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: | $[5,5,-w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 9x^{2} + x + 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-e^{3} - 3e^{2} + 4e + 6$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 2]$ | $-e^{3} - 3e^{2} + 5e + 7$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}e^{3} + 2e^{2} - 6e - 4$ |
| 9 | $[9, 3, 3]$ | $-e^{3} - 2e^{2} + 5e + 2$ |
| 11 | $[11, 11, w]$ | $\phantom{-}e - 1$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}2e^{3} + 5e^{2} - 10e - 12$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}3e^{3} + 8e^{2} - 13e - 16$ |
| 17 | $[17, 17, -w - 8]$ | $-4e^{3} - 10e^{2} + 19e + 21$ |
| 31 | $[31, 31, w + 14]$ | $-2e^{3} - 5e^{2} + 9e + 10$ |
| 31 | $[31, 31, w + 16]$ | $\phantom{-}4e^{3} + 10e^{2} - 19e - 23$ |
| 37 | $[37, 37, w + 15]$ | $-4e^{3} - 13e^{2} + 14e + 31$ |
| 37 | $[37, 37, w + 21]$ | $\phantom{-}4e^{3} + 11e^{2} - 18e - 24$ |
| 41 | $[41, 41, w + 18]$ | $\phantom{-}9e^{3} + 24e^{2} - 40e - 52$ |
| 41 | $[41, 41, w + 22]$ | $-4e^{3} - 9e^{2} + 20e + 14$ |
| 43 | $[43, 43, -w - 3]$ | $-e^{2} - 4e + 9$ |
| 43 | $[43, 43, w - 4]$ | $\phantom{-}3e^{3} + 10e^{2} - 10e - 24$ |
| 53 | $[53, 53, -w - 1]$ | $-4e^{3} - 10e^{2} + 18e + 19$ |
| 53 | $[53, 53, w - 2]$ | $\phantom{-}7e^{3} + 18e^{2} - 31e - 36$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5,5,-w + 1]$ | $-1$ |