Base field \(\Q(\sqrt{6}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 6\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[29,29,3w + 5]$ |
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:
\(x^{3} + 2x^{2} - 3x - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 3]$ | $-e^{2} + 3$ |
5 | $[5, 5, w + 1]$ | $-e^{2} - e$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}e^{2} - 5$ |
19 | $[19, 19, w + 5]$ | $\phantom{-}3e^{2} + 3e - 8$ |
19 | $[19, 19, -w + 5]$ | $-e - 3$ |
23 | $[23, 23, -2w + 1]$ | $\phantom{-}2e^{2} - e - 5$ |
23 | $[23, 23, -2w - 1]$ | $-e^{2} + 5$ |
29 | $[29, 29, -3w + 5]$ | $\phantom{-}e^{2} + 3e - 5$ |
29 | $[29, 29, -3w - 5]$ | $\phantom{-}1$ |
43 | $[43, 43, -w - 7]$ | $\phantom{-}e^{2} - 5e - 5$ |
43 | $[43, 43, w - 7]$ | $-e^{2} - e$ |
47 | $[47, 47, 4w - 7]$ | $\phantom{-}e^{2} + 4e$ |
47 | $[47, 47, 6w - 13]$ | $-4e - 5$ |
49 | $[49, 7, -7]$ | $-3e^{2} - e + 4$ |
53 | $[53, 53, -3w - 1]$ | $-2e^{2} + 2e + 5$ |
53 | $[53, 53, 3w - 1]$ | $\phantom{-}2e^{2} - e - 10$ |
67 | $[67, 67, -7w + 19]$ | $-e^{2} - e - 6$ |
67 | $[67, 67, -3w + 11]$ | $-4e^{2} + 9$ |
71 | $[71, 71, -4w - 5]$ | $\phantom{-}4e^{2} + 6e - 15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29,29,3w + 5]$ | $-1$ |