# Stored data for newform 27.10.e.a, downloaded from the LMFDB on 25 April 2024. {"label": "27.10.e.a", "space_label": "27.10.e", "level": 27, "weight": 10, "hecke_orbit": 1, "hecke_orbit_code": 275045679131, "dim": 156, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 27, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2700, "analytic_conductor": 13.905967576424574, "level_radical": 3, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [27, 9, [2], [1]], "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [4, 7, 13, 16, 22, 25], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 26, "sato_tate_group": "9.2.3.c9", "trace_display": [-6, -6, 2382, -6], "traces": [156, -6, -6, -6, 2382, -6822, -6, 36861, 2538, -3, -121767, 319935, -6, -720417, -706356, 1530, 1002249, 922437, -3, -8448573, -3497394, -1585014, 9316482, 7959258, 2192178, -33129678, -3148155, -12, 19657236, 21174507, -4633692, -37550952, -19055889, 14341770, 34449663, 137733552, -3, -92022060, -89330160, 6645801, -33127221, 227141658, 2356203, 1001541, -78992532, -3, -33488952, 248865393, -93214644, -72027753, -101541537, 160531713, 4841352, -315431874, -12, -91770981, -103852992, -320682489, 538090854, 1127571210, 36683436, -55862958, -419972706, -956301315, -852347310, 472205277, -109026897, -508886217, -1234413090, -815297649, 940878639, 2831326452, -221849931, 838884579, -226667796, 908401146, -967811358, -1247881230, -1228059150, -2497115154, -392600970, -12, -297703284, 1027656618, 1535949369, 2930201574, 2687612040, 2837227002, 1774997208, 7127326206, 551343507, -6896645517, -7299151842, 414852915, -9000269169, -2644638174, 3371772333, 6901039926, 5248107342, -5100000003, 11069692806, 15120243135, -879644130, -640359015, -8106304203, 5152736997, -21668621868, -30501776997, -12, 1605514878, 6791072775, -3565194441, 15507109662, 23574516948, -9648515076, 24158939070, 278770644, -3, -20474215299, -51077701836, 11446562541, -23815048242, -19071987948, -4369349799, 21415407375, 56328836841, -3, 58548727641, 8345303502, 2819951580, -728376114, -52690626054, 7941307227, -67837520676, -47816913474, 805306356, -17224922679, -13968558396, -372733494, 121993204548, 72403614522, 313867944, 33801102123, 1369795743, -3, -74510945265, -46017761778, -2798757768, -35612129352, -26657764686, 43869611334, 44424715575, 30485711466, -3, 96254948370, 91429324512, -12658117218, -86012942277, -44274441330, -74059992900, -48010917912, -76668175215, 29105226330, -68195747739, 7142328576, -7537976160, 39344214372, 167466979899, 68375170866, 67874052096, 28276069770, -3, -73000054356, -108532577745, -26569761921, -100989318237, 15349056516, -154011594924, 59158613682, 194462964684, -3, 97221943992, 57561924678, 126058132596, 13150843941, -70346526363, 17206125939, -525323689404, -187455768300, 5999999988, 64696299600, 63180728787, -24358971003, 34886948550, 11713089240, 10381852929, 26971432677, 138587073741, -3, 90238170957, 31165856142, -55297504365, 69035275086, 71213305167, -51415103004, 147349098600, 187008711084, -402653187, -83097698313, -171104409765, 13759554396, -84036433194, -159043239135, 7351268562, -123682557408, -76717882854, 71940450660, 14384939604, -137984050290, -71607819567, -74296733103, 16596161136, -278478202668, -33114903003, 84899428902, -27577525683, 497357650569, 578154776694, 45211540440, 783134979345, 316360715472, 455850463569, -115013665557, -348472355247, 40721333955, -339021489567, -421503120534, -13796541927, -391921105026, -292811131872, -429812727009, 769043490330, 304198792974, -214390333452, -616035436407, -950073467652, 148984598265, -630142215783, -375162185682, 566878432035, 103419223677, 98251561125, 117818879505, 1142044792125, 1272668599341, 32496936258, 731172786279, 694103072796, -327575646831, -278213911557, -517420685772, -155052541875, -522942195426, -1528033913019, -99333956502, -689661581307, -6613364943, 423346350636, -115557013512, -13643269227, 197434893408, -631479498606, -541269450123, 