# Stored data for newform 158.5.f.a, downloaded from the LMFDB on 21 May 2024. {"Nk2": 3950, "analytic_conductor": 16.332454167247402, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 79, "char_degree": 12, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 26, "char_parity": -1, "char_values": [158, 26, [3], [21]], "cm_discs": [], "conrey_index": 15, "dim": 336, "has_non_self_twist": 1, "hecke_cutters": [], "hecke_orbit": 1, "hecke_orbit_code": 343681269918, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 79, 6, -1, 26, 0]], "is_cm": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "158.5.f.a", "level": 158, "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": true, "level_primes": [2, 79], "level_radical": 158, "minimal_twist": "158.5.f.a", "prim_orbit_index": 6, "related_objects": [], "relative_dim": 28, "rm_discs": [], "sato_tate_group": "4.2.3.c26", "self_twist_discs": [], "self_twist_type": 0, "space_label": "158.5.f", "trace_display": [0, 0, 0, 0], "traces": [336, 0, 0, -224, 0, 0, 0, 0, 728, -64, -396, 0, 504, 0, -1300, -1792, 0, -1152, -212, 0, -528, 3520, -204, 0, -1492, 768, -2730, 0, 0, 0, -4052, 0, 0, 0, -7722, 5824, -12064, -1536, -12896, -512, 0, 11712, 0, 13056, 3140, 448, -4836, 0, 27612, -23040, 72, 4032, 0, 0, 12448, 0, 11440, 0, 9360, 0, 0, 2688, -83538, -14336, -31656, -7488, 62392, 9360, 53352, -13728, 33852, -9216, 23778, 27456, 43992, 9328, -17316, 0, -316, 0, -56400, -30784, -111372, -58720, -88088, -44928, 18866, -5120, -15756, 132640, 32734, 2736, -45864, 56576, 57384, 0, 163566, 129024, 136574, -31072, -59616, -57280, 0, 6144, 26116, 0, -99450, 0, 0, 84480, -54426, 0, 84630, 0, -9348, 0, -423794, -91520, -51336, 0, -61168, 149760, 53784, 46624, -24336, 0, 0, 0, 82264, 4096, 91092, -127920, 259740, -41472, 0, 0, -65520, 183040, -501748, 0, -177116, -131040, 316332, 46592, 671710, -384, 252200, 0, 312, -315744, -16012, 17664, 559260, 0, 122352, 103168, 0, -327936, 66568, -4096, -95472, -250368, -69948, 0, -1119482, 27072, 210570, 40448, 51668, 0, -365284, 18720, -642330, 100608, -373672, -25344, 62500, -15616, 547254, -221152, 337540, 0, 656416, 3584, -292110, 355680, -289432, -196560, -150876, 131776, 128856, 0, 116064, -220800, 0, 105664, -78624, 238720, 309608, -64512, -372684, -97600, 116376, 576, -106340, -178464, 244232, -92544, -490230, -485376, -1414270, -189696, -114692, 0, 190008, 49920, 594386, 209664, 689234, 141184, -218166, 1433920, -39280, 0, 984048, 549120, 1125696, -134992, 1125436, 327936, -127456, 93184, 356460, 353024, -201838, 0, 403268, 18816, -721932, -144768, 298228, -683712, -795340, -176384, -471030, -674176, -1190526, -68352, -2041858, -828288, -888108, 0, 170272, -1334112, 753590, -114688, -274044, -253312, -541756, 167328, 0, 195680, 996852, 372736, 2179268, 1148160, 417326, 499136, 189210, 134784, 291018, 0, 828556, -442624, 100206, -111488, -562842, 0, -152036, 0, 457704, 276864, -899336, 776880, 30212, 470720, -956808, 192512, 1171988, -499200, 1766232, -129056, 0, 273312, -809900, 0, -1879800, 0, 324336, -569088, 602760, -631104, -212394, -13568, -257322, 173056, -130104, 151008, 