Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, -w + 9]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} + 6x^{2} - 4x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 9]$ | $-1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} + 3e - 2$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} + e^{2} + 4e + \frac{2}{3}$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{2}{3}e^{3} + e^{2} + 4e - \frac{8}{3}$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{1}{3}e^{3} - e^{2} - 2e - \frac{2}{3}$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{1}{3}e^{3} + e^{2} + 2e - \frac{4}{3}$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{1}{3}e^{3} - e^{2} - 2e - \frac{2}{3}$ |
| 13 | $[13, 13, w + 12]$ | $\phantom{-}\frac{1}{3}e^{3} + e^{2} + 2e - \frac{4}{3}$ |
| 43 | $[43, 43, -w - 6]$ | $\phantom{-}\frac{1}{2}e^{3} - 12$ |
| 43 | $[43, 43, w - 6]$ | $-\frac{1}{2}e^{3} - 2$ |
| 47 | $[47, 47, w + 19]$ | $-\frac{2}{3}e^{3} - 2e^{2} - 8e - \frac{4}{3}$ |
| 47 | $[47, 47, w + 28]$ | $-\frac{4}{3}e^{3} - 2e^{2} - 8e + \frac{16}{3}$ |
| 59 | $[59, 59, w + 16]$ | $-\frac{5}{3}e^{3} - 5e^{2} - 11e - \frac{10}{3}$ |
| 59 | $[59, 59, w + 43]$ | $\phantom{-}\frac{7}{6}e^{3} + 4e^{2} + 7e - \frac{14}{3}$ |
| 71 | $[71, 71, w + 24]$ | $-\frac{1}{3}e^{3} + e^{2} - 2e + \frac{4}{3}$ |
| 71 | $[71, 71, w + 47]$ | $-\frac{5}{3}e^{3} - 5e^{2} - 14e - \frac{10}{3}$ |
| 73 | $[73, 73, 3w - 28]$ | $-e^{3} + 12$ |
| 73 | $[73, 73, 12w - 107]$ | $\phantom{-}e^{3} - 8$ |
| 79 | $[79, 79, -w]$ | $\phantom{-}8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 9]$ | $1$ |