Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $135$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $-1$ |
| 2 | $[2, 2, w + 1]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}4$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}4$ |
| 7 | $[7, 7, w + 1]$ | $-4$ |
| 7 | $[7, 7, w + 5]$ | $-4$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}2$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}3$ |
| 11 | $[11, 11, w + 7]$ | $\phantom{-}3$ |
| 29 | $[29, 29, w + 6]$ | $\phantom{-}8$ |
| 29 | $[29, 29, w + 22]$ | $\phantom{-}8$ |
| 41 | $[41, 41, w + 13]$ | $-5$ |
| 41 | $[41, 41, w + 27]$ | $-5$ |
| 43 | $[43, 43, w + 16]$ | $-9$ |
| 43 | $[43, 43, w + 26]$ | $-9$ |
| 47 | $[47, 47, w + 2]$ | $\phantom{-}6$ |
| 47 | $[47, 47, w + 44]$ | $\phantom{-}6$ |
| 73 | $[73, 73, w + 33]$ | $\phantom{-}1$ |
| 73 | $[73, 73, w + 39]$ | $\phantom{-}1$ |
| 83 | $[83, 83, -4w - 37]$ | $\phantom{-}7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |
| $2$ | $[2, 2, w + 1]$ | $1$ |