Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[29,29,w - 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $108$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 5x^{3} + 5x^{2} + 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 7]$ | $-e^{3} + 6e^{2} - 7e - 3$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}e^{3} - 3e^{2} - 2e + 3$ |
| 9 | $[9, 3, 3]$ | $-e^{2} + 2e + 1$ |
| 19 | $[19, 19, w + 5]$ | $-e^{3} + 3e^{2} + 2e - 6$ |
| 19 | $[19, 19, w - 6]$ | $-e^{3} + 5e^{2} - 3e - 3$ |
| 23 | $[23, 23, w + 8]$ | $-2e^{3} + 10e^{2} - 9e - 1$ |
| 23 | $[23, 23, -w + 9]$ | $-e^{3} + 4e^{2} - e$ |
| 25 | $[25, 5, 5]$ | $-3e^{3} + 15e^{2} - 15e - 4$ |
| 29 | $[29, 29, -w - 4]$ | $\phantom{-}2e^{3} - 8e^{2} + 2e + 7$ |
| 29 | $[29, 29, w - 5]$ | $-1$ |
| 37 | $[37, 37, -w - 3]$ | $\phantom{-}e^{3} - 3e^{2} + 2e - 2$ |
| 37 | $[37, 37, w - 4]$ | $-e^{3} + 3e^{2} - 2e + 3$ |
| 41 | $[41, 41, -w - 9]$ | $\phantom{-}2e^{3} - 8e^{2} + 6e - 2$ |
| 41 | $[41, 41, w - 10]$ | $-2e^{3} + 6e^{2} - e + 2$ |
| 43 | $[43, 43, -w - 2]$ | $-2e^{3} + 9e^{2} - 8e - 1$ |
| 43 | $[43, 43, w - 3]$ | $-4e^{3} + 18e^{2} - 13e - 7$ |
| 47 | $[47, 47, -w - 1]$ | $\phantom{-}2e^{3} - 11e^{2} + 14e + 7$ |
| 47 | $[47, 47, w - 2]$ | $\phantom{-}e^{3} - 2e^{2} - 3e + 7$ |
| 53 | $[53, 53, 2w - 13]$ | $-4e^{3} + 18e^{2} - 15e - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29,29,w - 5]$ | $1$ |