Base field 4.4.13824.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 6\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 24x^{4} + 176x^{2} - 368\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + w + 2]$ | $\phantom{-}0$ |
3 | $[3, 3, w^{2} - w - 3]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{2} + w + 1]$ | $-\frac{1}{2}e^{3} + 5e$ |
11 | $[11, 11, -w^{2} - w + 1]$ | $-\frac{1}{2}e^{3} + 5e$ |
13 | $[13, 13, w^{3} - 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 7e^{2} + 20$ |
13 | $[13, 13, -w^{3} + 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - 7e^{2} + 20$ |
25 | $[25, 5, -w^{2} - 2w + 1]$ | $-\frac{1}{2}e^{4} + 8e^{2} - 26$ |
25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{1}{2}e^{4} + 8e^{2} - 26$ |
37 | $[37, 37, w^{3} - 3w - 1]$ | $-e^{4} + 15e^{2} - 46$ |
37 | $[37, 37, w^{3} - 3w + 1]$ | $-e^{4} + 15e^{2} - 46$ |
59 | $[59, 59, w^{2} - w - 5]$ | $-\frac{1}{2}e^{5} + 7e^{3} - 19e$ |
59 | $[59, 59, -w^{2} - w + 5]$ | $-\frac{1}{2}e^{5} + 7e^{3} - 19e$ |
61 | $[61, 61, -w^{3} + w^{2} + 4w - 7]$ | $\phantom{-}e^{4} - 15e^{2} + 46$ |
61 | $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ | $\phantom{-}e^{4} - 15e^{2} + 46$ |
73 | $[73, 73, 2w^{2} - w - 5]$ | $\phantom{-}3e^{2} - 22$ |
73 | $[73, 73, 2w - 1]$ | $-e^{4} + 13e^{2} - 26$ |
73 | $[73, 73, -2w - 1]$ | $-e^{4} + 13e^{2} - 26$ |
73 | $[73, 73, 2w^{2} + w - 5]$ | $\phantom{-}3e^{2} - 22$ |
83 | $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{15}{2}e^{3} + 21e$ |
83 | $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{15}{2}e^{3} + 21e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-w^{2}+w+2]$ | $1$ |