Base field \(\Q(\sqrt{53}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 13\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[212, 106, 4w - 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $90$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w - 3]$ | $\phantom{-}0$ |
| 9 | $[9, 3, 3]$ | $-5$ |
| 11 | $[11, 11, w + 1]$ | $-4$ |
| 11 | $[11, 11, w - 2]$ | $-4$ |
| 13 | $[13, 13, w]$ | $\phantom{-}1$ |
| 13 | $[13, 13, w - 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w - 5]$ | $\phantom{-}5$ |
| 17 | $[17, 17, w - 6]$ | $\phantom{-}5$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}6$ |
| 29 | $[29, 29, -w - 6]$ | $\phantom{-}5$ |
| 29 | $[29, 29, w - 7]$ | $\phantom{-}5$ |
| 37 | $[37, 37, 2w - 5]$ | $\phantom{-}1$ |
| 37 | $[37, 37, -2w - 3]$ | $\phantom{-}1$ |
| 43 | $[43, 43, -w - 7]$ | $-10$ |
| 43 | $[43, 43, w - 8]$ | $-10$ |
| 47 | $[47, 47, 3w + 7]$ | $-6$ |
| 47 | $[47, 47, 3w - 10]$ | $-6$ |
| 53 | $[53, 53, 2w - 1]$ | $-1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |
| $53$ | $[53, 53, 2w - 1]$ | $1$ |