Base field \(\Q(\sqrt{37}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 9\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[324,54,-6w + 6]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 3]$ | $-1$ |
| 3 | $[3, 3, -w - 2]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w + 2]$ | $-1$ |
| 11 | $[11, 11, w + 4]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w + 5]$ | $-2$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}4$ |
| 37 | $[37, 37, 2w - 1]$ | $-5$ |
| 41 | $[41, 41, 3w - 8]$ | $\phantom{-}3$ |
| 41 | $[41, 41, 3w + 5]$ | $-4$ |
| 47 | $[47, 47, -w - 7]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w - 8]$ | $\phantom{-}0$ |
| 53 | $[53, 53, -3w - 4]$ | $\phantom{-}10$ |
| 53 | $[53, 53, 3w - 7]$ | $-2$ |
| 67 | $[67, 67, 4w - 11]$ | $\phantom{-}3$ |
| 67 | $[67, 67, 4w + 7]$ | $\phantom{-}7$ |
| 71 | $[71, 71, 3w - 5]$ | $-6$ |
| 71 | $[71, 71, -3w - 2]$ | $\phantom{-}7$ |
| 73 | $[73, 73, -3w - 11]$ | $-4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w + 2]$ | $-1$ |
| $3$ | $[3,3,w - 3]$ | $1$ |
| $4$ | $[4,2,2]$ | $1$ |