Base field \(\Q(\sqrt{3}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[69, 69, 2w - 9]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} - x^{2} - 4x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-1$ |
| 11 | $[11, 11, -2w + 1]$ | $-2e^{2} + 6$ |
| 11 | $[11, 11, 2w + 1]$ | $\phantom{-}e^{2} - e - 2$ |
| 13 | $[13, 13, w + 4]$ | $-e^{2} + e + 4$ |
| 13 | $[13, 13, -w + 4]$ | $-e^{2} + e + 4$ |
| 23 | $[23, 23, -3w + 2]$ | $-1$ |
| 23 | $[23, 23, 3w + 2]$ | $\phantom{-}2e^{2} - 2e - 4$ |
| 25 | $[25, 5, 5]$ | $-e^{2} - 3e + 4$ |
| 37 | $[37, 37, 2w - 7]$ | $\phantom{-}4e^{2} - 4e - 10$ |
| 37 | $[37, 37, -2w - 7]$ | $\phantom{-}2e$ |
| 47 | $[47, 47, -4w - 1]$ | $-3e^{2} + 3e + 10$ |
| 47 | $[47, 47, 4w - 1]$ | $-2e^{2} - 2e + 8$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2e^{2} + 2e - 6$ |
| 59 | $[59, 59, 5w - 4]$ | $-e^{2} - 3e + 6$ |
| 59 | $[59, 59, -5w - 4]$ | $\phantom{-}4e^{2} - 8$ |
| 61 | $[61, 61, -w - 8]$ | $-6e$ |
| 61 | $[61, 61, w - 8]$ | $\phantom{-}2e^{2} - 2e - 6$ |
| 71 | $[71, 71, 5w - 2]$ | $\phantom{-}2e^{2} - 4e - 14$ |
| 71 | $[71, 71, -5w - 2]$ | $-2e^{2} + 6e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $1$ |
| $23$ | $[23, 23, -3w + 2]$ | $1$ |