Base field 6.6.1081856.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 7x^{2} + 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ |
| Dimension: | $14$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{14} - 6x^{13} - 23x^{12} + 168x^{11} + 135x^{10} - 1470x^{9} - 377x^{8} + 5386x^{7} + 1046x^{6} - 7870x^{5} - 1832x^{4} + 3170x^{3} + 798x^{2} - 378x - 100\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - w^{3} - 4w^{2} + w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 5w]$ | $\phantom{-}\frac{396927767}{3804363708}e^{13} - \frac{2375232155}{3804363708}e^{12} - \frac{2268308530}{951090927}e^{11} + \frac{16487453573}{951090927}e^{10} + \frac{52722227585}{3804363708}e^{9} - \frac{566956798769}{3804363708}e^{8} - \frac{12616140677}{317030309}e^{7} + \frac{1005146850623}{1902181854}e^{6} + \frac{109406658451}{951090927}e^{5} - \frac{450832794575}{634060618}e^{4} - \frac{116947809325}{634060618}e^{3} + \frac{183160523566}{951090927}e^{2} + \frac{75802307593}{1902181854}e - \frac{2357875160}{317030309}$ |
| 17 | $[17, 17, -w^{2} + w + 2]$ | $-\frac{6560370067}{125544002364}e^{13} + \frac{1313644817}{3804363708}e^{12} + \frac{3439959086}{3487333399}e^{11} - \frac{293111950589}{31386000591}e^{10} - \frac{162758854871}{125544002364}e^{9} + \frac{3205699525165}{41848000788}e^{8} - \frac{1665143636455}{62772001182}e^{7} - \frac{16202311314931}{62772001182}e^{6} + \frac{3077636254112}{31386000591}e^{5} + \frac{20713216752137}{62772001182}e^{4} - \frac{692982776309}{6974666798}e^{3} - \frac{2484843285050}{31386000591}e^{2} + \frac{114264182279}{6974666798}e + \frac{141587322416}{31386000591}$ |
| 23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ | $\phantom{-}\frac{11459911081}{376632007092}e^{13} - \frac{7698770507}{34239273372}e^{12} - \frac{81262215371}{188316003546}e^{11} + \frac{562829305726}{94158001773}e^{10} - \frac{1202958053287}{376632007092}e^{9} - \frac{17964060074867}{376632007092}e^{8} + \frac{1541525391466}{31386000591}e^{7} + \frac{30050474518667}{188316003546}e^{6} - \frac{16480731284201}{94158001773}e^{5} - \frac{41926735112635}{188316003546}e^{4} + \frac{13261605706975}{62772001182}e^{3} + \frac{9167059002803}{94158001773}e^{2} - \frac{7236330348889}{188316003546}e - \frac{1071028296133}{94158001773}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w]$ | $\phantom{-}\frac{5862680437}{188316003546}e^{13} - \frac{4199163143}{17119636686}e^{12} - \frac{32248947983}{94158001773}e^{11} + \frac{1205514037393}{188316003546}e^{10} - \frac{1105997371999}{188316003546}e^{9} - \frac{4640078536810}{94158001773}e^{8} + \frac{736649809246}{10462000197}e^{7} + \frac{14927898774365}{94158001773}e^{6} - \frac{22696281601789}{94158001773}e^{5} - \frac{20393990862979}{94158001773}e^{4} + \frac{8907435941797}{31386000591}e^{3} + \frac{9466984230175}{94158001773}e^{2} - \frac{4751303407423}{94158001773}e - \frac{1416650231108}{94158001773}$ |
| 31 | $[31, 31, -w^{3} + 4w + 1]$ | $-\frac{65373782285}{376632007092}e^{13} + \frac{9382445455}{8559818343}e^{12} + \frac{681540486109}{188316003546}e^{11} - \frac{2836739096363}{94158001773}e^{10} - \frac{5030078019535}{376632007092}e^{9} + \frac{23983408891300}{94158001773}e^{8} - \frac{121642821461}{6974666798}e^{7} - \frac{167890145824021}{188316003546}e^{6} + \frac{19752791858705}{188316003546}e^{5} + \frac{113462292107773}{94158001773}e^{4} - \frac{5275058393327}{62772001182}e^{3} - \frac{67995918119183}{188316003546}e^{2} + \frac{1719469009957}{94158001773}e + \frac{2863551371099}{94158001773}$ |
