# Stored data for newform 162.7.d.e, downloaded from the LMFDB on 19 April 2024. {"label": "162.7.d.e", "space_label": "162.7.d", "level": 162, "weight": 7, "hecke_orbit": 5, "hecke_orbit_code": 18014604785352866, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 723840150533070790, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [14774554437890625, 0, -6180849281250, 0, 2464171875, 0, -50850, 0, 1]]], "qexp_display": "q+\\zeta_{24}^{5}q^{2}+2^{5}\\zeta_{24}^{2}q^{4}+(5\\zeta_{24}-5\\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": 7938, "analytic_conductor": 37.26876154641586, "hecke_ring_index": 544195584, "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": 7, "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, 10], [3, 12]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.086", "prec": 17}, {"__RealLiteral__": 0, "data": "7.583", "prec": 17}, {"__RealLiteral__": 0, "data": "7.406", "prec": 17}, {"__RealLiteral__": 0, "data": "399.474", "prec": 24}, {"__RealLiteral__": 0, "data": "853.073", "prec": 24}, {"__RealLiteral__": 0, "data": "33630.859", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "6.2.3.c6", "trace_display": [0, 0, 0, -836], "traces": [0, 8, 0, 0, 128, 0, 0, -836, 0, 0, -3840, 0, 0, -440, 0, 0, -4096, 0, 0, -13376, 0, 0, -19200, 0, 0, 39200, 0, 0, -53504, 0, 0, -160172, 0, 0, 78336, 0, 0, -301088, 0, 0, -61440, 0, 0, -90152, 0, 0, 274944, 0, 0, 202560, 0, 0, 14080, 0, 0, -269640, 0, 0, -86016, 0, 0, -584144, 0, 0, -262144, 0, 0, 766792, 0, 0, 867840, 0, 0, 3149512, 0, 0, -214016, 0, 0, -323000, 0, 0, 2081280, 0, 0, 2720520, 0, 0, 614400, 0, 0, -3921808, 0, 0, -1970688, 0, 0, -4432940, 0, 0, 2508800, 0, 0, 336088, 0, 0, 5484672, 0, 0, -7351328, 0, 0, -856064, 0, 0, -5852880, 0, 0, 224256, 0, 0, -1753888, 0, 0, 5125504, 0, 0, -4344392, 0, 0, -10053120, 0, 0, 5690144, 0, 0, 5013504, 0, 0, -128528, 0, 0, 7633152, 0, 0, -9725040, 0, 0, -4817408, 0, 0, -11816900, 0, 0, 2613504, 0, 0, 12728656, 0, 0, 1966080, 0, 0, 7220464, 0, 0, 1400064, 0, 0, -25904172, 0, 0, -5769728, 0, 0, 22189600, 0, 0, 15895296, 0, 0, 14493184, 0, 0, 4399104, 0, 0, -2786616, 0, 0, 49344000, 0, 0, -4104764, 0, 0, -6481920, 0, 0, -30426392, 0, 0, -5264256, 0, 0, 20373840, 0, 0, 901120, 0, 0, 18370576, 0, 0, -2626560, 0, 0, 64152536, 0, 0, -4314240, 0, 0, -7670456, 0, 0, -54228480, 0, 0, -35134136, 0, 0, 2752512, 0, 0, -51978960, 0, 0, 26263296, 0, 0, 41430664, 0, 0, -37385216, 0, 0, -93696064, 0, 0, -58800000, 0, 0, 2731680, 0, 0, -4194304, 0, 0, 21572624, 0, 0, -58242048, 0, 0, 81643140, 0, 0, -24537344, 0, 0, -8311880, 0, 0, 6501120, 0, 0, 65212048, 0, 0, 55541760, 0, 0, -117643328, 0, 0, -61645056, 0, 0, 31688936, 0, 0, 50392192, 0, 0, 41154120, 0, 0, -36605184, 0, 0, -79867816, 0, 0, 6848512, 0, 0, -127633520, 0, 0, 69884160, 0, 0, 89557948, 0, 0, -20672000, 0, 0, 48588408, 0, 0, -52992768, 0, 0, 607235200, 0, 0, 33300480, 0, 0, -76490216, 0, 0, -61209600, 0, 0, 109381096, 0, 0, -87056640, 0, 0, -203370376, 0, 0, 96461952, 0, 0, 81872992, 0, 0, 39321600, 0, 0, 74227320, 0, 0, -160017408, 0, 0, 40894008, 0, 0, -62748928, 0, 0, -1825388, 0, 0, 45611520, 0, 0, -24088328, 0, 0, 63062016, 0, 0, -138718208, 0, 0, -38578944, 0, 0, -1215900, 0, 0, -283708160, 0, 0, -164497824, 0, 0, 124659072, 0, 0, 346899472, 0, 0, 40140800, 0, 0, -48411880, 0, 0, -42800640, 0, 0, -120659444, 0, 0, -10754816, 0, 0, -617007960, 0, 0, -92375808, 0, 0, 275895856, 0, 0, 351019008, 0, 0, -151199440, 0, 0, 348403200, 0, 0, 71911384, 0, 0, -117621248, 0, 0, -446793380, 