 0, 0, -122880, 0, 0, -11016, 0, 0, -112896, 0, 0, -264072, 0, 0, 302528, 0, 0, 318676, 0, 0, -704640, 0, 0, 174904, 0, 0, -205824, 0, 0, 1017088, 0, 0, -236352, 0, 0, -629244, 0, 0, -25280, 0, 0, -277344, 0, 0, -402912, 0, 0, -1238384, 0, 0, 45056, 0, 0, 805400, 0, 0, 739200, 0, 0, -124436, 0, 0, 158272, 0, 0, -483480, 0, 0, 214464, 0, 0, 368176, 0, 0, -281088, 0, 0, -322960, 0, 0, 30336, 0, 0, -270632, 0, 0, -326528, 0, 0, -587300, 0, 0, -711936, 0, 0, -1035288, 0, 0, 34816, 0, 0, -237024, 0, 0, 384, 0, 0, -371156, 0, 0, 758016, 0, 0, 847924, 0, 0, 811584, 0, 0, 389552, 0, 0, 58368, 0, 0, 471424, 0, 0, -571776, 0, 0, 513824, 0, 0, 214784, 0, 0, -725456, 0, 0, -1150272, 0, 0, -784080, 0, 0, 103936, 0, 0, -141896, 0, 0, -110592, 0, 0, 378360, 0, 0, 42976, 0, 0, -566308, 0, 0, 2537472, 0, 0, 684360, 0, 0, 273408, 0, 0, -262352, 0, 0, 567744, 0, 0, 462908, 0, 0, -1042432, 0, 0, 1544724, 0, 0, 662400, 0, 0, 293920, 0, 0, -221184, 0, 0, -2071976, 0, 0, 57984, 0, 0, 849704, 0, 0, -182144, 0, 0, 2404832, 0, 0, -142464, 0, 0, -417888, 0, 0, 1022976, 0, 0, -778808, 0, 0, 1765824, 0, 0, -696080, 0, 0, -310464, 0, 0, -874044, 0, 0, -432384, 0, 0, 478976, 0, 0, 68608, 0, 0, -5869584, 0, 0, -1407360, 0, 0, 605452, 0, 0, 49600, 0, 0, -565544, 0, 0, -225408, 0, 0, 3047056, 0, 0, 56064, 0, 0, 946984, 0, 0, 1886592, 0, 0, 1038788, 0, 0, 474496, 0, 0, -49016, 0, 0, 582432, 0, 0, 348096, 0, 0, -98304, 0, 0, -2655200, 0, 0, -1033344, 0, 0, -133776, 0, 0, -1088, 0, 0, -595332, 0, 0, -2274432, 0, 0, -1209152, 0, 0, 434688, 0, 0, -4492224, 0, 0, -217344, 0, 0, 381028, 0, 0, -746688, 0, 0, 2026004, 0, 0, 544800, 0, 0, 4253616, 0, 0, 454144, 0, 0, -25520, 0, 0, -2175360, 0, 0, -1537056, 0, 0, -1215488, 0, 0, -1889536, 0, 0, 148416, 0, 0, 438016, 0, 0, 1446912, 0, 0, -1264392, 0, 0, -1623168, 0, 0, 4591760, 0, 0, -664064, 0, 0, 611212, 0, 0, 1253184, 0, 0, 3138208, 0, 0, 233472, 0, 0, -264944, 0, 0, 2477376, 0, 0, 2380068, 0, 0, -1565568, 0, 0, 542068, 0, 0, -2124672, 0, 0, -803504, 0, 0, 582144, 0, 0, -5968, 0, 0, 817536, 0, 0, -1360172, 0, 0, -1123616, 0, 0, 3913216, 0, 0, 375648, 0, 0, 2098872, 0, 0, 1904640, 0, 0, -2265680, 0, 0, 930624, 0, 0, 5862848, 0, 0, 2166688, 0, 0, -2953584, 0, 0, -1554432, 0, 0, -454320, 0, 0, 109824, 0, 0, -8368256, 0, 0, 69312, 0, 0, 1650176, 0, 0, -3679488, 0, 0, 1991932, 0, 0, -2410176, 0, 0, 558160, 0, 0, -266240, 0, 0, -999144, 0, 0, -1195008, 0, 0, 812492, 0, 0, -633728, 0, 0, 3712192, 0, 0, 888192, 0, 0, 4121896, 0, 0, 921600, 0, 0, -3672848, 0, 0, -1636992, 0, 0, 3090024, 0, 0, -2688928, 0, 0, 139184, 0, 0, -118272, 0, 0, -113672, 0, 0, 2304, 0, 0, -4621952, 0, 0, 238848, 0, 0, -441244, 0, 0, 1042048, 0, 0, 499068, 0, 0, 1949760, 0, 0, -2406672, 0, 0, 192000, 0, 0, 3283024, 0, 0, -2663808, 0, 0, -1551348, 0, 0, 440512, 0, 0, -7189976, 0, 0, -286176, 0, 0, -2148224, 0, 0, -1081344, 0, 0, -5633664, 0, 0, 748224, 0, 0, 5470504, 0, 0, 1317312, 0, 0, -2761920, 0, 0, 3686016, 0, 0, 279752, 0, 0, 843264, 0, 0, -1639728, 0, 0, -2701056, 0, 0, -1719552, 0, 0, -1414016, 0, 0, 5559388, 0, 0, 2014944, 0, 0, 3331616, 0, 0, 891904, 0, 0, 1948968, 0, 0, 3442944, 0, 0, 3742740, 0, 0, -385024, 0, 0, 235384, 0, 0, -359424, 0, 0, -2149160, 0, 0, 1549824], "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, 9, 3, 1, 3, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "54.5.b.b", "char_is_minimal": false, "conrey_index": 