Base field \(\Q(\sqrt{86}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 86\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| 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:
| \(x^{4} + 8x^{3} + 18x^{2} + 8x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w + 102]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w - 9]$ | $\phantom{-}e + 4$ |
| 5 | $[5, 5, w + 9]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 4w - 37]$ | $-e^{2} - 5e - 2$ |
| 7 | $[7, 7, 4w + 37]$ | $\phantom{-}e^{2} + 3e - 2$ |
| 9 | $[9, 3, 3]$ | $-e^{2} - 4e - 2$ |
| 11 | $[11, 11, 7w + 65]$ | $\phantom{-}\frac{1}{2}e^{3} + 3e^{2} + 2e - 5$ |
| 11 | $[11, 11, -7w + 65]$ | $-\frac{1}{2}e^{3} - 3e^{2} - 2e + 3$ |
| 17 | $[17, 17, -2w - 19]$ | $-e^{3} - 6e^{2} - 8e + 1$ |
| 17 | $[17, 17, 2w - 19]$ | $\phantom{-}e^{3} + 6e^{2} + 8e + 1$ |
| 29 | $[29, 29, -15w + 139]$ | $-2e^{2} - 7e$ |
| 29 | $[29, 29, -15w - 139]$ | $\phantom{-}2e^{2} + 9e + 4$ |
| 37 | $[37, 37, -w - 7]$ | $-2e^{2} - 10e - 8$ |
| 37 | $[37, 37, w - 7]$ | $\phantom{-}2e^{2} + 6e$ |
| 41 | $[41, 41, -40w + 371]$ | $\phantom{-}3e^{2} + 12e + 5$ |
| 41 | $[41, 41, 62w - 575]$ | $\phantom{-}3e^{2} + 12e + 5$ |
| 43 | $[43, 43, -51w + 473]$ | $-2e^{2} - 8e - 6$ |
| 59 | $[59, 59, -5w + 47]$ | $\phantom{-}e^{3} + 7e^{2} + 10e - 6$ |
| 59 | $[59, 59, 5w + 47]$ | $-e^{3} - 5e^{2} - 2e + 2$ |
| 61 | $[61, 61, -w - 5]$ | $-e^{3} - 4e^{2} + e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -11w + 102]$ | $-1$ |