Base field \(\Q(\sqrt{67}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 67\); 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: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 4x^{3} + x^{2} - 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -27w + 221]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w + 8]$ | $-e - 2$ |
| 3 | $[3, 3, -w - 8]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -11w + 90]$ | $\phantom{-}e^{3} + 4e^{2} + e - 4$ |
| 7 | $[7, 7, -11w - 90]$ | $-e^{3} - 2e^{2} + 3e + 2$ |
| 11 | $[11, 11, 6w - 49]$ | $\phantom{-}e^{3} + 2e^{2} - 4e - 2$ |
| 11 | $[11, 11, 6w + 49]$ | $-e^{3} - 4e^{2} + 6$ |
| 17 | $[17, 17, 4w + 33]$ | $\phantom{-}2e + 2$ |
| 17 | $[17, 17, -4w + 33]$ | $-2e - 2$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}2e^{2} + 4e - 5$ |
| 29 | $[29, 29, -70w + 573]$ | $\phantom{-}2e^{3} + 6e^{2} - 7$ |
| 29 | $[29, 29, 151w - 1236]$ | $-2e^{3} - 6e^{2} + 1$ |
| 31 | $[31, 31, -w - 6]$ | $\phantom{-}e^{3} + 4e^{2} + 2e$ |
| 31 | $[31, 31, w - 6]$ | $-e^{3} - 2e^{2} + 2e + 4$ |
| 37 | $[37, 37, -21w - 172]$ | $\phantom{-}2e^{3} + 3e^{2} - 10e - 6$ |
| 37 | $[37, 37, -21w + 172]$ | $-2e^{3} - 9e^{2} - 2e + 10$ |
| 43 | $[43, 43, 2w - 15]$ | $-2e^{2} - 7e + 2$ |
| 43 | $[43, 43, 2w + 15]$ | $-2e^{2} - e + 8$ |
| 67 | $[67, 67, -w]$ | $\phantom{-}4e^{2} + 8e - 10$ |
| 73 | $[73, 73, -3w - 26]$ | $-4e^{3} - 14e^{2} - 2e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -27w + 221]$ | $-1$ |