53, "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, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 0, 0, 0, 0], [0, 1, 0, -1, -3, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-17, 0, 17, 0, 0, 0, -1, 1], [0, 0, 0, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [24, 0, 0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, -30, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 130, 0, 0, 0, 2, 0], [0, -8, 0, 8, 17, 17, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-64, 0, 64, 0, 0, 0, 0, 0], [0, 0, 0, 2, 108, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [272, 0, 0, 0, 0, 0, 0, -2], [0, 8, 0, 0, 0, -24, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 240, 0, 0, 0, 1, 0], [0, 20, 0, -20, 114, 114, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [176, 0, -176, 0, 0, 0, 6, -6], [0, 0, 0, -16, 130, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-136, 0, 0, 0, 0, 0, 0, 8], [0, -22, 0, 0, 0, -264, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -203, 0, 0, 0, -15, 0], [0, 0, 0, 0, 64, 64, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-864, 0, 864, 0, 0, 0, -2, 2], [0, 0, 0, 41, 780, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-268, 0, 0, 0, 0, 0, 0, 14], [0, 16, 0, 0, 0, -272, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 192, 0, 0, 0, -8, 0], [0, -68, 0, 68, 330, 330, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1774, 0, -1774, 0, 0, 0, -6, 6], [0, 0, 0, -8, 240, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-912, 0, 0, 0, 0, 0, 0, -20], [0, 30, 0, 0, 0, -804, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3720, 0, 0, 0, 34, 0], [0, 48, 0, -48, -176, -176, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1040, 0, 1040, 0, 0, 0, 16, -16], [0, 0, 0, -119, 549, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, 0, 0, 0, -27], [0, -64, 0, 0, 0, 136, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2112, 0, 0, 0, 22, 0], [0, 98, 0, -98, -228, -228, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3484, 0, -3484, 0, 0, 0, -24, 24], [0, 0, 0, 120, -203, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-512, 0, 0, 0, 0, 0, 0, 0], [0, 82, 0, 0, 0, 1068, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -806, 0, 0, 0, 6, 0], [0, -16, 0, 16, 864, 864, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6240, 0, 6240, 0, 0, 0, -41, 41], [0, 0, 0, 62, -1998, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2153, 0, 0, 0, 0, 0, 0, -18], [0, -112, 0, 0, 0, 268, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2176, 0, 0, 0, -16, 0], [0, -223, 0, 223, -219, -219, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2890, 0, -2890, 0, 0, 0, 28, -28], [0, 0, 0, 64, 192, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2640, 0, 0, 0, 0, 0, 0, 68], [0, -27, 0, 0, 0, 1698, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4050, 0, 0, 0, -114, 0], [0, -48, 0, 48, -1774, -1774, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1920, 0, 1920, 0, 0, 0, 8, -8], [0, 0, 0, -262, -2826, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9454, 0, 0, 0, 0, 0, 0, 96], [0, 160, 0, 0, 0, 912, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6432, 0, 0, 0, -30, 0], [0, 320, 0, -320, -2274, -2274, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-395, 0, 395, 0, 0, 0, 88, -88], [0, 0, 0, -272, -3720, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1408, 0, 0, 0, 0, 0, 0, -48]]}