Base field 4.4.19796.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ |
| Dimension: | $23$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{23} + x^{22} - 33x^{21} - 31x^{20} + 466x^{19} + 411x^{18} - 3687x^{17} - 3057x^{16} + 17971x^{15} + 14042x^{14} - 55880x^{13} - 41217x^{12} + 110998x^{11} + 76994x^{10} - 137190x^{9} - 87680x^{8} + 99858x^{7} + 54906x^{6} - 39760x^{5} - 15060x^{4} + 8571x^{3} + 1159x^{2} - 780x + 71\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $\phantom{-}\frac{3809368861215801}{222008610784847869}e^{22} + \frac{8335414394411184}{222008610784847869}e^{21} - \frac{127995054890826271}{222008610784847869}e^{20} - \frac{277211324320752718}{222008610784847869}e^{19} + \frac{1844808275684855753}{222008610784847869}e^{18} + \frac{3957664359280767381}{222008610784847869}e^{17} - \frac{14908944278103451523}{222008610784847869}e^{16} - \frac{31741877465199390027}{222008610784847869}e^{15} + \frac{73989234791285070178}{222008610784847869}e^{14} + \frac{156950345370010979987}{222008610784847869}e^{13} - \frac{231542684119165266361}{222008610784847869}e^{12} - \frac{493198812516498094082}{222008610784847869}e^{11} + \frac{449309368049796453310}{222008610784847869}e^{10} + \frac{976435476269087452446}{222008610784847869}e^{9} - \frac{504847197683440691690}{222008610784847869}e^{8} - \frac{1159554357960731242797}{222008610784847869}e^{7} + \frac{277071686542511292979}{222008610784847869}e^{6} + \frac{737284526357981349606}{222008610784847869}e^{5} - \frac{47176990293502124714}{222008610784847869}e^{4} - \frac{196135623779421658929}{222008610784847869}e^{3} + \frac{8552307267905965608}{222008610784847869}e^{2} + \frac{17412796150566038239}{222008610784847869}e - \frac{1857328131969494511}{222008610784847869}$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}\frac{7564897230327055}{222008610784847869}e^{22} + \frac{12323330525698742}{222008610784847869}e^{21} - \frac{248826044494063971}{222008610784847869}e^{20} - \frac{401536745836551912}{222008610784847869}e^{19} + \frac{3493267284641696954}{222008610784847869}e^{18} + \frac{5625020129459712447}{222008610784847869}e^{17} - \frac{27330646690772005297}{222008610784847869}e^{16} - \frac{44384581782543204346}{222008610784847869}e^{15} + \frac{130290387740107547749}{222008610784847869}e^{14} + \frac{216684292084589062650}{222008610784847869}e^{13} - \frac{387413038113892102122}{222008610784847869}e^{12} - \frac{675001702848028902705}{222008610784847869}e^{11} + \frac{701273172445940555696}{222008610784847869}e^{10} + \frac{1329489725665412373825}{222008610784847869}e^{9} - \frac{704696615550024474182}{222008610784847869}e^{8} - \frac{1572667676142045450549}{222008610784847869}e^{7} + \frac{294895400133810761766}{222008610784847869}e^{6} + \frac{991096103484214440042}{222008610784847869}e^{5} + \frac{12417188236794379848}{222008610784847869}e^{4} - \frac{255758234989406977060}{222008610784847869}e^{3} - \frac{3455059928131899774}{222008610784847869}e^{2} + \frac{22678458655571721523}{222008610784847869}e - \frac{2343835354367547125}{222008610784847869}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $-1$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-\frac{36496306772261865}{222008610784847869}e^{22} - \frac{72592994026219107}{222008610784847869}e^{21} + \frac{1178928058132162438}{222008610784847869}e^{20} + \frac{2301904499933017178}{222008610784847869}e^{19} - \frac{16251391091477725829}{222008610784847869}e^{18} - \frac{31144523900808326749}{222008610784847869}e^{17} + \frac{124991044190707489208}{222008610784847869}e^{16} + \frac{235298341666813143370}{222008610784847869}e^{15} - \frac{587968706738346815926}{222008610784847869}e^{14} - \frac{1089770080196043813425}{222008610784847869}e^{13} + \frac{1741477808598717018890}{222008610784847869}e^{12} + \frac{3192585472523251393637}{222008610784847869}e^{11} - \frac{3213165063964322029641}{222008610784847869}e^{10} - \frac{5876471834031525705581}{222008610784847869}e^{9} + \frac{3505220976571616577056}{222008610784847869}e^{8} + \frac{6494676173439258749801}{222008610784847869}e^{7} - \frac{2016603121285328042042}{222008610784847869}e^{6} - \frac{3879523342390345244622}{222008610784847869}e^{5} + \frac{515313301151091279337}{222008610784847869}e^{4} + \frac{1003176553402310854553}{222008610784847869}e^{3} - \frac{103502760392782795731}{222008610784847869}e^{2} - \frac{88762715515051071714}{222008610784847869}e + \frac{13442226473350588590}{222008610784847869}$ |
| 19 | $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ | $-\frac{4061826332766332}{222008610784847869}e^{22} + \frac{19898578712040332}{222008610784847869}e^{21} + \frac{145427084153204752}{222008610784847869}e^{20} - \frac{652125202722745039}{222008610784847869}e^{19} - \frac{2206673975351425929}{222008610784847869}e^{18} + \frac{9076173353948073948}{222008610784847869}e^{17} + \frac{18584013150252591641}{222008610784847869}e^{16} - \frac{70064193091228929150}{222008610784847869}e^{15} - \frac{95629748283496008586}{222008610784847869}e^{14} + \frac{328774210995862318100}{222008610784847869}e^{13} + \frac{312224223847799945470}{222008610784847869}e^{12} - \frac{966901843554683743152}{222008610784847869}e^{11} - \frac{650672289206206897021}{222008610784847869}e^{10} + \frac{1773153849288981771641}{222008610784847869}e^{9} + \frac{847227728923314772776}{222008610784847869}e^{8} - \frac{1952826538616767226004}{222008610784847869}e^{7} - \frac{647037447271483936795}{222008610784847869}e^{6} + \frac{1190993996950583190100}{222008610784847869}e^{5} + \frac{243374032478069214058}{222008610784847869}e^{4} - \frac{344110313058807241604}{222008610784847869}e^{3} - \frac{20598789301412161582}{222008610784847869}e^{2} + \frac{35385335843046701032}{222008610784847869}e - \frac{2962260958611371540}{222008610784847869}$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-\frac{14504672666384995}{222008610784847869}e^{22} - \frac{41504815954153183}{222008610784847869}e^{21} + \frac{445605103059870319}{222008610784847869}e^{20} + \frac{1306601010978743072}{222008610784847869}e^{19} - \frac{5772182824119442436}{222008610784847869}e^{18} - \frac{17497383904377791065}{222008610784847869}e^{17} + \frac{41049226899075502584}{222008610784847869}e^{16} + \frac{130341576940855824083}{222008610784847869}e^{15} - \frac{174521565959798193639}{222008610784847869}e^{14} - \frac{592506718323160858889}{222008610784847869}e^{13} + \frac{451290518924345751125}{222008610784847869}e^{12} + \frac{1695506222244483133860}{222008610784847869}e^{11} - \frac{685542232318140264633}{222008610784847869}e^{10} - \frac{3037162206998455606356}{222008610784847869}e^{9} + \frac{545781765063656787175}{222008610784847869}e^{8} + \frac{3270916859451833671309}{222008610784847869}e^{7} - \frac{161380354122232083973}{222008610784847869}e^{6} - \frac{1937589845667870055293}{222008610784847869}e^{5} + \frac{7469709080006628677}{222008610784847869}e^{4} + \frac{532034035116593809673}{222008610784847869}e^{3} - \frac{33359207212941739739}{222008610784847869}e^{2} - \frac{53256885249745974862}{222008610784847869}e + \frac{8297075325263136426}{222008610784847869}$ |
