Base field \(\Q(\sqrt{29}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 7\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[49, 49, w + 7]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 12x^{2} + 25\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $-e^{2} + 6$ |
| 5 | $[5, 5, w + 1]$ | $-1$ |
| 5 | $[5, 5, w - 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{14}{5}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{2}{5}e$ |
| 13 | $[13, 13, w + 4]$ | $-e^{2} + 8$ |
| 13 | $[13, 13, w - 5]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{9}{5}e$ |
| 23 | $[23, 23, -w - 5]$ | $\phantom{-}\frac{2}{5}e^{3} - \frac{24}{5}e$ |
| 23 | $[23, 23, w - 6]$ | $-\frac{4}{5}e^{3} + \frac{38}{5}e$ |
| 29 | $[29, 29, 2w - 1]$ | $-\frac{3}{5}e^{3} + \frac{21}{5}e$ |
| 53 | $[53, 53, 3w - 5]$ | $\phantom{-}2e^{2} - 11$ |
| 53 | $[53, 53, -3w - 2]$ | $-2e^{2} + 7$ |
| 59 | $[59, 59, -3w - 1]$ | $-2e^{2} + 6$ |
| 59 | $[59, 59, 3w - 4]$ | $-\frac{2}{5}e^{3} + \frac{24}{5}e$ |
| 67 | $[67, 67, 3w - 13]$ | $\phantom{-}2e^{3} - 14e$ |
| 67 | $[67, 67, -3w - 10]$ | $\phantom{-}2e$ |
| 71 | $[71, 71, 2w - 11]$ | $\phantom{-}2e^{2} - 14$ |
| 71 | $[71, 71, -2w - 9]$ | $-2e^{2} + 4$ |
| 83 | $[83, 83, -w - 9]$ | $\phantom{-}14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w]$ | $1$ |