# Stored data for newform 16.14.a.b, downloaded from the LMFDB on 24 April 2024.
{"label": "16.14.a.b", "space_label": "16.14.a", "level": 16, "weight": 14, "hecke_orbit": 2, "hecke_orbit_code": 4503599862251536, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2059901994275078084, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [468, 1]]], "qexp_display": "q-468q^{3}+56214q^{5}-333032q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3136, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 17.156948632306033, "hecke_ring_index": 1, "level_radical": 2, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [16, 1, [15, 5], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "0.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "1.918", "prec": 17}, {"__RealLiteral__": 0, "data": "0.012", "prec": 17}, {"__RealLiteral__": 0, "data": "4.785", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "13.2.3.c1", "atkin_lehner_eigenvals": [[2, -1]], "trace_display": [0, -468, 56214, -333032], "traces": [0, 1, 0, -468, 0, 56214, 0, -333032, 0, -1375299, 0, 6397380, 0, 15199742, 0, -26308152, 0, 43114194, 0, 365115484, 0, 155858976, 0, 57226824, 0, 1939310671, 0, 1389783096, 0, -46418994, 0, 5682185824, 0, -2993973840, 0, -18721060848, 0, -1887185098, 0, -7113479256, 0, -7336802934, 0, 26886674980, 0, -77311057986, 0, -101839834224, 0, 14021302617, 0, -20177442792, 0, 278731884294, 0, 359622319320, 0, -170874046512, 0, -59573945772, 0, -27484470418, 0, 458018576568, 0, 854438296788, 0, -784410054932, 0, -26782153632, 0, 360365227992, 0, -1592635413718, 0, -907597394028, 0, -2130532256160, 0, 23161184752, 0, 1542252338649, 0, -2050158110436, 0, 2423621301516, 0, 21724089192, 0, -3485391237126, 0, -5062000477744, 0, -2659262965632, 0, 20524601817576, 0, 6706667416802, 0, -8798310316620, 0, 10653736099446, 0, 10924465533496, 0, 8761456476864, 0, -12587565522204, 0, -436641848098, 0, 883202625864, 0, -31831198952526, 0, 3216948684336, 0, -20904189972858, 0, -14358406256208, 0, 6403758720469, 0, 3433623773112, 0, 40395804590844, 0, -39407680341632, 0, -12582963890640, 0, -73744029229140, 0, -121595139867488, 0, 78125266958544, 0, 85410026296938, 0, 79782728036164, 0, 47661042416832, 0, 97238525475960, 0, -2609397328716, 0, -6561969624756, 0, 189340621038054, 0, -283931821277240, 0, -59294907894006, 0, 319418393910336, 0, 27493181043278, 0, -130446521849592, 0, -19058363650368, 0, 374651855577100, 0, -168303245441760, 0, -126476544252168, 0, -71842949725689, 0, -502142960029716, 0, -362732128582626, 0, -645852511384472, 0, 27880606621296, 0, 317214254387772, 0, 455668962760070, 0, 12862732155624, 0, -106086223098972, 0, 275817882411720, 0, -462842244027072, 0, 966029530347072, 0, -182063056758334, 0, -399877122896784, 0, 862598124343638, 0, -324819447518888, 0, 367103905708176, 0, 15459010409808, 0, -412431040131876, 0, -78703993820376, 0, 2335782495031920, 0, 703122653862556, 0, -168650926700256, 0, 1511407547325720, 0, -1892349709338368, 0, 745353373620024, 0, 655324625337948, 0, -1508649743016800, 0, -2667132026515629, 0, -2503060674367284, 0, -1221116802675466, 0, 997089095882880, 0, 3537908036396874, 0, -5724824441067936, 0, -10839434463936, 0, 3112798054881744, 0, -4570914891142606, 0, -2937537249451740, 0, 788193505312038, 0, 5549661157005128, 0, 959473995684048, 