Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[6, 6, w + 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 8x^{4} + 16x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 6]$ | $\phantom{-}1$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} + 2e$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}e^{3} + 3e$ |
5 | $[5, 5, w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} + 3e^{3} + 2e$ |
11 | $[11, 11, w + 1]$ | $-\frac{3}{2}e^{5} - 9e^{3} - 10e$ |
11 | $[11, 11, w + 10]$ | $-\frac{1}{2}e^{5} - 2e^{3} + e$ |
17 | $[17, 17, -3w + 17]$ | $-2e^{2} - 4$ |
29 | $[29, 29, w + 11]$ | $\phantom{-}\frac{3}{2}e^{5} + 9e^{3} + 9e$ |
29 | $[29, 29, w + 18]$ | $\phantom{-}4e$ |
37 | $[37, 37, w + 16]$ | $\phantom{-}\frac{5}{2}e^{5} + 17e^{3} + 25e$ |
37 | $[37, 37, w + 21]$ | $-2e$ |
47 | $[47, 47, -w - 9]$ | $\phantom{-}3e^{4} + 17e^{2} + 12$ |
47 | $[47, 47, w - 9]$ | $-e^{4} - 5e^{2} - 6$ |
49 | $[49, 7, -7]$ | $-e^{4} - 5e^{2} - 4$ |
61 | $[61, 61, w + 20]$ | $-\frac{1}{2}e^{5} - 4e^{3} - e$ |
61 | $[61, 61, w + 41]$ | $\phantom{-}4e^{3} + 14e$ |
89 | $[89, 89, 2w - 15]$ | $-e^{4} - 8e^{2} - 12$ |
89 | $[89, 89, -2w - 15]$ | $-e^{4} - 8e^{2} - 12$ |
103 | $[103, 103, -14w + 81]$ | $-e^{4} - 3e^{2} + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w - 6]$ | $-1$ |
$3$ | $[3, 3, w + 2]$ | $-\frac{1}{2}e^{3} - 2e$ |