0, 0, 417973248, 0, 0, 211281480, 0, 0, 27394048, 0, 0, -729599904, 0, 0, -290164224, 0, 0, 97565068, 0, 0, -374584320, 0, 0, 92746612, 0, 0, 43202304, 0, 0, -252214672, 0, 0, 3588096, 0, 0, -709395200, 0, 0, 71357952, 0, 0, 234163424, 0, 0, 56124416, 0, 0, -90639632, 0, 0, 97793280, 0, 0, 77796720, 0, 0, 328032256, 0, 0, 287842456, 0, 0, 382058496, 0, 0, 1736387640, 0, 0, -69510272, 0, 0, -344240548, 0, 0, -210573312, 0, 0, 617792040, 0, 0, 321699840, 0, 0, -477561296, 0, 0, -355858176, 0, 0, -247377028, 0, 0, 364169216, 0, 0, -151124940, 0, 0, 49006080, 0, 0, 814072480, 0, 0, 80216064, 0, 0, 442459288, 0, 0, 435494400, 0, 0, 398679752, 0, 0, 4112896, 0, 0, -2665312672, 0, 0, -220574208, 0, 0, -291026880, 0, 0, 488521728, 0, 0, -138803768, 0, 0, 12800256, 0, 0, 2335323760, 0, 0, -155600640, 0, 0, -826337052, 0, 0, 160951296, 0, 0, 203422304, 0, 0, 154157056, 0, 0, -2004978960, 0, 0, 518622720, 0, 0, 701324812, 0, 0, -756281600, 0, 0, -273663368, 0, 0, 425955840, 0, 0, -95076272, 0, 0, 41816064, 0, 0, -1160468504, 0, 0, -645490176, 0, 0, -894617500, 0, 0, -407316992, 0, 0, 80769544, 0, 0, -355239552, 0, 0, 880378752, 0, 0, 125829120, 0, 0, -924509600, 0, 0, -585967104, 0, 0, -530536464, 0, 0, 115527424, 0, 0, 1738678140, 0, 0, 112710144, 0, 0, 662262688, 0, 0, -44802048, 0, 0, 455124672, 0, 0, -197299200, 0, 0, 1136525284, 0, 0, -1657867008, 0, 0, -1321380844, 0, 0, -809416320, 0, 0, 1770758640, 0, 0, -92315648, 0, 0, -464680880, 0, 0, -72245760, 0, 0, 125977248, 0, 0, -710067200, 0, 0, -406559488, 0, 0, 1413217536, 0, 0, 725918464, 0, 0, 1017298944, 0, 0, 661482360, 0, 0, -411508224, 0, 0, 426105680, 0, 0, 231890944, 0, 0, -837046196, 0, 0, -1662931200, 0, 0, -695652416, 0, 0, -140771328, 0, 0, 964338064, 0, 0, 1142284032, 0, 0, 821653380, 0, 0, -178343424, 0, 0, -8312012, 0, 0, -875770368, 0, 0, 4621401232, 0, 0, 789504000, 0, 0, 664637456, 0, 0, 1080224256, 0, 0, 900785332, 0, 0, 131352448, 0, 0, -2719467200, 0, 0, 197625984, 0, 0, -1378538568, 0, 0, -414842880, 0, 0, 1973180080, 0, 0, -2175893760, 0, 0, -1152475456, 0, 0, -486822272, 0, 0, -28405296, 0, 0, 1505058816, 0, 0, -2088254160, 0, 0, 168456192, 0, 0, 1283182144, 0, 0, 1009452288, 0, 0, 2957932352, 0, 0, 1303925760, 0, 0, -547356644, 0, 0, 250715904, 0, 0, -1369236080, 0, 0, 14417920, 0, 0, 2141574840, 0, 0, -4818776064, 0, 0, -1802197588, 0, 0, -587858432, 0, 0, 2356753984, 0, 0, -2251353600, 0, 0, -1769067512, 0, 0, -168099840, 0, 0, -1675196432, 0, 0, 2009442816, 0, 0, 1180872360, 0, 0, 1026440576, 0, 0, 835695344, 0, 0, -2691729408, 0, 0, 904029976, 0, 0, 138055680, 0, 0, -106129856, 0, 0, -306435072, 0, 0, -1126249756, 0, 0, -490909184, 0, 0, -882847620, 0, 0, -905207040, 0, 0, -6686656272, 0, 0, -867655680, 0, 0, -1629899792, 0, 0, 6070310400, 0, 0, 1457507916, 0, 0, 1124292352, 0, 0, -1213577624, 0, 0, -79542912, 0, 0, 8329600, 0, 0, 176160768, 0, 0, 1455522816, 0, 0, 678134016, 0, 0, -2063504792, 0, 0, -831663360, 0, 0, -753491520, 0, 0, -2674051584, 0, 0, 159340808, 0, 0, -840425472, 0, 0, -1730113200, 0, 0, -2510681088, 0, 0, -2884747872, 0, 0, 2651562496, 0, 0, -403453124, 0, 0, 4102293120, 0, 0, -100053472, 0, 0, -598163456, 0, 0, -2541752568, 0, 0, 5195394048, 0, 0, 2194976340, 0, 0, 2998274048, 0, 0, 2205840184, 0, 0, 1337601024, 0, 0, 305332120, 0, 0, -3763200000], "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": "54.7.b.c", "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, 32, 0, 0, 0, 0, 0], [0, 5, 0, -5, -15, -15, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-209, 