0, 1663317001905300, 0, 366101739321120, 0, -1134254769109488, 0, -3740522836521726, 0, 628493027557136, 0, 63839996029206, 0, -2506157776421352, 0, 15668634143702916, 0, 1631163098974968, 0, -81129982670082, 0, 2291408802506800, 0, 2369016223584192, 0, 12406507300441980, 0, 998960307482726, 0, -7814704481561376, 0, -11758003102314054, 0, -3812373638412044, 0, -9605513650625568, 0, 2443390154715888, 0, -8045744308636301, 0, -3138720351063336, 0, 18983079522948150, 0, -3348889787627208, 0, 8890970582688480, 0, 869832960279408, 0, -8954123141939360, 0, -4985948494540728, 0, -1545012020077452, 0, -15202097546210372, 0, -5112649869676128, 0, -19648629162159192, 0, -19994252842377382, 0, 25747056263193552, 0, -24456461290397586, 0, -296959943835720, 0, 5890980664391472, 0, 15741659809579896, 0, 29477021857046882, 0, 204348384909864, 0, 33915923671287168, 0, 33992443483613572, 0, 2595443778094302, 0, -44094826827947448, 0, -2887183035494638, 0, 14897001109782168, 0, 36351101946741120, 0, 27597598460719280, 0, -1505531984269248, 0, -33601121683234380, 0, -19052688341090290, 0, 21124344495161232, 0, -68547375932093982, 0, 20257570926342288, 0, 6719734127905344, 0, 11515414775891256, 0, 91256333194297197, 0, -2996959081179492, 0, -89528407146743652, 0, 943078961967952, 0, 10090297738327266, 0, -92826636890199408, 0, 27434453204114246, 0, -18905236548514992, 0, -705556732699548, 0, -65132658943109612, 0, 18442794399883776, 0, 87834445767126144, 0, -119765740247778240, 0, -36977217213319020, 0, -40928249341090026, 0, 2467288391939856, 0, 34512205679237520, 0, 1301982839648928, 0, 25377606630246782, 0, 56906525457984384, 0, -81198461546163630, 0, 86367758520857408, 0, 86696172964814886, 0, -12073040202243240, 0, 156903059661641786, 0, -39971892306966984, 0, 19840030308340704, 0, -115247588020049304, 0, -37338316720924752, 0, 19165867577647884, 0, 22062861443818166, 0, 140060222168432976, 0, 83611816495764174, 0, 9153208152247376, 0, -45507629922749280, 0, 136346835968196624, 0, -43494919999192078, 0, 1221197949839088, 0, 20894399542542816, 0, 208497563333221672, 0, -19283483467857483, 0, -249282611233714476, 0, -195927783003800964, 0, -88611410645809272, 0, 145109873387955906, 0, -46936316353912920, 0, 132880092357748320, 0, -284555294855901216, 0, -198127166900027734, 0, 59919378018864624, 0, -230381995342550850, 0, -364296360673153424, 0, -149487808350037248, 0, 21717482203717020, 0, 261233649414113824, 0, -12866808728254104, 0, 172004276783552400, 0, 708072354268529764, 0, -383339681737653906, 0, 198718990347079584, 0, -28684726595844716, 0, 8919314188372224, 0, 377008602168107628, 0, -471597862471979336, 0, -175337068410082800, 0, 114636339459987300, 0, -2001317512600836, 0, -494588216138476680, 0, -120013152608631744, 0, -12879360668887556, 0, 59191022710014624, 0, 272812154344161768, 0, 598889121094257444, 0, 33622500471622452, 0, 408824236278402606, 0, 530398557101332976, 0, 507431327751058464, 0, 614107905499944144, 0, -651508118667933120, 0, 169758636176668968, 0, -468975502839432726, 0, -612358729613548604, 0, 302258975327932896, 0, 244982861959985856, 0, -500761452551340407, 0, 81931988046285828, 0, -111517511701643028, 0, -707597408265175656, 0, -148456271053477296, 0, 89699600935943460, 0, 468270288292416974, 0, -213253074571712760, 0, -24545384848980972, 