954236, -180800, 1815060, 0, -216316, 351936, 0, 228352, 1238316, -725408, -486512, 0, -1285340, 0, -49998, -12320, -566090, -850176, -1109088, -186368, -571134, 943488, -638274, 660912, -932256, 864576, -2308980, 129280, 702110, 148992, 1413472, 0, 492924, 764736, -2060058, 678912, -2113410, -624000, 889044, -973520, -865800, -1078272, 1920672, -40960, 135486, 1543296, 1874600, 134784, 202514, 203040, -3812562, -226816, -365240, -915456, -1406860, -261872, 59340, -3277376, -241822, -13056, -3095950, 409344, -1229256, 0, -258076, 1280448, 5519410, 0, 3919968, 5289248, 1637142, 1165440, 568788, 967200, 1072740, 0, 4708340, -194688, 3677258, 15184, -956736, 794560, -2766946, -365568, -431262, 0, 1041252, -200544, -793880, -792480, 2478848, -657920, 1697514, -1539200, 262166, -569904, -6031244, 956928, -5548530, -458240, -904410, -1173120, -331968, -1526720, -1116564, -5796512, -4850268, 49152, -2637816, -2440192, 0, 483072, -413712, -174720, 4504136, 0, 36114, 3722688, -257054, 795600, 2701166, 1224288, -260100, -264576, 3783438, 990912, -3294400, 0, -3154590, -1033344, -2060424, 1214976, -5895704, 49920, 1651104, -205568, -1901412, -1238880, 4947874, 0, 5649540, -1076480, 0, 280800, 1476904, 1680640, 915408, 718848, 3175552, -1204320, -720952, -351424, 2729454, -2834112, 3438110, 0, 1098968, 1025024, 4891560, -216480, -428792, 4072224, 1667512, 732160, 0, 1076864, 2631248, -410688, -585312, -1045440, -48576, 0, -3791554, -408960, -3839698, -784704, -2408784, 1368640, -1053428, 0, -3288194, -102944, -3380832, 816112, -1416128, 1691520, 2996030, -13056, -5942388, 0, 107900, 1561248, -3243292, 1073280, -4403022, 0, 1938076, 771648, -3558152, -1052480, 5086302, -8843456, 82238, 0, -5560620, -1566592, 6142266, 2633280, -3268824, 2969280, -1683896, 32768, -416832, 2888704, 3636964, -903648, 10375166, -2457280, -4310670, 299520, 8356780, 0, -938860, 2016352, 1259310, 2089152, 5486208, 2363904, 325260, 3557792, 5348616, 1752192, 494046, 461760, 3873636, 425984, 2000934, -3002496, -17654, 224640, -71370, -1186784, -3201666, 0, 582320, -43968, -1326560, -1029808, 3671412, -2481120, -4196218, -439296, -2455652, 95936, -4402560, 703008, -3698760, -1491840, -2232360, -2196480, -8577108, -4516928, 267410, -5084640, -2998382, -1903104, -2740572, -5378048, 0, 2982912, -8482152, 614016, 6474546, 1389440, -8590530, -3072, 6084064, -1600768, 6127290, 449280, 738728, -4249440, 7734330, -1286272, -2451336, 3773952, 6485826, -2437344, 4418556, 8934432, -3911166, 1377792, 6889116, 2693568, 1437956, -956768, 3136086, -4047680, -1689974, -98304, 0, 505856, 4984200, 2045680, -3485144, 636480, 1242796, -1357824, 5323680, 1476512, -1302808, -1394880, 4669574, -2303808, -3596424, 0, 822724, -1939776, -3768128, 1824992, 2348352, 4229056, 0, 2118912, 3687508, -2702144, -827502, -1034944, -7289956, -5684640, 71916, -32768, -589752, -2345984, 45636, 0, -12926344, 2718144, 5530512, -1337344, 1333488, 1233792, -3536364, 319840, 5293068, 2961472, -4532036, 0, 7346068, -594816, -4911660, -3068000, -13656630, -8910720, 5781310, 762368, -27924156, -2095808, -14404, -4472448, -4758390, 2175872, -4352400, -208896, 