Base field \(\Q(\sqrt{3}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[61, 61, -w - 8]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 10x^{4} + 23x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 9e$ |
| 11 | $[11, 11, -2w + 1]$ | $\phantom{-}e^{3} - 5e$ |
| 11 | $[11, 11, 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 13e$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 5$ |
| 13 | $[13, 13, -w + 4]$ | $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 1$ |
| 23 | $[23, 23, -3w + 2]$ | $\phantom{-}e^{5} - 11e^{3} + 26e$ |
| 23 | $[23, 23, 3w + 2]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$ |
| 25 | $[25, 5, 5]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} - 5$ |
| 37 | $[37, 37, 2w - 7]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{2} + 3$ |
| 37 | $[37, 37, -2w - 7]$ | $-e^{4} + 7e^{2} - 6$ |
| 47 | $[47, 47, -4w - 1]$ | $-\frac{3}{2}e^{5} + \frac{33}{2}e^{3} - 42e$ |
| 47 | $[47, 47, 4w - 1]$ | $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3} - 6e$ |
| 49 | $[49, 7, -7]$ | $-2e^{2} + 6$ |
| 59 | $[59, 59, 5w - 4]$ | $\phantom{-}e^{5} - 9e^{3} + 20e$ |
| 59 | $[59, 59, -5w - 4]$ | $\phantom{-}e^{5} - 8e^{3} + 11e$ |
| 61 | $[61, 61, -w - 8]$ | $-1$ |
| 61 | $[61, 61, w - 8]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{2} - 5$ |
| 71 | $[71, 71, 5w - 2]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{31}{2}e^{3} + 42e$ |
| 71 | $[71, 71, -5w - 2]$ | $\phantom{-}e^{5} - 7e^{3} + 6e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $61$ | $[61, 61, -w - 8]$ | $1$ |