0, -1116108302757722996, 0, 37799364681404982, 0, -16948293461103096, 0, -7713415680328064, 0, 49648352410318896, 0, -278972996588388450, 0, 408670522933855160, 0, -129082768968684960, 0, 497446108616742588, 0, -1789359017917296564, 0, -513619380844953768, 0, 1156535003004963930, 0, -88014962752765868, 0, -452101820202429696, 0, 110980590450638904, 0, -154048129795441342, 0, 85205510562900312, 0, 682768255834721952, 0, 1783153781944749720, 0, -1175108135134239612, 0, -1461113904643961724, 0, 2074654027307698816, 0, -403695922192822584, 0, 1323717200623180818, 0, -807143449286476512, 0, 152015501438839584, 0, 1543250474746700040, 0, 266564324178438650, 0, 1078798364137924668, 0, 359980892712444366, 0, 1032813282165950752, 0, -7234816871790144, 0, -1547939205527570208, 0, -451541280745588618, 0, 193017726781717968, 0, -1868698635269928246, 0, 1237237618430421220, 0, 79532872632967104, 0, 1160746814482546032, 0, -96512837165842259, 0, -1093146207674938560, 0, -81364464429081012, 0, -602949442486809752, 0, -329061402007676208, 0, -2215263342724501248, 0, 213120182282324814, 0, -495609937692169608, 0, 2687833301629079682, 0, 1922605140695672236, 0, -707338732148436960, 0, -1548294892937413992, 0, -381117169202877360, 0, 885619663970356224, 0, -2118678527719586178, 0, -4145446859086875960, 0, 2190349891850951682, 0, 1713757470500782044, 0, -339226139764007962, 0, -306691924658159664, 0, -6835349192510970432, 0, -2656411599895056, 0, 706048079731862400, 0, -175828601362704840, 0, 19960663323281954, 0, 2695221188448217416, 0, -3267444788377428042, 0, -2233534863152403664, 0, 1171432395603888912, 0, -980130018496892508, 0, 4801239218256072732, 0, 571482663652118088, 0, 4236652728442652148, 0, 2721452079908411452, 0, 2930118881364591840, 0, 4484906273824923096, 0, -316320345036245196, 0, -1655740961033737032, 0, 587143117623057390, 0, -689040500453857432, 0, 2679217838419794048, 0, -3548035040670700272, 0, -3678038066296362154, 0, -31853554228240848, 0, 325173448085342976, 0, 5466166471105615440, 0, -1456789489684656192, 0, 2246089731903594864, 0, -3638196605551239872, 0, 2139188169054739608, 0, -90020850401284974, 0, -6280820086726448504, 0, -1084080942568475307, 0, 1159197321102666120, 0, 5840677960868928398, 0, -368874560486033784, 0, -5018169197220878160, 0, 6402491090486212300, 0, -2597241421478399904, 0, -6617169652386922056, 0, 10643593671033167556, 0, 2819580399124520364, 0, 4192062120990642528, 0, -1097599476209942576, 0, -778432356891680400, 0, -15960943401278769360, 0, -8916992483146692922, 0, -171335614002284160, 0, -8551667918713393638, 0, 145415707955773136, 0, -3333203952353653284, 0, -905508605656390824, 0, -3404202799496751358, 0, 1750564687492167768, 0, 4271867214173115030, 0, 11019523603088127904, 0, -294134736896739648, 0, -2678780354260030056, 0, 2305393302251460960, 0, -64512333194525424, 0, 1545501679166829492, 0, 2010200967685144924, 0, 1172881839365192736, 0, 10600807849557638832, 0, -417756859360232156, 0, -7332920779252964688, 0, -1681311643363833138, 0, -4390742369661375456, 0, 4793455083028150674, 0, -10188693943011258840, 0, -1071346854241786752, 0, 37968831889598376, 0, 8897418238258646154, 0, -7391518821461146844, 0, -1072379319573182400, 0, 21060679409411099400, 0, 9816741348473390320, 0, 6961764195040845456, 0, 4725754002670149126, 0, -2480898418352227928, 