| 31 | $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ | $\phantom{-}\frac{25304793850}{94158001773}e^{13} - \frac{58209628187}{34239273372}e^{12} - \frac{527898945349}{94158001773}e^{11} + \frac{8825811350969}{188316003546}e^{10} + \frac{3846167016193}{188316003546}e^{9} - \frac{150030379341245}{376632007092}e^{8} + \frac{2117151122969}{62772001182}e^{7} + \frac{132112736749513}{94158001773}e^{6} - \frac{37063683775939}{188316003546}e^{5} - \frac{361461310767901}{188316003546}e^{4} + \frac{5526897590243}{31386000591}e^{3} + \frac{114347150528293}{188316003546}e^{2} - \frac{4526231835223}{188316003546}e - \frac{4415490373084}{94158001773}$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 5w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}\frac{94302162677}{376632007092}e^{13} - \frac{58161574171}{34239273372}e^{12} - \frac{424893327773}{94158001773}e^{11} + \frac{8684297761501}{188316003546}e^{10} - \frac{145999571057}{376632007092}e^{9} - \frac{143863087537153}{376632007092}e^{8} + \frac{6071033642141}{31386000591}e^{7} + \frac{248380792630291}{188316003546}e^{6} - \frac{69427190681533}{94158001773}e^{5} - \frac{343282673051825}{188316003546}e^{4} + \frac{54673421572595}{62772001182}e^{3} + \frac{63349743718681}{94158001773}e^{2} - \frac{33408885874811}{188316003546}e - \frac{6603680152043}{94158001773}$ |
| 47 | $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ | $-1$ |
| 49 | $[49, 7, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 3]$ | $\phantom{-}\frac{1919707859}{8559818343}e^{13} - \frac{51526156127}{34239273372}e^{12} - \frac{35616868091}{8559818343}e^{11} + \frac{702827876143}{17119636686}e^{10} + \frac{47772630875}{17119636686}e^{9} - \frac{11757835440835}{34239273372}e^{8} + \frac{849740305181}{5706545562}e^{7} + \frac{10301152560143}{8559818343}e^{6} - \frac{10028464220465}{17119636686}e^{5} - \frac{29203683028601}{17119636686}e^{4} + \frac{1993871772943}{2853272781}e^{3} + \frac{11638509082103}{17119636686}e^{2} - \frac{2498441177285}{17119636686}e - \frac{680927797214}{8559818343}$ |
| 71 | $[71, 71, -w^{4} + 5w^{2} + w - 3]$ | $-\frac{43827173473}{125544002364}e^{13} + \frac{25809317869}{11413091124}e^{12} + \frac{436602567613}{62772001182}e^{11} - \frac{216287218449}{3487333399}e^{10} - \frac{2204656184465}{125544002364}e^{9} + \frac{65623544572321}{125544002364}e^{8} - \frac{3743181514993}{31386000591}e^{7} - \frac{12763140149663}{6974666798}e^{6} + \frac{16280580661394}{31386000591}e^{5} + \frac{17518535165165}{6974666798}e^{4} - \frac{12133203601583}{20924000394}e^{3} - \frac{26188795227305}{31386000591}e^{2} + \frac{8060524389959}{62772001182}e + \frac{843815968511}{10462000197}$ |
| 71 | $[71, 71, w^{4} - 5w^{2} - 2w + 4]$ | $\phantom{-}\frac{110956166567}{376632007092}e^{13} - \frac{33880616717}{17119636686}e^{12} - \frac{509693644868}{94158001773}e^{11} + \frac{10114682340031}{188316003546}e^{10} + \frac{997571165179}{376632007092}e^{9} - \frac{41853863102731}{94158001773}e^{8} + \frac{1380594260933}{6974666798}e^{7} + \frac{288260977079131}{188316003546}e^{6} - \frac{142590764631923}{188316003546}e^{5} - \frac{196873211190703}{94158001773}e^{4} + \frac{55663707957149}{62772001182}e^{3} + \frac{137060347485503}{188316003546}e^{2} - \frac{18804345479908}{94158001773}e - \frac{7296698921015}{94158001773}$ |
| 73 | $[73, 73, -2w^{5} + w^{4} + 10w^{3} - 9w - 1]$ | $\phantom{-}\frac{72357399533}{188316003546}e^{13} - \frac{81790955813}{34239273372}e^{12} - \frac{1546842687941}{188316003546}e^{11} + \frac{6184272277297}{94158001773}e^{10} + \frac{6673633307227}{188316003546}e^{9} - \frac{208990088626997}{376632007092}e^{8} - \frac{983879949973}{62772001182}e^{7} + \frac{181682993167822}{94158001773}e^{6} - \frac{4694973842335}{188316003546}e^{5} - \frac{478580427747073}{188316003546}e^{4} - \frac{3487334367004}{31386000591}e^{3} + \frac{122687042535685}{188316003546}e^{2} + \frac{7641185678765}{188316003546}e - \frac{2833985802328}{94158001773}$ |
| 73 | $[73, 73, -w^{5} + 6w^{3} + 2w^{2} - 5w - 1]$ | $-\frac{30138725489}{62772001182}e^{13} + \frac{8964319610}{2853272781}e^{12} + \frac{294299420362}{31386000591}e^{11} - \frac{2699720545483}{31386000591}e^{10} - \frac{1188791731045}{62772001182}e^{9} + \frac{22694403522545}{31386000591}e^{8} - \frac{726258199317}{3487333399}e^{7} - \frac{79416503150755}{31386000591}e^{6} + \frac{27241726324871}{31386000591}e^{5} + \frac{109900123239968}{31386000591}e^{4} - \frac{10440952130120}{10462000197}e^{3} - \frac{38596630514939}{31386000591}e^{2} + \frac{6703130858015}{31386000591}e + \frac{3904369650166}{31386000591}$ |
