Base field \(\Q(\sqrt{193}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 48\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, -18w - 116]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -9w - 58]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -9w + 67]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -2w + 15]$ | $\phantom{-}0$ |
| 3 | $[3, 3, 2w + 13]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 186w - 1385]$ | $-e - 1$ |
| 7 | $[7, 7, -186w - 1199]$ | $\phantom{-}e + 2$ |
| 23 | $[23, 23, -38w - 245]$ | $-2e + 4$ |
| 23 | $[23, 23, 38w - 283]$ | $\phantom{-}2e - 2$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}2e - 2$ |
| 31 | $[31, 31, 16w - 119]$ | $-2e$ |
| 31 | $[31, 31, 16w + 103]$ | $\phantom{-}2e + 6$ |
| 43 | $[43, 43, 4w + 25]$ | $\phantom{-}5e - 1$ |
| 43 | $[43, 43, -4w + 29]$ | $\phantom{-}8$ |
| 59 | $[59, 59, 12w - 89]$ | $\phantom{-}5e + 1$ |
| 59 | $[59, 59, -12w - 77]$ | $-4e + 4$ |
| 67 | $[67, 67, 92w + 593]$ | $-3e + 11$ |
| 67 | $[67, 67, 92w - 685]$ | $-2e + 2$ |
| 83 | $[83, 83, 204w - 1519]$ | $-5e + 10$ |
| 83 | $[83, 83, 204w + 1315]$ | $-6e + 4$ |
| 97 | $[97, 97, -24w + 179]$ | $-6e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -9w - 58]$ | $-1$ |
| $2$ | $[2, 2, -9w + 67]$ | $-1$ |