Base field 4.4.1957.1
Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
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:
\(x^{2} + x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w^{3} + 3w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}2e$ |
16 | $[16, 2, 2]$ | $-1$ |
19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $\phantom{-}e - 1$ |
23 | $[23, 23, w^{3} + w^{2} - 4w - 2]$ | $-2e - 2$ |
27 | $[27, 3, -2w^{3} + w^{2} + 6w - 1]$ | $-e - 2$ |
31 | $[31, 31, -w^{3} + 5w]$ | $-2e + 6$ |
37 | $[37, 37, -w^{3} + 5w + 1]$ | $\phantom{-}4$ |
43 | $[43, 43, w^{2} + w - 3]$ | $-3e + 5$ |
43 | $[43, 43, -w^{2} + 2w + 3]$ | $-e - 3$ |
47 | $[47, 47, -w^{3} + w^{2} + 2w + 2]$ | $\phantom{-}4e - 2$ |
47 | $[47, 47, 3w^{3} - w^{2} - 10w - 2]$ | $-4e - 4$ |
53 | $[53, 53, -w^{3} + w^{2} + 2w - 3]$ | $-4e + 2$ |
59 | $[59, 59, -2w^{3} + w^{2} + 8w + 1]$ | $-5e - 5$ |
59 | $[59, 59, w^{3} - 2w^{2} - 3w + 3]$ | $-e - 4$ |
61 | $[61, 61, -w^{3} + w^{2} + w - 2]$ | $-2e + 2$ |
67 | $[67, 67, 2w^{3} - 5w - 2]$ | $\phantom{-}3e + 5$ |
71 | $[71, 71, 2w^{2} - w - 3]$ | $\phantom{-}2e - 4$ |
73 | $[73, 73, 2w^{2} - w - 5]$ | $-3e + 1$ |
73 | $[73, 73, w^{3} - 2w^{2} - 2w + 5]$ | $\phantom{-}3e + 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$16$ | $[16, 2, 2]$ | $1$ |