Base field 5.5.180769.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 7x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[25, 5, -w^{3} + 4w]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 8x^{3} + 20x^{2} + 16x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $\phantom{-}1$ |
5 | $[5, 5, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}1$ |
7 | $[7, 7, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-e^{2} - 5e - 4$ |
19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $\phantom{-}e^{3} + 5e^{2} + 6e - 2$ |
23 | $[23, 23, -w^{2} + 3]$ | $-e^{3} - 5e^{2} - 6e$ |
32 | $[32, 2, 2]$ | $-e^{3} - 6e^{2} - 6e + 3$ |
37 | $[37, 37, -w^{4} + 2w^{3} + 3w^{2} - 7w + 4]$ | $-e^{3} - 5e^{2} - 8e - 10$ |
41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-2e^{3} - 10e^{2} - 10e - 2$ |
43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 5w - 3]$ | $\phantom{-}3e^{3} + 16e^{2} + 20e + 2$ |
43 | $[43, 43, -w^{2} + w + 3]$ | $-e^{3} - 9e^{2} - 22e - 10$ |
47 | $[47, 47, 2w^{4} - 3w^{3} - 9w^{2} + 8w + 3]$ | $\phantom{-}e^{3} + 6e^{2} + 8e$ |
61 | $[61, 61, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 2]$ | $-2e^{3} - 7e^{2} + 3e + 8$ |
79 | $[79, 79, w^{2} - w - 5]$ | $\phantom{-}8e^{2} + 32e + 14$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 3w - 3]$ | $-2e^{3} - 14e^{2} - 24e - 6$ |
79 | $[79, 79, -2w^{4} + 4w^{3} + 7w^{2} - 14w + 2]$ | $\phantom{-}6e^{3} + 36e^{2} + 56e + 14$ |
97 | $[97, 97, w^{3} - 6w]$ | $-2e^{2} - 9e - 8$ |
101 | $[101, 101, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $\phantom{-}5e^{3} + 29e^{2} + 39e + 2$ |
101 | $[101, 101, 2w^{4} - 3w^{3} - 9w^{2} + 10w + 1]$ | $\phantom{-}4e^{3} + 23e^{2} + 27e - 8$ |
107 | $[107, 107, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 2]$ | $-2e^{3} - 16e^{2} - 40e - 24$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,w^{4}-2w^{3}-4w^{2}+6w+1]$ | $-1$ |
$5$ | $[5,5,w^{4}-w^{3}-5w^{2}+3w+1]$ | $-1$ |