81255887904, -1094269446087, -1028731865679, -55935754476, 51188126100, 193641418656, -2194693635, 992375805414, 2826320609817, -456928481166, 3015237202704, 1301204252079, -341116458384, 344059660137, -323484917580, -209272723233, -2629037157489, -746923491381, 1455061915671, 226384582938, -529818482574, 1004489535288, -1033951537122, -646663036788, -12, -696414929136, -2107380414633, -1200842624796, -2170070322645, -2165763714588, -733510297494, 508577520009, 2310344346717, -154729188255, 4624279137996, 2612188674132, 1264230991533, 2512196544678, 3758615997804, 1006962821364, 1531271343570, -373067140887, -116026735557, -831739176888, -1604806093035, -807767547180, -3140579184177, -2189629210743, -1699447801533, -1303682804388, -3317469850431, -12, -3098285904801, -1930106620218, -580490164698, -1422483330342, -878305169619, 1055499634722, 1999536705957, 3146352764427, -651654747057, 4309359981420, 6575832397500, 1016509302516, 4587314282100, 3268669019688, 632217251241, 1448822541993, 1198262745117, 241936531233, -1343608044972, -2161167956928, -3068426171067, -4521310346091, -6554022996087, -1082382076734, -7831884429354, -4147134225498, 805306356, -2933672305560, -3347851730553, 3108787688511, 24957196236, 3114203897079, 569562163398, 2639083573341, 5142760523559, -407605512987, 6843804693540, 5056348729053, -3187916910498, 4831761579033, 5546385862623, -2109212227050, 5642565493911, 3497313897549, 5999999997, -181080934560, -2672682021561, 2276631136758, -9161632661697, -7868038733163, 1557211501509, -7710986498340, -13924981627596, 1453270410312, -13200825415614, -3783714836259, -1798829627829, 647911607442, 7009361528103, -838634712423, 8348140327785, 5156090634996, -3, 3922826442888, 13886232434010, 782659032867, 9170531547165, 3239086965381, 417227759181, 7310759275803, 9896859320022, -3, 4465604438079, 361645770333, -1169605813947, -7734266060637, -15087753660474, 1117923050010, -26975691182436, -17551601019648, 2649601720500, -10714631480895, -10105380488394, -757515700491, 4909643708436, 4425285694887, -2374820900235, 8365388264535, 11221882004700, -3, 15985665645984, 7031845341960, 3803677008288, 11435675537706, 22786941279285, -866141265732, 14468066689650, 7638187519638, -402653187, 936190924758, -3307728773673, 197570020530, -18602124104574, -19922029859313, 1569145386225, -21720492178128, -37281457429254, 2098080635172, -21783369004359, -7830947904795, 2874360642243, 2502437316519, 4723239032136, 1926184444464, 23557062255939, 16600222811376, -355763629494, 14781008310528, 15383174779176, -9007295986629, 21621785703207, 18656235350082, 1291679886936, 11815314329421, 12110212519434, 892182765642, 2489318263113, -5231663545170, -821727435480, -21383876677584, -40389722035029, -1445417532987, -36201824508216, -25631915812803, -4608125917512, -14903084620644, -20258213268789, 1283677693068, -705286302603, 5184117199566, 2559738639105, 16738073420139, 30834160430049, 2714326465191, 35054568433440, 20264227261116, 5411235108099, 18143857120902, 19746909816813, -508356614307, 29049126708537, 8003332594656, -528960640926, 179768226054, -20281461477849, -1898080196043, -32160211797828, -28848700183860, -5007739631025, -37643474114592, -44104714910253, -5582064788760, -38764122863073, -17220093676140, -5275623917403, -5969196822891, 7888432746384, -2033496131967, 22442104136424, 17485555214304, 3162461083740, 31725051942537, 54923748233589, 172443284148, 64412899346487, 30706834463892, 10964487644505, 18808285315743, 26648071242615, 2089408466247, -12931039762704, -16732179092448, 10474079656830, -29982284594994, -53343274111929, 2561345930373, -68416239265662, -27700962191865, -9799183388064, -34827565939620, -42458664377937, -7461226564044, -15936160210962, 855034780410, -9918617789721, 17759529277515, 44873674612812, 3019048988208, 77474662175337, 61314681051231, 11844795603846, 44032527182853, 77539457966346, -6995846281902, 27216558452916, 12043357271064, 