Base field \(\Q(\sqrt{55}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 55\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6, 6, -w - 7]$ |
| Dimension: | $4$ |
| CM: | no |
| 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:
| \(x^{4} - 5x^{2} - x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 1]$ | $-1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -2w + 15]$ | $\phantom{-}e^{3} - e^{2} - 4e + 1$ |
| 11 | $[11, 11, 3w - 22]$ | $\phantom{-}e^{2} - 5$ |
| 13 | $[13, 13, w + 4]$ | $-e^{2} - e + 3$ |
| 13 | $[13, 13, w + 9]$ | $-e^{3} + e^{2} + 5e$ |
| 17 | $[17, 17, w + 2]$ | $-2e^{3} - e^{2} + 7e + 3$ |
| 17 | $[17, 17, w + 15]$ | $\phantom{-}e^{3} + e^{2} - 6e - 4$ |
| 19 | $[19, 19, -w - 6]$ | $-e^{2} + e$ |
| 19 | $[19, 19, w - 6]$ | $-4e^{3} + 2e^{2} + 13e - 3$ |
| 23 | $[23, 23, w + 3]$ | $\phantom{-}3e^{3} - 4e^{2} - 10e + 8$ |
| 23 | $[23, 23, w + 20]$ | $\phantom{-}e^{3} + 2e^{2} - 3e - 4$ |
| 47 | $[47, 47, w + 14]$ | $\phantom{-}2e^{3} - e^{2} - 7e - 1$ |
| 47 | $[47, 47, w + 33]$ | $-2e^{3} + 5e^{2} + 3e - 14$ |
| 49 | $[49, 7, -7]$ | $-2e^{3} + 5e^{2} + 8e - 11$ |
| 67 | $[67, 67, w + 16]$ | $\phantom{-}3e^{3} - 10e^{2} - 8e + 22$ |
| 67 | $[67, 67, w + 51]$ | $\phantom{-}3e^{3} - 2e^{2} - 10e + 1$ |
| 73 | $[73, 73, w + 36]$ | $-7e^{3} + 5e^{2} + 19e - 10$ |
| 73 | $[73, 73, w + 37]$ | $-e^{3} + 7e^{2} + 3e - 21$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $-1$ |
| $3$ | $[3, 3, w + 1]$ | $1$ |