| 31 | $[31, 31, -w^{2} + w + 1]$ | $\phantom{-}\frac{34350368929612116}{222008610784847869}e^{22} + \frac{76359721797541111}{222008610784847869}e^{21} - \frac{1087532847063849585}{222008610784847869}e^{20} - \frac{2409847779763971598}{222008610784847869}e^{19} + \frac{14614494079171985389}{222008610784847869}e^{18} + \frac{32402922411223040121}{222008610784847869}e^{17} - \frac{108750403890019137990}{222008610784847869}e^{16} - \frac{242837022676617655368}{222008610784847869}e^{15} + \frac{489394111567696888954}{222008610784847869}e^{14} + \frac{1113059293819410249013}{222008610784847869}e^{13} - \frac{1361290050305911822790}{222008610784847869}e^{12} - \frac{3218174647742244973700}{222008610784847869}e^{11} + \frac{2278525235283288000449}{222008610784847869}e^{10} + \frac{5828246861968403472318}{222008610784847869}e^{9} - \frac{2079370634022857688508}{222008610784847869}e^{8} - \frac{6320014105665081083044}{222008610784847869}e^{7} + \frac{749964990504129282731}{222008610784847869}e^{6} + \frac{3701175544697391972748}{222008610784847869}e^{5} + \frac{63866739015402328913}{222008610784847869}e^{4} - \frac{947304704058120736949}{222008610784847869}e^{3} - \frac{4053907217887325231}{222008610784847869}e^{2} + \frac{87814909426953671026}{222008610784847869}e - \frac{9281906266318865234}{222008610784847869}$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 4w - 3]$ | $-\frac{62661555586952675}{222008610784847869}e^{22} - \frac{55953009586330929}{222008610784847869}e^{21} + \frac{2029232243775821729}{222008610784847869}e^{20} + \frac{1690474651695791724}{222008610784847869}e^{19} - \frac{27959154546331829561}{222008610784847869}e^{18} - \frac{21755221057528037971}{222008610784847869}e^{17} + \frac{214152433810841409678}{222008610784847869}e^{16} + \frac{156436837307797708214}{222008610784847869}e^{15} - \frac{999444975499275527604}{222008610784847869}e^{14} - \frac{691988022760885733752}{222008610784847869}e^{13} + \frac{2928473314381131845622}{222008610784847869}e^{12} + \frac{1948577422267236536538}{222008610784847869}e^{11} - \frac{5348401663973761451048}{222008610784847869}e^{10} - \frac{3477247964916298292796}{222008610784847869}e^{9} + \frac{5831522695046427512045}{222008610784847869}e^{8} + \frac{3759962354293920452308}{222008610784847869}e^{7} - \frac{3460212605910181774149}{222008610784847869}e^{6} - \frac{2211525515481566467889}{222008610784847869}e^{5} + \frac{955842719347920655807}{222008610784847869}e^{4} + \frac{562776126358957072579}{222008610784847869}e^{3} - \frac{130830217425980898765}{222008610784847869}e^{2} - \frac{50817619775378300440}{222008610784847869}e + \frac{10177132066161320411}{222008610784847869}$ |
| 49 | $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ | $\phantom{-}\frac{88723452756751656}{222008610784847869}e^{22} + \frac{79310761687421805}{222008610784847869}e^{21} - \frac{2904480350661120291}{222008610784847869}e^{20} - \frac{2453786378547820315}{222008610784847869}e^{19} + \frac{40519820474746447963}{222008610784847869}e^{18} + \frac{32537176490818632603}{222008610784847869}e^{17} - \frac{314762594426390174457}{222008610784847869}e^{16} - \frac{242716125605721015366}{222008610784847869}e^{15} + \frac{1491740344121200177201}{222008610784847869}e^{14} + \frac{1121275474474709233635}{222008610784847869}e^{13} - \frac{4438608389517903537784}{222008610784847869}e^{12} - \frac{3314473855098137321193}{222008610784847869}e^{11} + \frac{8201179733162769444767}{222008610784847869}e^{10} + \frac{6215328265021637040844}{222008610784847869}e^{9} - \frac{8918130551891749604541}{222008610784847869}e^{8} - \frac{7007134939519784175535}{222008610784847869}e^{7} + \frac{5034468869080454976103}{222008610784847869}e^{6} + \frac{4173431099294447029332}{222008610784847869}e^{5} - \frac{1122687555238997498536}{222008610784847869}e^{4} - \frac{971703869764177823182}{222008610784847869}e^{3} + \frac{117453617824072580786}{222008610784847869}e^{2} + \frac{72619525649348263534}{222008610784847869}e - \frac{8860450156180208395}{222008610784847869}$ |
| 53 | $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ | $\phantom{-}\frac{14631433446465094}{222008610784847869}e^{22} + \frac{83341132482838005}{222008610784847869}e^{21} - \frac{441262915234473183}{222008610784847869}e^{20} - \frac{2692831058579660605}{222008610784847869}e^{19} + \frac{5615328713346797919}{222008610784847869}e^{18} + \frac{37089279784785302020}{222008610784847869}e^{17} - \frac{39203405968708223937}{222008610784847869}e^{16} - \frac{284716578364160242627}{222008610784847869}e^{15} + \frac{162373019967954232037}{222008610784847869}e^{14} + \frac{1336120137840664508165}{222008610784847869}e^{13} - \frac{395885926711047367971}{222008610784847869}e^{12} - \frac{3952422282442653725242}{222008610784847869}e^{11} + \frac{494975335312739185886}{222008610784847869}e^{10} + \frac{7320110616295987762422}{222008610784847869}e^{9} - \frac{85161014638946492879}{222008610784847869}e^{8} - \frac{8123826259759403783336}{222008610784847869}e^{7} - \frac{501866108598466032819}{222008610784847869}e^{6} + \frac{4891386811160246337415}{222008610784847869}e^{5} + \frac{432454972731161966200}{222008610784847869}e^{4} - \frac{1305799477502435526163}{222008610784847869}e^{3} - \frac{22285542253421012686}{222008610784847869}e^{2} + \frac{125072901097511736667}{222008610784847869}e - \frac{14178171878560325308}{222008610784847869}$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $-\frac{57881652592085472}{222008610784847869}e^{22} - \frac{70068868472894372}{222008610784847869}e^{21} + \frac{1865031635064062760}{222008610784847869}e^{20} + \frac{2144945770641983376}{222008610784847869}e^{19} - \frac{25586839163409718879}{222008610784847869}e^{18} - \frac{27930186098034092455}{222008610784847869}e^{17} + \frac{195414862174179716898}{222008610784847869}e^{16} + \frac{202561096870827264212}{222008610784847869}e^{15} - \frac{911610616415086161572}{222008610784847869}e^{14} - \frac{898792539504840786561}{222008610784847869}e^{13} + \frac{2682051866195907084070}{222008610784847869}e^{12} + \frac{2519536185150183034188}{222008610784847869}e^{11} - \frac{4961783256831268609696}{222008610784847869}e^{10} - \frac{4437808793624659168001}{222008610784847869}e^{9} + \frac{5583095604162898845295}{222008610784847869}e^{8} + \frac{4709729617303241970868}{222008610784847869}e^{7} - \frac{3570005227845754495216}{222008610784847869}e^{6} - \frac{2741001680988336509143}{222008610784847869}e^{5} + \frac{1172673544519680906309}{222008610784847869}e^{4} + \frac{724751210427958578772}{222008610784847869}e^{3} - \frac{189456956116307456997}{222008610784847869}e^{2} - \frac{63491194780632692601}{222008610784847869}e + \frac{12026504008117035067}{222008610784847869}$ |