677039244708, -13256065553136, -32036566889394, -3215019345498, -71292132754872, -39972892014279, 5250685744395, -42327563324832, -79172330326929, -12, -59799693613665, -36533114770251, 18841268039220, -20092142626746, -1234469327112, 11279169070545, 25969563542649, 42179645326680, -5259439072419, 56828608429497, 107700267089304, -13822101022830, 91867687144755, 57378501885015, -9539504921304, 22124856604743, 11880454905198, 1439683064187, -45268663159995, -31410243559800, -731632805781, -41462799359286, -75499733362788, 12783538740, -66116607095586, -44610914734164, 805306356, -45739873211757, -72262727028279, -1110630808347, -49037804600880, -24930112156938, -3323150663496, 29810911408809, 91475380872612, -3491717956779, 96025289546118, 79157179454064, -11888735061657, 95530561046304, 108323298656469, 2113408546902, 47101130629014, 1217285866872, -5387958603939, -49140644030430, -67158856275309, 15618254828523, -76049685826596, -45762187804983, 14850883259775, -47777075965278, -84536913759552, 711527258970, -83789459408523, -40283874759963, -23574280669530, -42383830863234, -51683467794678, -14844741927828, 54519409013376, 63352844788698, -749849425923, 110011668812826, 127761722636382, 11411200203168, 146233673882208, 78294567612060, -11700742044777, 34298139270543, -2106921850218, 1035151757889, -41666198640141, -74397237059124, -38721730661646, -46617457039284, -75643868125764, -10730130687069, -125839392091098, -62458065332658, 350847665610, -30388789662525, -93649375648029, 46373879901249, -41139700709133, 3105401497965, 52793274828150, 34550253456579, 97345028799396, -3, 168519421561458, 110718005218188, -1158015757236, 103342459412415, 118141571964762, -10238976114285, 44994527114247, 6456158080155, 5597346813, -34243325696427, -83176000160850, -18447282531429, -113071485813612, -80300961877068, -33844129793118, -96498852220224, -150078857089257, 26985425753958, -128740979235963, -76841529772938, -13199981777283, -19542550249488, -19438388982549, -23648011000944, 84756049036809, 51735890971494, -3, 92709383960532, 225445231167849, 21464989228128, 152989272073689, 97641367812729, 38672585720106, 47096099375451, 3356080088481, -3, 6598309842816, -28196801992470, 82312770372681, -92413615661706, -169341013289691, 19299259117272, -129204242354532, -103660819515504, 24669168187134, -81458730920598, -93419608045509, -48147621749898, -6712608802554, 21647067742440, -45901905672540, 10456294474323, 114888463504920, 7635588514305, 178196594057472, 75382186489530, -28627221029532, 86501608096842, 140218414375500, 8636246394006, 74747675684235, 62351514185292, -16390508482659, 7699842216534, -46274801761026, -21133925844921, -136004987866755, -140201105068260, -1953312895704, -115410441392424, -163314377885169, 12048952172106, -181895516395710, -101781235781289, 63616203862626, -7149816984144, 39063187215621, 15809399446620, 78316982063451, 55488594510162, 20088902184957, 68363991555690, 109810098205353, 12209981893347, 134784856484361, 60577817525874, -17502064242075, 47667890195055, 128448136448154, -5654561524419, 14365404837180, 25305339123573, -54676847901927, -72056878753623, -136826184229515, -3435891363744, -185554248438702, -89517995014707, -58000648630668, -88777823699016, -13379475871551, -39041413591920, 12390199296108, 47201663388123, -40303142253459, 98755126901799, 80212394043621, 4271473067721, 75686361523086, 5500720406865, 19017698049513, -6675750004746, 56521297696896, 43028805343854, 118740281762994, 20058186703338, 27254064259683, 5416815050748, -4897085297472, 44308974067680, -121681999837968, -72541065282228, 58997329329453, -167440398771300, -228465979439013, -13610630349300, -42878929190304, -18704622317967, 15489731496390, 40402277237472, 94896394207335, 7928907450288, 118833376226538, 40106415615237, -26587097981553, -2645403023886, 27718733246232, -91770314670024, 20425426347852, -18687448603890, -143076911993073, 127680763671153, 136246218428025, 39796546569909, 14529459039573, 23074168526409, -29299050702870, -10946085579924, -90461025323001, 9057812768991, -110732922626904, -94926875543748, -2266006683660, -10325054013108, 64115616475359, 91754377729338, 53075988899793, 48040852870062, 186888441562482, 109194410108955, 60206652556938, -37995949894935, -61833538236531, -9192812274684, 103070761005165, -19809565758966, 74443771389861, -505737422127, 99577767810393, 32921952026805, 19813178131665, 15576616893966, 29493911039865, -126086463263253, -73848778427175, -76806377151210, -149829463098084, -162560365488612, -205062271037424, -12, -71791101178050, -11878213420164, -171970406832864, 96592329468894, 155771716613994, -46755164628678, 704413027464, 16431985211193, -8353429887975, -11645991683232, -39803068901691, 105758541412284, -35014457824026, 19040273083818, 219684051436197, -17471177600211, 135505719341298, -54324492903255, 129531010425012, 22322506609536, 135564835444320, 79283030063184, -37565088668379, 35678645312214, -83979733140444, 77341157766216, -49461628879020, 30653047326018, 40211121147912, -35838324888216, 102674693332140, 55020418795332, -178655009828418, -10715548066677, -55713937013757, 36431427903171, -159763775873679, -61441535884089, -278881500922965, -9467075151573, -185295071849562, -102344626111902, -62958117853689, -19075583560869, -25025882885181, 100851034225350, 118588332109743, 170546600261307, -9313666048365, -7566090318243, 203059097794386, 87307403032440, 164340321240096, -46094776920012, -125992219431243, -82220925296886, 81150577439433, -11687860228782, -7371890106021, 110780611941738, -99325595139810, -128832402847176, 1936126186671, -133852241795358, -236326033631226, 64259441918796, -348457545091245, -17350495245234, 27827474662698, -12508639697592, -7810782881616, -3, 71814863727360, 118923448686336, -172563638426502, 40183883369214, 123477198017580, -209346315491235, 478686624515190, 236987119453932, 130654613385204, 208029030977517, 247583968435134, -94412450616651, 63679781718825, 83017551633264, -80039901653766, -58250746762167, -313860944325780, -355763629494, -165364618694418, -85412850957186, 258324165366825, -213118305353493, -374137124651460, 182086144533399, -288033853244172, -110307434552766, -16282511036931, -146879355390090, -12431607914712, 8459890555593, 233436790598658, 242623655943975, 212594912597628, 297463151836308, 126203619431889, 79305216208260, 421973941388751, 118473886214736, 144468140019627, -211010739273405, -159057621394578, -92433914768793, -209970988597344, -131927338497546, -60967852122708, -116380810547610, -253267706746476, -347552284936152, -173915776340361, -217554960076560, -374458872167433, -153340319415852, -398270305570221, -41574112843836, 28700470371927, 151068756519285, 94317689844573, 355614376766190, 576750238677234, 135807086038872, 696925515316092, 547267223885283, 86344637244972, 305930261974062, 188130535668231, 179113687564749, 35527778330451, -157169712104460, 353018760601455, -291976692667713, -237200911703379, 65797140784209, -226511208072840, -245663503763652, 257760902149383, -166564958707560, -418143439969596, 3334793133108, -377429988299253, -98147791026666, -61736750349078, -128504436614322, -205137766967544, -281695448132124, 762812563405362, 498678832285596, -728812439497518, 254523990144564, 921139868157048, -154741659493152, 464323296327567, 97024158387492, -402489757839984, -100729248541608, -685216191756879, -6603499638261, -664172873385867, -216739957176774, 2172369034392, -401821589538942, -613758043216008, 279053454144789, -374790624693471, -417547453161024, 435999553743321, -224235318311313, -511876898307891, 134144909907819, -4480917176727, 128344144836894, 426683445302538, 569145297542781, 1128650474845026, 196372380656550, 1266272452887432, 694515645404667, 100296001458780], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 27, 5, 1, 9, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "27.10.e.a", "char_is_minimal": true, "conrey_index": 4, "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}