10191662, 7018560, -16762564, 293744, 6767148, -2842368, -5635916, 0, 2831776, -950112, 11464320, 2010240, 842400, 3290976, 24400312, 0, 6234072, 19752512, -857948, 4960800, 15156310, 12676544, -1624740, 2362368, 14615870, 4296864, 1815594, 6006000, 5679492, 661024, -1736878, -202752, 2316900, 1161472, 5986422, 1311824, 1539876, 0, -8780362, -124928, 1160106, -3101696, 3294704, -265152, -12895428, -2283008, -4573356, 1903232, -7651002, -1736640, -2862912, -4272880, -8177364, -5472896, -15943488, 978432, -1142338, -12345216, -14823168, -4610784, 4150148, -18202176, 0, 587776, -31755990, -1835392, -5913076, -2821104, -17394702, 6169536, 2202744, -2845440, 1969110, 2359968, -13895952, -2058368, 4932426, -5954208, -5523598, 0, 7726854, 592384, 5763522, 9015776, -2683002, 3017664, 38936638, -1421824, 10981014, 12962080, 13679754, 2041104, 10729810, 517824, 0, 0, 12663690, -1996800, -11310624, 0, 4058940, -4380480, 2134952, 1428480, 1244724, -7638464, 13364052, -5975840, 2315664, 1909440, -2684878, 1524224, 5843916, 1129856, 5852420, 628992, 0, 2771584, 5280612, 1909760, -4550000, -420480, -3833744, -1538368, 4777734, -5788640, -4829164, 1241088, -2596676, 3581760, -10763682, 2403648, -1944332, -3226752, -87152, -1699328, -15313032, 2598720, 7498322, 1979328, -48538496, 0, -3728904, -2894080, -13488878, 3339648, -32777368, -9490416, -370278, -86432, -18173350, 379392, 20826546, -8837376, -4425954, 3520096, -7762456, -2281344, 37640824, 258048, -1529658, 4950912, 19954382, -3921840, 5240508, 15585440, 8169414, -1812992, 24812844, 2367552, 7850440, -3071328, 26867832, 0, -2790996, 1347840, 6204068, 6439680, 14786616, 5272544, 60138, 10551360, 37277898, 1956864, -2684298, 13565760, -2268084, -2218320, 4487184, 3045504, -4511190, 0, 6503432, 2750208, -311922, 0, 10381746, 3863360, 2353294, -718848, 9098164, -7085088, -13440726, 4861792, -8008040, -11601696, -23945948, 1420672, -5095038, -22351808, -2182050, -109200, -42403610, -4883840, 3419526, -5418240, -13545018, -1478400, 1317280, -6325440, 0, 3143072, -35987718, 0, 9368554, -6279936, -24372894, 7872384, 5230714, -18350592, 1454180, 505856, -19083936, -8012992, 12576708, -1160640, -22058500, 6582784, 11865768, 384384, 3225184, 16554624, -34534486, -2456688, 31999578, 3656992, -547790, 7435776, 12754848, -617344, 10802220, 5107200, 0, 1493856, 58590558, 0, -6081972, 2261376, 23802252, -1073280, 1792036, 8036064, -5477082, -3798528, 11458772, -8112000, -454688, 3149120, 1999482, 1171200, -6588140, -599040, -1059716, 4562688, 0, 88672, 6393248, 5351136, -9784840, 1328640, -7261140, 937664, 7939724, -2498208, 2594282, -9834368, -8587704, 0, -17750368, 14976000, 7841730, -5887792, 6203028, -7177792, -37994312, 1579008, 13942432, -10689152, -51775308, 0, 10547784, -10726176, -10333232, 1128192, -6741228, -29149952, 17082424, 4081680, -52639704, 8731008, 17590014, -3180288, -4223050, 22446528, -4471012, 942144, 20288424, 14452192, -25590656, -227328, 14512526, -7455744, -10017540, 16334864, 8092068, -1885824, 35623220, 765184], "weight": 5, "weight_parity": -1, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}