Base field 4.4.7537.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 4x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 16, w^{2} + w - 4]$ |
Dimension: | $3$ |
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:
\(x^{3} - 9x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 1]$ | $\phantom{-}0$ |
3 | $[3, 3, w]$ | $\phantom{-}e$ |
8 | $[8, 2, -w^{3} + 5w + 1]$ | $-e^{2} + e + 5$ |
19 | $[19, 19, w^{3} - w^{2} - 3w + 2]$ | $-e$ |
19 | $[19, 19, -w^{3} + 4w - 2]$ | $\phantom{-}4$ |
23 | $[23, 23, w^{3} + w^{2} - 4w - 5]$ | $-e^{2} + 8$ |
27 | $[27, 3, -w^{3} + w^{2} + 5w - 4]$ | $\phantom{-}4$ |
31 | $[31, 31, w^{3} + w^{2} - 4w - 1]$ | $-e - 4$ |
47 | $[47, 47, -w^{2} - w + 5]$ | $-e^{2} + 4e + 8$ |
53 | $[53, 53, 2w^{3} - 2w^{2} - 9w + 10]$ | $-2e^{2} + e + 10$ |
59 | $[59, 59, 2w - 1]$ | $\phantom{-}2e + 4$ |
59 | $[59, 59, w^{3} - 2w - 2]$ | $-2e^{2} + 12$ |
61 | $[61, 61, -w^{2} - 2w + 4]$ | $\phantom{-}2e^{2} - 10$ |
67 | $[67, 67, 2w^{2} - 7]$ | $\phantom{-}2e^{2} - 4e - 12$ |
73 | $[73, 73, 5w^{3} + w^{2} - 23w - 8]$ | $\phantom{-}2e^{2} + 2e - 14$ |
79 | $[79, 79, -2w^{3} - w^{2} + 9w + 7]$ | $-4e$ |
79 | $[79, 79, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}2e - 8$ |
79 | $[79, 79, w^{3} - w^{2} - w - 2]$ | $\phantom{-}e^{2} + 4e - 8$ |
79 | $[79, 79, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}e + 4$ |
83 | $[83, 83, w^{3} + w^{2} - 3w - 4]$ | $\phantom{-}2e^{2} - 4e - 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w - 1]$ | $1$ |