0, 209, 0, 0, 0, -1, 1], [0, 0, 0, 0, -32, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-480, 0, 0, 0, 0, 0, 0, 5], [0, -29, 0, 0, 0, -150, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -110, 0, 0, 0, -22, 0], [0, 32, 0, -32, -209, -209, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1024, 0, 1024, 0, 0, 0, 0, 0], [0, 0, 0, 106, 612, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1672, 0, 0, 0, 0, 0, 0, 46], [0, 160, 0, 0, 0, -480, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -4800, 0, 0, 0, -29, 0], [0, -260, 0, 260, 1074, 1074, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9800, 0, -9800, 0, 0, 0, 150, -150], [0, 0, 0, -704, 110, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6688, 0, 0, 0, 0, 0, 0, 32], [0, -422, 0, 0, 0, -672, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -40043, 0, 0, 0, -15, 0], [0, 0, 0, 0, -1024, -1024, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [19584, 0, -19584, 0, 0, 0, 106, -106], [0, 0, 0, 1525, 6780, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-37636, 0, 0, 0, 0, 0, 0, -106], [0, 1472, 0, 0, 0, -1672, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -15360, 0, 0, 0, 160, 0], [0, 2468, 0, -2468, 8130, 8130, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-22538, 0, 22538, 0, 0, 0, -654, 654], [0, 0, 0, -928, 4800, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [34368, 0, 0, 0, 0, 0, 0, -260], [0, -3810, 0, 0, 0, -15396, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 50640, 0, 0, 0, 418, 0], [0, -4800, 0, 4800, 9800, 9800, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3520, 0, -3520, 0, 0, 0, -704, 704], [0, 0, 0, -43, 42849, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-33705, 0, 0, 0, 0, 0, 0, -315], [0, 1024, 0, 0, 0, -6688, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -21504, 0, 0, 0, -422, 0], [0, 2938, 0, -2938, 876, 876, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-146036, 0, 146036, 0, 0, 0, -312, 312], [0, 0, 0, -480, 40043, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-32768, 0, 0, 0, 0, 0, 0, 0], [0, 10010, 0, 0, 0, -78540, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 191698, 0, 0, 0, 366, 0], [0, -3392, 0, 3392, 19584, 19584, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [216960, 0, -216960, 0, 0, 0, 1525, -1525], [0, 0, 0, -2762, 59634, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [393689, 0, 0, 0, 0, 0, 0, -162], [0, -3392, 0, 0, 0, -37636, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -53504, 0, 0, 0, 1472, 0], [0, 1261, 0, -1261, 10209, 10209, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-80750, 0, 80750, 0, 0, 0, 4996, -4996], [0, 0, 0, 5120, 15360, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [260160, 0, 0, 0, 0, 0, 0, 2468], [0, -19719, 0, 0, 0, 10938, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 680130, 0, 0, 0, -4650, 0], [0, 20928, 0, -20928, -22538, -22538, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [153600, 0, -153600, 0, 0, 0, -928, 928], [0, 0, 0, -1862, 124182, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-490226, 0, 0, 0, 0, 0, 0, 4488], [0, -8320, 0, 0, 0, 34368, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -492672, 0, 0, 0, -3810, 0], [0, -30440, 0, 30440, 192750, 192750, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1108235, 0, 1108235, 0, 0, 0, -4232, 4232], [0, 0, 0, 13376, -50640, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [313600, 0, 0, 0, 0, 0, 0, -4800]]}