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