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: | $[16, 4, 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $104$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 6x^{3} + 7x^{2} + 6x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 2e + 4$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 2e + 4$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e^{2} + 5e + 4$ |
| 11 | $[11, 11, w]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + 2e$ |
| 11 | $[11, 11, w + 10]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + 2e$ |
| 13 | $[13, 13, w + 6]$ | $-e^{3} + 3e^{2} + 4e - 6$ |
| 17 | $[17, 17, -w - 8]$ | $\phantom{-}e^{3} - 5e^{2} + 6e + 2$ |
| 31 | $[31, 31, w + 14]$ | $-2e^{2} + 5e + 6$ |
| 31 | $[31, 31, w + 16]$ | $-2e^{2} + 5e + 6$ |
| 37 | $[37, 37, w + 15]$ | $\phantom{-}2e^{2} - 7e$ |
| 37 | $[37, 37, w + 21]$ | $\phantom{-}2e^{2} - 7e$ |
| 41 | $[41, 41, w + 18]$ | $\phantom{-}e^{3} - 6e^{2} + 7e + 4$ |
| 41 | $[41, 41, w + 22]$ | $\phantom{-}e^{3} - 6e^{2} + 7e + 4$ |
| 43 | $[43, 43, -w - 3]$ | $-e^{2} + 2e$ |
| 43 | $[43, 43, w - 4]$ | $-e^{2} + 2e$ |
| 53 | $[53, 53, -w - 1]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 3e + 4$ |
| 53 | $[53, 53, w - 2]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 3e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |