Among newforms over real quadratic fields ordered by discriminant, this newform is the first one of dimension $2$ with level norm $1$. It corresponds to an isogeny class of abelian surfaces with everywhere good reduction defined over the real quadratic field $\Q(\sqrt{10})$ (of discriminant $40$).
Base field \(\Q(\sqrt{10}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 10\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-e$ |
| 3 | $[3, 3, w + 2]$ | $-e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}2e$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 7]$ | $\phantom{-}0$ |
| 31 | $[31, 31, -2w + 3]$ | $\phantom{-}4$ |
| 31 | $[31, 31, 2w + 3]$ | $\phantom{-}4$ |
| 37 | $[37, 37, w + 11]$ | $-6e$ |
| 37 | $[37, 37, w + 26]$ | $-6e$ |
| 41 | $[41, 41, 3w + 7]$ | $\phantom{-}0$ |
| 41 | $[41, 41, -3w + 7]$ | $\phantom{-}0$ |
| 43 | $[43, 43, w + 15]$ | $\phantom{-}3e$ |
| 43 | $[43, 43, w + 28]$ | $\phantom{-}3e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}8$ |
| 53 | $[53, 53, w + 13]$ | $\phantom{-}4e$ |
| 53 | $[53, 53, w + 40]$ | $\phantom{-}4e$ |
| 67 | $[67, 67, w + 12]$ | $-3e$ |
| 67 | $[67, 67, w + 55]$ | $-3e$ |
| 71 | $[71, 71, -w - 9]$ | $-12$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).