| 61 | $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ | $\phantom{-}\frac{9485546385932993}{222008610784847869}e^{22} - \frac{20009655574426040}{222008610784847869}e^{21} - \frac{358902264441537816}{222008610784847869}e^{20} + \frac{607623262746720796}{222008610784847869}e^{19} + \frac{5777671437605409002}{222008610784847869}e^{18} - \frac{7660213011632362562}{222008610784847869}e^{17} - \frac{51833321181938892783}{222008610784847869}e^{16} + \frac{51687506308875028458}{222008610784847869}e^{15} + \frac{284965099933757711496}{222008610784847869}e^{14} - \frac{199410021731143402729}{222008610784847869}e^{13} - \frac{993442326410505110849}{222008610784847869}e^{12} + \frac{427345323569265655254}{222008610784847869}e^{11} + \frac{2193204885226639914949}{222008610784847869}e^{10} - \frac{415300502807421028591}{222008610784847869}e^{9} - \frac{2965545025784868410953}{222008610784847869}e^{8} - \frac{47732249853683735942}{222008610784847869}e^{7} + \frac{2281082386791520488136}{222008610784847869}e^{6} + \frac{388622782209336175751}{222008610784847869}e^{5} - \frac{878047681629091380516}{222008610784847869}e^{4} - \frac{211007502839280792135}{222008610784847869}e^{3} + \frac{152510822215509440800}{222008610784847869}e^{2} + \frac{33337693595550425464}{222008610784847869}e - \frac{8838694050885962421}{222008610784847869}$ |
| 61 | $[61, 61, 2w^{2} - 7]$ | $\phantom{-}\frac{89790259944568837}{222008610784847869}e^{22} + \frac{93870644891918544}{222008610784847869}e^{21} - \frac{2896751255284329564}{222008610784847869}e^{20} - \frac{2847059290026850244}{222008610784847869}e^{19} + \frac{39756865472167200763}{222008610784847869}e^{18} + \frac{36715186529584379342}{222008610784847869}e^{17} - \frac{303300301907029833431}{222008610784847869}e^{16} - \frac{263719311285690082732}{222008610784847869}e^{15} + \frac{1409515410790261244044}{222008610784847869}e^{14} + \frac{1159552254854201167778}{222008610784847869}e^{13} - \frac{4109991836970321216502}{222008610784847869}e^{12} - \frac{3222756563120921938518}{222008610784847869}e^{11} + \frac{7456857042741653881263}{222008610784847869}e^{10} + \frac{5620046537728283392208}{222008610784847869}e^{9} - \frac{8036699549849040977225}{222008610784847869}e^{8} - \frac{5848683393235713468313}{222008610784847869}e^{7} + \frac{4641063794497607631774}{222008610784847869}e^{6} + \frac{3212325791760608586554}{222008610784847869}e^{5} - \frac{1183280177421985448041}{222008610784847869}e^{4} - \frac{697839855731551450419}{222008610784847869}e^{3} + \frac{139821895201163052194}{222008610784847869}e^{2} + \frac{47340436663516187370}{222008610784847869}e - \frac{7680402815787177760}{222008610784847869}$ |
| 71 | $[71, 71, w^{2} - 3w - 5]$ | $-\frac{3562871502241345}{222008610784847869}e^{22} + \frac{63029407841739678}{222008610784847869}e^{21} + \frac{161872967050649458}{222008610784847869}e^{20} - \frac{2036671455956555352}{222008610784847869}e^{19} - \frac{2937772828434546386}{222008610784847869}e^{18} + \frac{27940612884239400384}{222008610784847869}e^{17} + \frac{28686373375364810984}{222008610784847869}e^{16} - \frac{212453556498377924202}{222008610784847869}e^{15} - \frac{168800580911486063848}{222008610784847869}e^{14} + \frac{980146924993926830945}{222008610784847869}e^{13} + \frac{629520944211359894251}{222008610784847869}e^{12} - \frac{2821170383330236618194}{222008610784847869}e^{11} - \frac{1512514440180973902398}{222008610784847869}e^{10} + \frac{5009478391077606643496}{222008610784847869}e^{9} + \frac{2310098951150146750313}{222008610784847869}e^{8} - \frac{5205666079935524812905}{222008610784847869}e^{7} - \frac{2115640907129221294154}{222008610784847869}e^{6} + \frac{2800324775209301836920}{222008610784847869}e^{5} + \frac{984688578074136484033}{222008610784847869}e^{4} - \frac{586473634422669613742}{222008610784847869}e^{3} - \frac{128016261786123450218}{222008610784847869}e^{2} + \frac{35765854650537079862}{222008610784847869}e - \frac{2125453347572281076}{222008610784847869}$ |