0, -5806245416606846640, 0, 10202605667477005140, 0, -7916032028703180178, 0, -467513423901915768, 0, 604517161162045698, 0, -7109752458591371952, 0, 7897005806526031104, 0, 13707611597228931288, 0, -10258473989954630153, 0, 5502745451882977272, 0, -4038579575879881446, 0, -2132656574195232008, 0, 1784190862776836592, 0, -107997609458668752, 0, 9046006856817082790, 0, -28227464355110455224, 0, 5969414824479999738, 0, -10355010557739735116, 0, -1143506592407035584, 0, 3959227035493399584, 0, -20390623876143737964, 0, 3765408336441788868, 0, 148170900108749760, 0, -11922830457172227544, 0, -9223672991660373798, 0, -13453095594497959008, 0, 4384031090314337246, 0, -8884081216739734200, 0, -4000583698570364238, 0, 9474501965671045756, 0, 1567280420609533344, 0, 12210143957657149032, 0, 13124018599534388224, 0, 9866374266226339620, 0, -37183300363175524416, 0, 17831882096154215208, 0, -407081825410762944, 0, -263761349671141056, 0, 12017300533437069036, 0, 4190529630427620480, 0, 25614975072594574980, 0, -3273050939281057724, 0, -14652072603831984354, 0, -25069385557117868112, 0, -13115640492541057680, 0, 723065625396247536, 0, 24559121542238952480, 0, -5265471710300882744, 0, 7114581651626454096, 0, 5477458491249578064, 0, -3659838198703580758, 0, -15024406523751515304, 0, 1827193373979186978, 0, 5119394691316421628, 0, 9195558447890501856, 0, 15504826441892428080, 0, 37261453685003018, 0, 9357310330232614776, 0, 40875511169879907102, 0, -419861930226701616, 0, -26018213905737825408, 0, 25048939926347127612, 0, -24207647388576860756, 0, 11445623883906070248, 0, 28898055405610176474, 0, 54304384018930305408, 0, 138977253715116960, 0, -28444271877721856016, 0, 7869689441021516385, 0, 17311666275121638996, 0, -10234492672612987476, 0, -39569284620897394088, 0, -7367096790883391328, 0, -15385483855769992956, 0, -26570201483339769248, 0, -13795246229097940776, 0, -20046487543543693422, 0, -22297372192565129880, 0, 600513097047331302, 0, 5840067887528590728, 0, 48490090961853266532, 0, -15872652278162394624, 0, 1538639017025663520, 0, -32168704058142394976, 0, -15908463550331151696, 0, -18259400422826770032, 0, 2941734610476942326, 0, -2622777948223503408, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "4.14.a.a", "char_is_minimal": false, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [0], [-468], [0], [56214], [0], [-333032], [0], [-1375299], [0], [6397380], [0], [15199742], [0], [-26308152], [0], [43114194], [0], [365115484], [0], [155858976], [0], [57226824], [0], [1939310671], [0], [1389783096], [0], [-46418994], [0], [5682185824], [0], [-2993973840], [0], [-18721060848], [0], [-1887185098], [0], [-7113479256], [0], [-7336802934], [0], [26886674980], [0], [-77311057986], [0], [-101839834224], [0], [14021302617], [0], [-20177442792], [0], [278731884294], [0], [359622319320], [0], [-170874046512], [0], [-59573945772], [0], [-27484470418], [0], [458018576568], [0], [854438296788], [0], [-784410054932], [0], [-26782153632], [0], [360365227992], [0], [-1592635413718], [0], [-907597394028], [0], [-2130532256160], [0], [23161184752], [0], [1542252338649], [0], [-2050158110436], [0], [2423621301516], [0], [21724089192], [0], [-3485391237126], [0], [-5062000477744], [0], [-2659262965632], [0], [20524601817576], [0], [6706667416802], [0], [-8798310316620], [0]]}