Base field \(\Q(\sqrt{21}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[47,47,-3w + 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 4x^{2} + x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-e^{2} + 2e + 1$ |
| 5 | $[5, 5, w]$ | $-e + 2$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}2$ |
| 7 | $[7, 7, -w - 3]$ | $\phantom{-}e^{2} - 3e$ |
| 17 | $[17, 17, -2w + 3]$ | $\phantom{-}e^{2} - 3e + 2$ |
| 17 | $[17, 17, -2w - 1]$ | $-e^{2} + e + 2$ |
| 37 | $[37, 37, w + 6]$ | $\phantom{-}2e - 2$ |
| 37 | $[37, 37, -w + 7]$ | $\phantom{-}e^{2} - 3e - 6$ |
| 41 | $[41, 41, 3w + 1]$ | $-2e^{2} + 5e + 6$ |
| 41 | $[41, 41, -3w + 4]$ | $\phantom{-}4e - 2$ |
| 43 | $[43, 43, 3w + 8]$ | $\phantom{-}2e^{2} - 4e - 4$ |
| 43 | $[43, 43, 3w - 11]$ | $-2e^{2} + 6e$ |
| 47 | $[47, 47, 3w - 2]$ | $-2e^{2} + 4e + 8$ |
| 47 | $[47, 47, 3w - 1]$ | $-1$ |
| 59 | $[59, 59, -5w - 6]$ | $\phantom{-}3e^{2} - 11e$ |
| 59 | $[59, 59, -4w - 3]$ | $-e^{2} + 5e - 8$ |
| 67 | $[67, 67, -w - 8]$ | $-e^{2} - 2e + 4$ |
| 67 | $[67, 67, w - 9]$ | $-3e^{2} + 7e + 4$ |
| 79 | $[79, 79, 2w - 11]$ | $-5e^{2} + 17e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $47$ | $[47,47,-3w + 1]$ | $1$ |