Base field 4.4.19429.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[5, 5, w]$ |
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:
\(x^{2} + 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $\phantom{-}1$ |
7 | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}e + 2$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $-e - 3$ |
13 | $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}2e$ |
16 | $[16, 2, 2]$ | $-2e - 5$ |
17 | $[17, 17, -w + 2]$ | $\phantom{-}2$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $-4e - 6$ |
27 | $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ | $-e - 3$ |
31 | $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ | $-2e - 4$ |
31 | $[31, 31, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}4$ |
41 | $[41, 41, w^{2} - w - 1]$ | $\phantom{-}5e + 12$ |
43 | $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ | $\phantom{-}2e + 6$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ | $-4e - 8$ |
53 | $[53, 53, -w - 3]$ | $-5e - 12$ |
53 | $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ | $-10$ |
59 | $[59, 59, 2w^{2} - 3w - 6]$ | $\phantom{-}9e + 9$ |
59 | $[59, 59, w^{3} - w^{2} - 7w - 3]$ | $\phantom{-}7e + 7$ |
79 | $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ | $\phantom{-}2e + 8$ |
79 | $[79, 79, w^{2} - 2w - 1]$ | $\phantom{-}12e + 18$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w]$ | $-1$ |