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: | $[1, 1, 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 10x - 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-e^{2} + e + 6$ |
| 5 | $[5, 5, w + 4]$ | $-e^{2} + e + 6$ |
| 7 | $[7, 7, w + 2]$ | $-e^{2} + 2e + 7$ |
| 7 | $[7, 7, w + 4]$ | $-e^{2} + 2e + 7$ |
| 9 | $[9, 3, 3]$ | $-2e^{2} + 3e + 13$ |
| 11 | $[11, 11, w]$ | $\phantom{-}e - 1$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}e - 1$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}2e^{2} - 4e - 16$ |
| 17 | $[17, 17, -w - 8]$ | $\phantom{-}2e^{2} - 4e - 12$ |
| 31 | $[31, 31, w + 14]$ | $-e^{2} + 3e + 10$ |
| 31 | $[31, 31, w + 16]$ | $-e^{2} + 3e + 10$ |
| 37 | $[37, 37, w + 15]$ | $\phantom{-}e^{2} - e - 2$ |
| 37 | $[37, 37, w + 21]$ | $\phantom{-}e^{2} - e - 2$ |
| 41 | $[41, 41, w + 18]$ | $\phantom{-}4e^{2} - 8e - 30$ |
| 41 | $[41, 41, w + 22]$ | $\phantom{-}4e^{2} - 8e - 30$ |
| 43 | $[43, 43, -w - 3]$ | $-3e^{2} + 7e + 20$ |
| 43 | $[43, 43, w - 4]$ | $-3e^{2} + 7e + 20$ |
| 53 | $[53, 53, -w - 1]$ | $\phantom{-}e^{2} - 3$ |
| 53 | $[53, 53, w - 2]$ | $\phantom{-}e^{2} - 3$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).