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: | $[9, 3, 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $84$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 13x^{2} - 4x + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{8}{3}e + \frac{1}{3}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{11}{3}e + \frac{4}{3}$ |
| 7 | $[7, 7, w + 2]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{11}{3}e - \frac{4}{3}$ |
| 7 | $[7, 7, w + 4]$ | $-e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{8}{3}e + \frac{2}{3}$ |
| 11 | $[11, 11, w + 10]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{8}{3}e + \frac{2}{3}$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{8}{3}e - \frac{10}{3}$ |
| 17 | $[17, 17, -w - 8]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{8}{3}e + \frac{2}{3}$ |
| 31 | $[31, 31, w + 14]$ | $\phantom{-}e^{2} - e - 8$ |
| 31 | $[31, 31, w + 16]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{7}{3}e^{2} - \frac{13}{3}e + \frac{20}{3}$ |
| 37 | $[37, 37, w + 15]$ | $-\frac{1}{3}e^{3} + \frac{5}{3}e^{2} + \frac{2}{3}e - \frac{34}{3}$ |
| 37 | $[37, 37, w + 21]$ | $-e^{2} + 2e + 2$ |
| 41 | $[41, 41, w + 18]$ | $\phantom{-}e^{3} - 3e^{2} - 7e + 12$ |
| 41 | $[41, 41, w + 22]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - \frac{11}{3}e - \frac{8}{3}$ |
| 43 | $[43, 43, -w - 3]$ | $-e^{3} + 3e^{2} + 6e - 12$ |
| 43 | $[43, 43, w - 4]$ | $-\frac{2}{3}e^{3} + \frac{1}{3}e^{2} + \frac{22}{3}e + \frac{4}{3}$ |
| 53 | $[53, 53, -w - 1]$ | $-e^{3} + 4e^{2} + 6e - 14$ |
| 53 | $[53, 53, w - 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e^{2} - \frac{2}{3}e + \frac{46}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $-1$ |