Base field \(\Q(\sqrt{221}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 55\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11,11,-w + 1]$ |
| Dimension: | $23$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $92$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{23} + 5x^{22} - 41x^{21} - 213x^{20} + 714x^{19} + 3779x^{18} - 7053x^{17} - 36477x^{16} + 44358x^{15} + 209432x^{14} - 187003x^{13} - 734102x^{12} + 532520x^{11} + 1551019x^{10} - 987576x^{9} - 1874651x^{8} + 1086316x^{7} + 1154565x^{6} - 586476x^{5} - 285267x^{4} + 95654x^{3} + 24461x^{2} - 2194x - 187\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $...$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 7 | $[7, 7, w + 2]$ | $...$ |
| 7 | $[7, 7, w + 4]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w]$ | $...$ |
| 11 | $[11, 11, w + 10]$ | $-1$ |
| 13 | $[13, 13, w + 6]$ | $...$ |
| 17 | $[17, 17, -w - 8]$ | $...$ |
| 31 | $[31, 31, w + 14]$ | $...$ |
| 31 | $[31, 31, w + 16]$ | $...$ |
| 37 | $[37, 37, w + 15]$ | $...$ |
| 37 | $[37, 37, w + 21]$ | $...$ |
| 41 | $[41, 41, w + 18]$ | $...$ |
| 41 | $[41, 41, w + 22]$ | $...$ |
| 43 | $[43, 43, -w - 3]$ | $...$ |
| 43 | $[43, 43, w - 4]$ | $...$ |
| 53 | $[53, 53, -w - 1]$ | $...$ |
| 53 | $[53, 53, w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-w + 1]$ | $1$ |