Base field \(\Q(\sqrt{273}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 68\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -4w + 35]$ | $-3$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}5$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 9]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 6]$ | $-2$ |
| 17 | $[17, 17, -2w + 17]$ | $-3$ |
| 17 | $[17, 17, -2w - 15]$ | $-3$ |
| 19 | $[19, 19, w + 5]$ | $-2$ |
| 19 | $[19, 19, w + 13]$ | $-2$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}7$ |
| 31 | $[31, 31, w + 2]$ | $\phantom{-}8$ |
| 31 | $[31, 31, w + 28]$ | $\phantom{-}8$ |
| 43 | $[43, 43, -38w + 333]$ | $-11$ |
| 43 | $[43, 43, 6w - 53]$ | $-11$ |
| 71 | $[71, 71, w + 14]$ | $\phantom{-}9$ |
| 71 | $[71, 71, w + 56]$ | $\phantom{-}9$ |
| 73 | $[73, 73, w + 22]$ | $\phantom{-}2$ |
| 73 | $[73, 73, w + 50]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $2$ | $[2, 2, w + 1]$ | $-1$ |