Base field \(\Q(\sqrt{69}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 17\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $3$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 9x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 5]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 3$ |
| 5 | $[5, 5, -w + 4]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -w - 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w + 3]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 5]$ | $\phantom{-}e^{2} - 2e - 6$ |
| 13 | $[13, 13, -w + 6]$ | $\phantom{-}e^{2} - 2e - 6$ |
| 17 | $[17, 17, -w]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w - 1]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -3w + 13]$ | $\phantom{-}0$ |
| 31 | $[31, 31, 2w - 11]$ | $-2e^{2} + e + 12$ |
| 31 | $[31, 31, -5w + 24]$ | $-2e^{2} + e + 12$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}14$ |
| 53 | $[53, 53, 2w - 5]$ | $\phantom{-}0$ |
| 53 | $[53, 53, -2w - 3]$ | $\phantom{-}0$ |
| 73 | $[73, 73, -w - 9]$ | $\phantom{-}e^{2} + 4e - 6$ |
| 73 | $[73, 73, w - 10]$ | $\phantom{-}e^{2} + 4e - 6$ |
| 83 | $[83, 83, -3w - 7]$ | $\phantom{-}0$ |
| 83 | $[83, 83, 3w - 10]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).