| 79 | $[79, 79, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{1801639363}{34239273372}e^{13} - \frac{4509471893}{17119636686}e^{12} - \frac{25997164763}{17119636686}e^{11} + \frac{65150311477}{8559818343}e^{10} + \frac{538317246197}{34239273372}e^{9} - \frac{1190806662481}{17119636686}e^{8} - \frac{60038342521}{634060618}e^{7} + \frac{4401945180719}{17119636686}e^{6} + \frac{5506094132753}{17119636686}e^{5} - \frac{2864251931114}{8559818343}e^{4} - \frac{2561268463307}{5706545562}e^{3} + \frac{684310161475}{17119636686}e^{2} + \frac{992369887849}{8559818343}e + \frac{95692343813}{8559818343}$ |
| 89 | $[89, 89, w^{5} - 7w^{3} - w^{2} + 9w]$ | $-\frac{20172130501}{125544002364}e^{13} + \frac{6172612463}{5706545562}e^{12} + \frac{187254612823}{62772001182}e^{11} - \frac{103404226348}{3487333399}e^{10} - \frac{221877540773}{125544002364}e^{9} + \frac{15721239986105}{62772001182}e^{8} - \frac{3540112009024}{31386000591}e^{7} - \frac{6213917735423}{6974666798}e^{6} + \frac{28516172536477}{62772001182}e^{5} + \frac{4527903326282}{3487333399}e^{4} - \frac{11629749946571}{20924000394}e^{3} - \frac{35027075332615}{62772001182}e^{2} + \frac{3469720822000}{31386000591}e + \frac{703762599704}{10462000197}$ |
| 97 | $[97, 97, 2w^{5} - 2w^{4} - 10w^{3} + 5w^{2} + 10w - 1]$ | $-\frac{119031103567}{188316003546}e^{13} + \frac{68878383065}{17119636686}e^{12} + \frac{1221016615721}{94158001773}e^{11} - \frac{10385478277886}{94158001773}e^{10} - \frac{8082236554241}{188316003546}e^{9} + \frac{174710167631171}{188316003546}e^{8} - \frac{382644282651}{3487333399}e^{7} - \frac{303417812591471}{94158001773}e^{6} + \frac{49655547818488}{94158001773}e^{5} + \frac{404540645647339}{94158001773}e^{4} - \frac{14539103447641}{31386000591}e^{3} - \frac{113908603641361}{94158001773}e^{2} + \frac{8017050183493}{94158001773}e + \frac{6894093475454}{94158001773}$ |
| 103 | $[103, 103, w^{5} - w^{4} - 4w^{3} + w^{2} + 3w + 2]$ | $-\frac{72526173949}{376632007092}e^{13} + \frac{20994437737}{17119636686}e^{12} + \frac{750788597657}{188316003546}e^{11} - \frac{6386215523471}{188316003546}e^{10} - \frac{5068083653465}{376632007092}e^{9} + \frac{27301390609307}{94158001773}e^{8} - \frac{1230013435292}{31386000591}e^{7} - \frac{193976951707511}{188316003546}e^{6} + \frac{39800142224407}{188316003546}e^{5} + \frac{135010629780140}{94158001773}e^{4} - \frac{15187466107525}{62772001182}e^{3} - \frac{91098145469473}{188316003546}e^{2} + \frac{5221402036142}{94158001773}e + \frac{4039827027688}{94158001773}$ |
| 103 | $[103, 103, -2w^{5} + w^{4} + 11w^{3} - w^{2} - 11w - 1]$ | $\phantom{-}\frac{3112021639}{188316003546}e^{13} - \frac{4529894731}{34239273372}e^{12} - \frac{17106514244}{94158001773}e^{11} + \frac{663644109631}{188316003546}e^{10} - \frac{301724672339}{94158001773}e^{9} - \frac{10776902725717}{376632007092}e^{8} + \frac{825720061255}{20924000394}e^{7} + \frac{9770319688484}{94158001773}e^{6} - \frac{26695397257085}{188316003546}e^{5} - \frac{34583735000477}{188316003546}e^{4} + \frac{5734021708015}{31386000591}e^{3} + \frac{27121019542079}{188316003546}e^{2} - \frac{9639880423073}{188316003546}e - \frac{2193733149926}{94158001773}$ |
| 103 | $[103, 103, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $-\frac{3861027505}{6974666798}e^{13} + \frac{40508709413}{11413091124}e^{12} + \frac{703897329521}{62772001182}e^{11} - \frac{3052625739563}{31386000591}e^{10} - \frac{350122408309}{10462000197}e^{9} + \frac{102680301370445}{125544002364}e^{8} - \frac{4187930476696}{31386000591}e^{7} - \frac{89367838445669}{31386000591}e^{6} + \frac{4183828285375}{6974666798}e^{5} + \frac{241442469357389}{62772001182}e^{4} - \frac{6197513980148}{10462000197}e^{3} - \frac{24870744524245}{20924000394}e^{2} + \frac{7024852835857}{62772001182}e + \frac{3041839189421}{31386000591}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $47$ | $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ | $1$ |