Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5,5,-w + 2]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} + 5x^{10} - 11x^{9} - 79x^{8} + 5x^{7} + 396x^{6} + 264x^{5} - 599x^{4} - 724x^{3} - 128x^{2} + 60x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{48465}{27167}e^{10} + \frac{197726}{27167}e^{9} - \frac{715586}{27167}e^{8} - \frac{3171832}{27167}e^{7} + \frac{3171772}{27167}e^{6} + \frac{16308489}{27167}e^{5} - \frac{2274298}{27167}e^{4} - \frac{27169880}{27167}e^{3} - \frac{1430834}{3881}e^{2} + \frac{3481939}{27167}e - \frac{129347}{27167}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{36506}{27167}e^{10} - \frac{150403}{27167}e^{9} + \frac{534500}{27167}e^{8} + \frac{2413885}{27167}e^{7} - \frac{2318852}{27167}e^{6} - \frac{12426542}{27167}e^{5} + \frac{1362721}{27167}e^{4} + \frac{20753116}{27167}e^{3} + \frac{1159394}{3881}e^{2} - \frac{2637395}{27167}e - \frac{19787}{27167}$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{88012}{27167}e^{10} + \frac{364113}{27167}e^{9} - \frac{1280175}{27167}e^{8} - \frac{5839685}{27167}e^{7} + \frac{5449392}{27167}e^{6} + \frac{30016093}{27167}e^{5} - \frac{2552539}{27167}e^{4} - \frac{49840279}{27167}e^{3} - \frac{2958994}{3881}e^{2} + \frac{5504511}{27167}e - \frac{28324}{27167}$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{31687}{3881}e^{10} - \frac{130218}{3881}e^{9} + \frac{464412}{3881}e^{8} + \frac{2089718}{3881}e^{7} - \frac{2018216}{3881}e^{6} - \frac{10753943}{3881}e^{5} + \frac{1208644}{3881}e^{4} + \frac{17939274}{3881}e^{3} + \frac{6977951}{3881}e^{2} - \frac{2247157}{3881}e + \frac{28698}{3881}$ |
| 11 | $[11, 11, w + 9]$ | $-\frac{108587}{27167}e^{10} - \frac{447191}{27167}e^{9} + \frac{1589080}{27167}e^{8} + \frac{7180832}{27167}e^{7} - \frac{6867390}{27167}e^{6} - \frac{36974818}{27167}e^{5} + \frac{3827987}{27167}e^{4} + \frac{61636621}{27167}e^{3} + \frac{3504037}{3881}e^{2} - \frac{7311578}{27167}e + \frac{150345}{27167}$ |
| 17 | $[17, 17, w + 2]$ | $-\frac{138024}{27167}e^{10} - \frac{564226}{27167}e^{9} + \frac{2034429}{27167}e^{8} + \frac{9061518}{27167}e^{7} - \frac{8954798}{27167}e^{6} - \frac{46664593}{27167}e^{5} + \frac{5965093}{27167}e^{4} + \frac{77875786}{27167}e^{3} + \frac{4215408}{3881}e^{2} - \frac{9773243}{27167}e + \frac{268600}{27167}$ |
| 17 | $[17, 17, w + 14]$ | $-\frac{289152}{27167}e^{10} - \frac{1195015}{27167}e^{9} + \frac{4214220}{27167}e^{8} + \frac{19174611}{27167}e^{7} - \frac{18039747}{27167}e^{6} - \frac{98649515}{27167}e^{5} + \frac{9105427}{27167}e^{4} + \frac{164309653}{27167}e^{3} + \frac{9538122}{3881}e^{2} - \frac{19432120}{27167}e + \frac{121680}{27167}$ |
| 19 | $[19, 19, w]$ | $\phantom{-}\frac{252957}{27167}e^{10} + \frac{1038805}{27167}e^{9} - \frac{3713484}{27167}e^{8} - \frac{16683552}{27167}e^{7} + \frac{16201548}{27167}e^{6} + \frac{85964357}{27167}e^{5} - \frac{10084537}{27167}e^{4} - \frac{143784839}{27167}e^{3} - \frac{7848303}{3881}e^{2} + \frac{18519715}{27167}e - \frac{490913}{27167}$ |
| 19 | $[19, 19, w + 18]$ | $-\frac{93635}{27167}e^{10} - \frac{385521}{27167}e^{9} + \frac{1370974}{27167}e^{8} + \frac{6188890}{27167}e^{7} - \frac{5949501}{27167}e^{6} - \frac{31874884}{27167}e^{5} + \frac{3556667}{27167}e^{4} + \frac{53273518}{27167}e^{3} + \frac{2923927}{3881}e^{2} - \frac{6785885}{27167}e + \frac{201634}{27167}$ |
