Base field \(\Q(\sqrt{110}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 110\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $4$ |
| CM: | yes |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 118x^{2} + 2401\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w]$ | $-\frac{1}{98}e^{3} + \frac{69}{98}e$ |
| 9 | $[9, 3, 3]$ | $-3$ |
| 11 | $[11, 11, -w + 11]$ | $-2$ |
| 17 | $[17, 17, w + 5]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 12]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 8]$ | $\phantom{-}e$ |
| 23 | $[23, 23, w + 15]$ | $\phantom{-}\frac{1}{49}e^{3} - \frac{118}{49}e$ |
| 29 | $[29, 29, w + 9]$ | $\phantom{-}0$ |
| 29 | $[29, 29, -w + 9]$ | $\phantom{-}0$ |
| 37 | $[37, 37, w + 6]$ | $-\frac{1}{42}e^{3} + \frac{125}{42}e$ |
| 37 | $[37, 37, w + 31]$ | $\phantom{-}\frac{1}{294}e^{3} - \frac{461}{294}e$ |
| 43 | $[43, 43, w + 14]$ | $\phantom{-}0$ |
| 43 | $[43, 43, w + 29]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w + 4]$ | $\phantom{-}\frac{3}{49}e^{3} - \frac{207}{49}e$ |
| 47 | $[47, 47, w + 43]$ | $\phantom{-}\frac{3}{49}e^{3} - \frac{207}{49}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}6$ |
| 53 | $[53, 53, w + 2]$ | $-\frac{3}{49}e^{3} + \frac{207}{49}e$ |
| 53 | $[53, 53, w + 51]$ | $-\frac{3}{49}e^{3} + \frac{207}{49}e$ |
| 59 | $[59, 59, -w - 13]$ | $-\frac{1}{6}e^{2} + \frac{101}{6}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |