Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 22x^{8} + 159x^{6} + 439x^{4} + 351x^{2} + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $-\frac{77}{1339}e^{8} - \frac{1372}{1339}e^{6} - \frac{6749}{1339}e^{4} - \frac{9110}{1339}e^{2} - \frac{373}{1339}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{31}{6695}e^{9} + \frac{178}{6695}e^{7} + \frac{9786}{6695}e^{5} + \frac{52466}{6695}e^{3} + \frac{64174}{6695}e$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{13}{515}e^{9} - \frac{241}{515}e^{7} - \frac{1312}{515}e^{5} - \frac{2552}{515}e^{3} - \frac{2028}{515}e$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{3}{1339}e^{9} + \frac{190}{1339}e^{7} + \frac{3841}{1339}e^{5} + \frac{16826}{1339}e^{3} + \frac{12819}{1339}e$ |
| 11 | $[11, 11, w + 1]$ | $-\frac{4}{103}e^{9} - \frac{90}{103}e^{7} - \frac{681}{103}e^{5} - \frac{2045}{103}e^{3} - \frac{1757}{103}e$ |
| 11 | $[11, 11, w + 10]$ | $-\frac{249}{6695}e^{9} - \frac{6993}{6695}e^{7} - \frac{64151}{6695}e^{5} - \frac{204886}{6695}e^{3} - \frac{139784}{6695}e$ |
| 17 | $[17, 17, -3w + 17]$ | $-\frac{55}{1339}e^{8} - \frac{980}{1339}e^{6} - \frac{5012}{1339}e^{4} - \frac{8420}{1339}e^{2} - \frac{649}{1339}$ |
| 29 | $[29, 29, w + 11]$ | $-\frac{492}{6695}e^{9} - \frac{10349}{6695}e^{7} - \frac{70373}{6695}e^{5} - \frac{183658}{6695}e^{3} - \frac{129797}{6695}e$ |
| 29 | $[29, 29, w + 18]$ | $\phantom{-}\frac{461}{6695}e^{9} + \frac{10527}{6695}e^{7} + \frac{80159}{6695}e^{5} + \frac{236124}{6695}e^{3} + \frac{200666}{6695}e$ |
| 37 | $[37, 37, w + 16]$ | $\phantom{-}\frac{2218}{6695}e^{9} + \frac{43416}{6695}e^{7} + \frac{260452}{6695}e^{5} + \frac{559882}{6695}e^{3} + \frac{327983}{6695}e$ |
| 37 | $[37, 37, w + 21]$ | $-\frac{876}{6695}e^{9} - \frac{15487}{6695}e^{7} - \frac{75494}{6695}e^{5} - \frac{113414}{6695}e^{3} - \frac{81036}{6695}e$ |
| 47 | $[47, 47, -w - 9]$ | $\phantom{-}\frac{271}{1339}e^{8} + \frac{4707}{1339}e^{6} + \frac{21701}{1339}e^{4} + \frac{27489}{1339}e^{2} + \frac{14981}{1339}$ |
| 47 | $[47, 47, w - 9]$ | $-\frac{333}{1339}e^{8} - \frac{5690}{1339}e^{6} - \frac{24892}{1339}e^{4} - \frac{22982}{1339}e^{2} + \frac{891}{1339}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{19}{1339}e^{8} + \frac{582}{1339}e^{6} + \frac{5578}{1339}e^{4} + \frac{14838}{1339}e^{2} - \frac{2186}{1339}$ |
| 61 | $[61, 61, w + 20]$ | $\phantom{-}\frac{356}{6695}e^{9} + \frac{10482}{6695}e^{7} + \frac{100779}{6695}e^{5} + \frac{336299}{6695}e^{3} + \frac{254326}{6695}e$ |
| 61 | $[61, 61, w + 41]$ | $\phantom{-}\frac{1052}{6695}e^{9} + \frac{23979}{6695}e^{7} + \frac{179103}{6695}e^{5} + \frac{495193}{6695}e^{3} + \frac{368052}{6695}e$ |
| 89 | $[89, 89, 2w - 15]$ | $\phantom{-}\frac{189}{1339}e^{8} + \frac{4098}{1339}e^{6} + \frac{28495}{1339}e^{4} + \frac{67400}{1339}e^{2} + \frac{25261}{1339}$ |
| 89 | $[89, 89, -2w - 15]$ | $\phantom{-}\frac{216}{1339}e^{8} + \frac{3727}{1339}e^{6} + \frac{16689}{1339}e^{4} + \frac{16391}{1339}e^{2} + \frac{4959}{1339}$ |
| 103 | $[103, 103, -14w + 81]$ | $\phantom{-}\frac{672}{1339}e^{8} + \frac{12339}{1339}e^{6} + \frac{64865}{1339}e^{4} + \frac{106042}{1339}e^{2} + \frac{30157}{1339}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 2]$ | $\frac{13}{515}e^{9} + \frac{241}{515}e^{7} + \frac{1312}{515}e^{5} + \frac{2552}{515}e^{3} + \frac{2028}{515}e$ |