Base field \(\Q(\sqrt{241}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 60\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, -786w - 5708]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 4x^{2} + 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -393w - 2854]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -393w + 3247]$ | $\phantom{-}1$ |
| 3 | $[3, 3, 4w - 33]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 4w + 29]$ | $\phantom{-}e - 3$ |
| 5 | $[5, 5, 42w + 305]$ | $-e^{2} + 4e - 1$ |
| 5 | $[5, 5, -42w + 347]$ | $\phantom{-}2e^{2} - 5e + 2$ |
| 29 | $[29, 29, 1820w + 13217]$ | $-4e^{2} + 9e - 1$ |
| 29 | $[29, 29, 1820w - 15037]$ | $-7e^{2} + 18e - 1$ |
| 41 | $[41, 41, -80w - 581]$ | $-3e^{2} + 6e - 4$ |
| 41 | $[41, 41, 80w - 661]$ | $\phantom{-}3e^{2} - 9e + 2$ |
| 47 | $[47, 47, 34w - 281]$ | $-3e^{2} + 13e - 5$ |
| 47 | $[47, 47, 34w + 247]$ | $\phantom{-}3e^{2} - 5e - 11$ |
| 49 | $[49, 7, -7]$ | $-3e^{2} + 13$ |
| 53 | $[53, 53, 6w + 43]$ | $\phantom{-}2e^{2} - e - 8$ |
| 53 | $[53, 53, 6w - 49]$ | $-e^{2} - e + 7$ |
| 59 | $[59, 59, 10w + 73]$ | $\phantom{-}e^{2} + e$ |
| 59 | $[59, 59, 10w - 83]$ | $\phantom{-}7e^{2} - 11e - 12$ |
| 61 | $[61, 61, 4178w + 30341]$ | $-4e^{2} + 10e + 3$ |
| 61 | $[61, 61, 4178w - 34519]$ | $-7e^{2} + 13e + 6$ |
| 67 | $[67, 67, -332w + 2743]$ | $-6e^{2} + 16e + 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -393w - 2854]$ | $-1$ |
| $2$ | $[2, 2, -393w + 3247]$ | $-1$ |