Base field \(\Q(\sqrt{161}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 40\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10, 10, -w + 6]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 6]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -w + 7]$ | $-1$ |
| 5 | $[5, 5, -6w - 35]$ | $\phantom{-}2$ |
| 5 | $[5, 5, -6w + 41]$ | $\phantom{-}1$ |
| 7 | $[7, 7, 32w - 219]$ | $\phantom{-}4$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}2$ |
| 17 | $[17, 17, 2w - 13]$ | $\phantom{-}6$ |
| 17 | $[17, 17, 2w + 11]$ | $-2$ |
| 19 | $[19, 19, 4w + 23]$ | $\phantom{-}4$ |
| 19 | $[19, 19, 4w - 27]$ | $-8$ |
| 23 | $[23, 23, 58w - 397]$ | $\phantom{-}0$ |
| 29 | $[29, 29, 20w - 137]$ | $-2$ |
| 29 | $[29, 29, -20w - 117]$ | $\phantom{-}6$ |
| 61 | $[61, 61, 2w - 11]$ | $-6$ |
| 61 | $[61, 61, -2w - 9]$ | $-10$ |
| 71 | $[71, 71, -10w - 59]$ | $\phantom{-}0$ |
| 71 | $[71, 71, 10w - 69]$ | $-8$ |
| 83 | $[83, 83, -44w + 301]$ | $\phantom{-}8$ |
| 83 | $[83, 83, 44w + 257]$ | $-4$ |
| 89 | $[89, 89, -70w - 409]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 6]$ | $-1$ |
| $5$ | $[5, 5, -6w + 41]$ | $-1$ |