| 73 | $[73, 73, 2w - 3]$ | $-\frac{28091274887870715}{222008610784847869}e^{22} + \frac{25014108544561941}{222008610784847869}e^{21} + \frac{901517707856482224}{222008610784847869}e^{20} - \frac{930048245285645426}{222008610784847869}e^{19} - \frac{12226179413631656280}{222008610784847869}e^{18} + \frac{14510310784383937794}{222008610784847869}e^{17} + \frac{91375998834553168389}{222008610784847869}e^{16} - \frac{124384676702646080183}{222008610784847869}e^{15} - \frac{411721905792596644874}{222008610784847869}e^{14} + \frac{643679708677685226548}{222008610784847869}e^{13} + \frac{1151207211002730096442}{222008610784847869}e^{12} - \frac{2078009339909267292437}{222008610784847869}e^{11} - \frac{1987246338268714284153}{222008610784847869}e^{10} + \frac{4169962549001247417016}{222008610784847869}e^{9} + \frac{2050454194857083748011}{222008610784847869}e^{8} - \frac{5006718977250619779090}{222008610784847869}e^{7} - \frac{1179562356614033393028}{222008610784847869}e^{6} + \frac{3298556991710958359034}{222008610784847869}e^{5} + \frac{295367785723892487064}{222008610784847869}e^{4} - \frac{1004610618357255788744}{222008610784847869}e^{3} + \frac{37408888249410999555}{222008610784847869}e^{2} + \frac{110622846216911959842}{222008610784847869}e - \frac{17302482601979871638}{222008610784847869}$ |
| 73 | $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ | $-\frac{116635169249823987}{222008610784847869}e^{22} - \frac{88060555809370571}{222008610784847869}e^{21} + \frac{3766912633215320264}{222008610784847869}e^{20} + \frac{2595102458804744180}{222008610784847869}e^{19} - \frac{51695325548567915256}{222008610784847869}e^{18} - \frac{32418090009322058838}{222008610784847869}e^{17} + \frac{393643130581238697404}{222008610784847869}e^{16} + \frac{225056125220441243950}{222008610784847869}e^{15} - \frac{1821050141060075462142}{222008610784847869}e^{14} - \frac{955238083317509581355}{222008610784847869}e^{13} + \frac{5263911147562125339811}{222008610784847869}e^{12} + \frac{2561089491466668056275}{222008610784847869}e^{11} - \frac{9403185953071683935000}{222008610784847869}e^{10} - \frac{4297464984543412635083}{222008610784847869}e^{9} + \frac{9853226835238594314528}{222008610784847869}e^{8} + \frac{4252108595685355666092}{222008610784847869}e^{7} - \frac{5372397671946952391153}{222008610784847869}e^{6} - \frac{2114576485002158411980}{222008610784847869}e^{5} + \frac{1164509165160441224448}{222008610784847869}e^{4} + \frac{321306682395853914173}{222008610784847869}e^{3} - \frac{77803483311084251429}{222008610784847869}e^{2} - \frac{2431676113826711925}{222008610784847869}e + \frac{839910901668297936}{222008610784847869}$ |
