Base field \(\Q(\sqrt{209}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 52\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 4x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w - 74]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -11w + 85]$ | $\phantom{-}e$ |
| 5 | $[5, 5, 4w - 31]$ | $\phantom{-}e^{2} - 3$ |
| 5 | $[5, 5, -4w - 27]$ | $\phantom{-}e^{2} - 3$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e^{2} + 1$ |
| 11 | $[11, 11, -70w - 471]$ | $\phantom{-}2e^{2} - 6$ |
| 13 | $[13, 13, -2w - 13]$ | $-2e^{3} + 7e$ |
| 13 | $[13, 13, -2w + 15]$ | $-2e^{3} + 7e$ |
| 19 | $[19, 19, 92w - 711]$ | $-e^{3}$ |
| 23 | $[23, 23, -26w + 201]$ | $\phantom{-}3e^{2} - 3$ |
| 23 | $[23, 23, -26w - 175]$ | $\phantom{-}3e^{2} - 3$ |
| 29 | $[29, 29, 18w - 139]$ | $-6e^{3} + 17e$ |
| 29 | $[29, 29, 18w + 121]$ | $-6e^{3} + 17e$ |
| 41 | $[41, 41, -10w - 67]$ | $\phantom{-}2e^{3} - 4e$ |
| 41 | $[41, 41, 10w - 77]$ | $\phantom{-}2e^{3} - 4e$ |
| 47 | $[47, 47, 2w - 17]$ | $\phantom{-}e^{2} - 8$ |
| 47 | $[47, 47, 2w + 15]$ | $\phantom{-}e^{2} - 8$ |
| 49 | $[49, 7, -7]$ | $-e^{2} + 12$ |
| 79 | $[79, 79, 40w - 309]$ | $\phantom{-}2e^{3} - 7e$ |
| 79 | $[79, 79, 40w + 269]$ | $\phantom{-}2e^{3} - 7e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).