Base field \(\Q(\sqrt{201}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 50\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10, 10, 3w + 20]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -17w - 112]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -17w + 129]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -124w + 941]$ | $-e$ |
| 5 | $[5, 5, -2w + 15]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -2w - 13]$ | $-2e - 2$ |
| 11 | $[11, 11, 12w + 79]$ | $-2$ |
| 11 | $[11, 11, -12w + 91]$ | $\phantom{-}5$ |
| 19 | $[19, 19, -90w - 593]$ | $-2e - 2$ |
| 19 | $[19, 19, 90w - 683]$ | $-3e - 6$ |
| 37 | $[37, 37, -4w - 27]$ | $\phantom{-}2e - 3$ |
| 37 | $[37, 37, -4w + 31]$ | $-e - 8$ |
| 41 | $[41, 41, 158w + 1041]$ | $\phantom{-}2e + 8$ |
| 41 | $[41, 41, 158w - 1199]$ | $-2e - 8$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2e + 2$ |
| 53 | $[53, 53, 46w - 349]$ | $\phantom{-}2e - 1$ |
| 53 | $[53, 53, 46w + 303]$ | $\phantom{-}2e + 6$ |
| 67 | $[67, 67, 586w - 4447]$ | $-2e + 4$ |
| 73 | $[73, 73, -32w - 211]$ | $\phantom{-}8e + 8$ |
| 73 | $[73, 73, 32w - 243]$ | $\phantom{-}11$ |
| 101 | $[101, 101, 2w - 11]$ | $-5e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -17w - 112]$ | $-1$ |
| $5$ | $[5, 5, -2w + 15]$ | $-1$ |