Base field \(\Q(\sqrt{22}) \)
Generator \(w\), with minimal polynomial \(x^2 - 22\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[81, 81, -2 w + 13]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $92$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3 w + 14]$ | $\phantom{-}2$ |
| 3 | $[3, 3, -w + 5]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 5]$ | $\phantom{-}0$ |
| 7 | $[7, 7, 2 w + 9]$ | $\phantom{-}0$ |
| 7 | $[7, 7, 2 w - 9]$ | $\phantom{-}4$ |
| 11 | $[11, 11, -7 w + 33]$ | $-3$ |
| 13 | $[13, 13, -w - 3]$ | $-4$ |
| 13 | $[13, 13, -w + 3]$ | $\phantom{-}4$ |
| 25 | $[25, 5, -5]$ | $-7$ |
| 29 | $[29, 29, 3 w + 13]$ | $-4$ |
| 29 | $[29, 29, -3 w + 13]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -w - 9]$ | $-11$ |
| 59 | $[59, 59, w - 9]$ | $\phantom{-}5$ |
| 61 | $[61, 61, 11 w - 51]$ | $-8$ |
| 61 | $[61, 61, 25 w - 117]$ | $\phantom{-}0$ |
| 67 | $[67, 67, 9 w - 43]$ | $\phantom{-}8$ |
| 67 | $[67, 67, -9 w - 43]$ | $\phantom{-}7$ |
| 79 | $[79, 79, 2 w - 3]$ | $-12$ |
| 79 | $[79, 79, -2 w - 3]$ | $-4$ |
| 89 | $[89, 89, 4 w - 21]$ | $\phantom{-}17$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w + 5]$ | $-1$ |