| 79 | $[79, 79, 2w^{2} - 5]$ | $-\frac{133003977153245036}{222008610784847869}e^{22} - \frac{71445485307413485}{222008610784847869}e^{21} + \frac{4352316690097737004}{222008610784847869}e^{20} + \frac{2071716293279697320}{222008610784847869}e^{19} - \frac{60665447495188004852}{222008610784847869}e^{18} - \frac{25537728711977382868}{222008610784847869}e^{17} + \frac{470746668796558262412}{222008610784847869}e^{16} + \frac{176213238086405775988}{222008610784847869}e^{15} - \frac{2229799883553132252482}{222008610784847869}e^{14} - \frac{753437061420452674095}{222008610784847869}e^{13} + \frac{6647062122951222309650}{222008610784847869}e^{12} + \frac{2077283353197033187872}{222008610784847869}e^{11} - \frac{12388097938920315640197}{222008610784847869}e^{10} - \frac{3679998509434806295619}{222008610784847869}e^{9} + \frac{13827856786247873083663}{222008610784847869}e^{8} + \frac{3951909111606713357784}{222008610784847869}e^{7} - \frac{8401658371023546684370}{222008610784847869}e^{6} - \frac{2183778571639712812123}{222008610784847869}e^{5} + \frac{2315216418820709733741}{222008610784847869}e^{4} + \frac{375965912378705006424}{222008610784847869}e^{3} - \frac{261611155556514511619}{222008610784847869}e^{2} - \frac{4690390558070239324}{222008610784847869}e + \frac{6721116324090032088}{222008610784847869}$ |
| 81 | $[81, 3, -3]$ | $-\frac{61352706366970158}{222008610784847869}e^{22} - \frac{20640716068966306}{222008610784847869}e^{21} + \frac{2020688666435506411}{222008610784847869}e^{20} + \frac{583953171211752074}{222008610784847869}e^{19} - \frac{28355930743974371067}{222008610784847869}e^{18} - \frac{7112171520696925662}{222008610784847869}e^{17} + \frac{221576355908230105608}{222008610784847869}e^{16} + \frac{49747397072842213358}{222008610784847869}e^{15} - \frac{1057178664857084701245}{222008610784847869}e^{14} - \frac{224265524893766681368}{222008610784847869}e^{13} + \frac{3175139182904171149078}{222008610784847869}e^{12} + \frac{681598950677214717431}{222008610784847869}e^{11} - \frac{5962759198255182519689}{222008610784847869}e^{10} - \frac{1376819997599334741299}{222008610784847869}e^{9} + \frac{6706631730415430989817}{222008610784847869}e^{8} + \frac{1708523230282208352074}{222008610784847869}e^{7} - \frac{4110199760235756460426}{222008610784847869}e^{6} - \frac{1096879078464023744081}{222008610784847869}e^{5} + \frac{1159927607169739187018}{222008610784847869}e^{4} + \frac{241385199089939212066}{222008610784847869}e^{3} - \frac{152933467302423766771}{222008610784847869}e^{2} - \frac{13211793638639781894}{222008610784847869}e + \frac{7431960297354499071}{222008610784847869}$ |
| 101 | $[101, 101, 2w^{2} - 4w - 9]$ | $-\frac{41735278831673542}{222008610784847869}e^{22} + \frac{2517952697934000}{222008610784847869}e^{21} + \frac{1414191400994911514}{222008610784847869}e^{20} - \frac{108402711971142525}{222008610784847869}e^{19} - \frac{20488075315085184603}{222008610784847869}e^{18} + \frac{1665523399877968811}{222008610784847869}e^{17} + \frac{165991787674415067112}{222008610784847869}e^{16} - \frac{12040217255527216492}{222008610784847869}e^{15} - \frac{825607731661134816106}{222008610784847869}e^{14} + \frac{40905684911067353929}{222008610784847869}e^{13} + \frac{2603209532019597394478}{222008610784847869}e^{12} - \frac{33976669820331180592}{222008610784847869}e^{11} - \frac{5181035721810181529452}{222008610784847869}e^{10} - \frac{172646770698563112327}{222008610784847869}e^{9} + \frac{6259624010131879838373}{222008610784847869}e^{8} + \frac{501897438252494487424}{222008610784847869}e^{7} - \frac{4207943732291333513486}{222008610784847869}e^{6} - \frac{440906389916342093403}{222008610784847869}e^{5} + \frac{1339800654319699317762}{222008610784847869}e^{4} + \frac{72807996629003192496}{222008610784847869}e^{3} - \frac{179168862767168187191}{222008610784847869}e^{2} + \frac{4601781210700506633}{222008610784847869}e + \frac{5406415937671231189}{222008610784847869}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $1$ |