| 37 | $[37, 37, -w - 4]$ | $\phantom{-}\frac{7712}{3881}e^{10} + \frac{31445}{3881}e^{9} - \frac{114109}{3881}e^{8} - \frac{505232}{3881}e^{7} + \frac{507620}{3881}e^{6} + \frac{2604910}{3881}e^{5} - \frac{369750}{3881}e^{4} - \frac{4367931}{3881}e^{3} - \frac{1603206}{3881}e^{2} + \frac{607788}{3881}e + \frac{11119}{3881}$ |
| 37 | $[37, 37, w - 5]$ | $\phantom{-}\frac{521278}{27167}e^{10} + \frac{2151067}{27167}e^{9} - \frac{7610486}{27167}e^{8} - \frac{34528217}{27167}e^{7} + \frac{32719583}{27167}e^{6} + \frac{177753419}{27167}e^{5} - \frac{17385892}{27167}e^{4} - \frac{296516505}{27167}e^{3} - \frac{16967185}{3881}e^{2} + \frac{35912152}{27167}e - \frac{343914}{27167}$ |
| 43 | $[43, 43, w + 16]$ | $\phantom{-}\frac{40467}{3881}e^{10} + \frac{166068}{3881}e^{9} - \frac{594100}{3881}e^{8} - \frac{2665803}{3881}e^{7} + \frac{2589459}{3881}e^{6} + \frac{13719253}{3881}e^{5} - \frac{1574488}{3881}e^{4} - \frac{22863819}{3881}e^{3} - \frac{8929427}{3881}e^{2} + \frac{2789648}{3881}e - \frac{46904}{3881}$ |
| 43 | $[43, 43, w + 26]$ | $-\frac{575053}{27167}e^{10} - \frac{2370280}{27167}e^{9} + \frac{8404903}{27167}e^{8} + \frac{38038435}{27167}e^{7} - \frac{36242372}{27167}e^{6} - \frac{195711452}{27167}e^{5} + \frac{19870272}{27167}e^{4} + \frac{325959799}{27167}e^{3} + \frac{18599798}{3881}e^{2} - \frac{38940168}{27167}e + \frac{533266}{27167}$ |
| 49 | $[49, 7, -7]$ | $-\frac{258932}{27167}e^{10} - \frac{1063162}{27167}e^{9} + \frac{3798734}{27167}e^{8} + \frac{17061502}{27167}e^{7} - \frac{16565802}{27167}e^{6} - \frac{87823859}{27167}e^{5} + \frac{10348505}{27167}e^{4} + \frac{146669941}{27167}e^{3} + \frac{7993913}{3881}e^{2} - \frac{18681085}{27167}e + \frac{478748}{27167}$ |
| 53 | $[53, 53, -w - 10]$ | $\phantom{-}\frac{143188}{27167}e^{10} + \frac{602241}{27167}e^{9} - \frac{2047181}{27167}e^{8} - \frac{9659497}{27167}e^{7} + \frac{8298792}{27167}e^{6} + \frac{49667407}{27167}e^{5} - \frac{1313034}{27167}e^{4} - \frac{82347549}{27167}e^{3} - \frac{5433624}{3881}e^{2} + \frac{7806233}{27167}e + \frac{173153}{27167}$ |
| 53 | $[53, 53, w - 11]$ | $-\frac{308642}{27167}e^{10} - \frac{1267691}{27167}e^{9} + \frac{4529810}{27167}e^{8} + \frac{20362556}{27167}e^{7} - \frac{19714967}{27167}e^{6} - \frac{104893918}{27167}e^{5} + \frac{11775702}{27167}e^{4} + \frac{175069372}{27167}e^{3} + \frac{9792020}{3881}e^{2} - \frac{21447794}{27167}e + \frac{271372}{27167}$ |
| 61 | $[61, 61, w + 15]$ | $\phantom{-}\frac{188883}{27167}e^{10} + \frac{772284}{27167}e^{9} - \frac{2794857}{27167}e^{8} - \frac{12424681}{27167}e^{7} + \frac{12429593}{27167}e^{6} + \frac{64152736}{27167}e^{5} - \frac{9063655}{27167}e^{4} - \frac{107698715}{27167}e^{3} - \frac{5569778}{3881}e^{2} + \frac{14807362}{27167}e - \frac{409805}{27167}$ |
| 61 | $[61, 61, w + 45]$ | $-\frac{269817}{27167}e^{10} - \frac{1104420}{27167}e^{9} + \frac{3975295}{27167}e^{8} + \frac{17729120}{27167}e^{7} - \frac{17550296}{27167}e^{6} - \frac{91323453}{27167}e^{5} + \frac{12360109}{27167}e^{4} + \frac{152948990}{27167}e^{3} + \frac{7937527}{3881}e^{2} - \frac{20945522}{27167}e + \frac{728711}{27167}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w + 2]$ | $-1$ |