Base field \(\Q(\zeta_{16})^+\)
Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} + 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[47,47,-w^{3} - w^{2} + 5w + 3]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $-4e + 4$ |
17 | $[17, 17, -w^{3} - w^{2} + 3w + 1]$ | $\phantom{-}2e - 5$ |
17 | $[17, 17, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}e$ |
17 | $[17, 17, w^{2} - w - 3]$ | $-2$ |
31 | $[31, 31, w^{3} + w^{2} - 2w - 3]$ | $\phantom{-}2e + 3$ |
31 | $[31, 31, -w^{3} + w^{2} + 4w - 1]$ | $-e + 4$ |
31 | $[31, 31, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}6$ |
31 | $[31, 31, -w^{3} + w^{2} + 2w - 3]$ | $-2e + 2$ |
47 | $[47, 47, -2w^{3} + w^{2} + 5w - 1]$ | $-4e$ |
47 | $[47, 47, 2w^{3} + w^{2} - 6w - 1]$ | $\phantom{-}8$ |
47 | $[47, 47, -2w^{3} + w^{2} + 6w - 1]$ | $-1$ |
47 | $[47, 47, 2w^{3} + w^{2} - 5w - 1]$ | $-6$ |
49 | $[49, 7, w^{2} + 1]$ | $\phantom{-}e - 2$ |
49 | $[49, 7, -2w^{2} + 3]$ | $-2e + 6$ |
79 | $[79, 79, -w^{3} - w^{2} + 4w - 1]$ | $\phantom{-}2e - 3$ |
79 | $[79, 79, -w^{3} + w^{2} + 2w - 5]$ | $-2e + 10$ |
79 | $[79, 79, w^{3} + w^{2} - 2w - 5]$ | $-e - 2$ |
79 | $[79, 79, w^{3} - w^{2} - 4w - 1]$ | $-8e + 5$ |
81 | $[81, 3, -3]$ | $\phantom{-}2e - 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$47$ | $[47,47,-w^{3} - w^{2} + 5w + 3]$ | $1$ |