Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[25, 25, -w^{3} + w^{2} + 3w - 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + x^{4} - 6x^{3} - 3x^{2} + 5x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}0$ |
7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $\phantom{-}3e^{4} + 4e^{3} - 16e^{2} - 15e + 8$ |
13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}3e^{4} + 5e^{3} - 16e^{2} - 19e + 8$ |
29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $-3e^{4} - 4e^{3} + 16e^{2} + 12e - 11$ |
29 | $[29, 29, -w^{2} + 2w + 3]$ | $-e^{4} - e^{3} + 6e^{2} + 4e - 5$ |
31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-e^{4} + 6e^{2} - 3e - 5$ |
31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}e^{4} + e^{3} - 6e^{2} - 5e + 3$ |
32 | $[32, 2, 2]$ | $-e^{2} + e + 2$ |
43 | $[43, 43, -w^{2} - w + 4]$ | $-4e^{4} - 5e^{3} + 22e^{2} + 19e - 10$ |
53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $-8e^{4} - 12e^{3} + 43e^{2} + 45e - 23$ |
53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $-6e^{4} - 8e^{3} + 32e^{2} + 28e - 15$ |
73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $\phantom{-}8e^{4} + 10e^{3} - 41e^{2} - 35e + 14$ |
73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $-e^{4} - 3e^{3} + 3e^{2} + 12e + 4$ |
81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $-4e^{4} - 8e^{3} + 22e^{2} + 31e - 18$ |
83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $\phantom{-}4e^{4} + 3e^{3} - 25e^{2} - 8e + 13$ |
89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $-4e^{4} - 4e^{3} + 24e^{2} + 16e - 17$ |
97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $-7e^{4} - 8e^{3} + 43e^{2} + 28e - 28$ |
101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $\phantom{-}6e^{4} + 9e^{3} - 33e^{2} - 30e + 15$ |
103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $\phantom{-}5e^{4} + 6e^{3} - 25e^{2} - 21e + 1$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w^{2} - w - 2]$ | $1$ |