Base field \(\Q(\sqrt{3}, \sqrt{11})\)
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 4\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8, 4, w + 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -\frac{1}{2}w^{3} + \frac{7}{2}w - 1]$ | $\phantom{-}0$ |
2 | $[2, 2, -w + 1]$ | $-1$ |
9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w]$ | $\phantom{-}2$ |
11 | $[11, 11, -w^{2} + w + 1]$ | $\phantom{-}e$ |
11 | $[11, 11, w^{2} + w - 1]$ | $-e$ |
25 | $[25, 5, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ | $\phantom{-}e - 2$ |
25 | $[25, 5, -\frac{1}{2}w^{3} - w^{2} + \frac{7}{2}w + 4]$ | $-e - 2$ |
37 | $[37, 37, -w^{3} + 7w + 1]$ | $\phantom{-}2e - 2$ |
37 | $[37, 37, -2w + 1]$ | $-2e - 2$ |
37 | $[37, 37, 2w + 1]$ | $\phantom{-}2e - 2$ |
37 | $[37, 37, -w^{3} + 7w - 1]$ | $-2e - 2$ |
49 | $[49, 7, \frac{1}{2}w^{3} - \frac{9}{2}w + 2]$ | $\phantom{-}3e - 2$ |
49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{9}{2}w + 2]$ | $-3e - 2$ |
83 | $[83, 83, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 2]$ | $-4e - 4$ |
83 | $[83, 83, w^{2} + w - 5]$ | $\phantom{-}2e - 4$ |
83 | $[83, 83, w^{2} - w - 5]$ | $-2e - 4$ |
83 | $[83, 83, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 2]$ | $\phantom{-}4e - 4$ |
97 | $[97, 97, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 8]$ | $-e + 14$ |
97 | $[97, 97, \frac{5}{2}w^{3} - w^{2} - \frac{31}{2}w + 6]$ | $\phantom{-}5e - 2$ |
97 | $[97, 97, -\frac{11}{2}w^{3} + 4w^{2} + \frac{71}{2}w - 26]$ | $-5e - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-\frac{1}{2}w^{3}+\frac{7}{2}w-1]$ | $-1$ |