Base field \(\Q(\sqrt{437}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 109\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $2$ |
| CM: | yes |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 13x + 28\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $-2$ |
| 9 | $[9, 3, 3]$ | $-3$ |
| 19 | $[19, 19, -w - 9]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 11]$ | $\phantom{-}4$ |
| 25 | $[25, 5, 5]$ | $-9$ |
| 37 | $[37, 37, w + 8]$ | $\phantom{-}0$ |
| 37 | $[37, 37, -w + 9]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w + 12]$ | $\phantom{-}e$ |
| 47 | $[47, 47, -w + 13]$ | $-e + 13$ |
| 49 | $[49, 7, 7]$ | $-5$ |
| 53 | $[53, 53, -w - 7]$ | $\phantom{-}0$ |
| 53 | $[53, 53, w - 8]$ | $\phantom{-}0$ |
| 67 | $[67, 67, -w - 6]$ | $\phantom{-}0$ |
| 67 | $[67, 67, w - 7]$ | $\phantom{-}0$ |
| 73 | $[73, 73, -w - 13]$ | $-3e + 25$ |
| 73 | $[73, 73, w - 14]$ | $\phantom{-}3e - 14$ |
| 79 | $[79, 79, -w - 5]$ | $\phantom{-}0$ |
| 79 | $[79, 79, w - 6]$ | $\phantom{-}0$ |
| 89 | $[89, 89, -w - 4]$ | $\phantom{-}0$ |
| 89 | $[89, 89, w - 5]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).