Base field 5.5.81589.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{3} + w^{2} + 3w - 4]$ |
Dimension: | $4$ |
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:
\(x^{4} - 3x^{3} - x^{2} + 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{2} - 3]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{4} + 5w^{2} + w - 4]$ | $\phantom{-}2e^{3} - 3e^{2} - 6e + 3$ |
13 | $[13, 13, -w^{3} + w^{2} + 3w - 4]$ | $\phantom{-}1$ |
16 | $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ | $\phantom{-}e^{3} - 2e^{2} - 2e + 6$ |
17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $-e^{2} + e$ |
31 | $[31, 31, w^{4} - 4w^{2} - w + 3]$ | $-2e^{3} + 4e^{2} + 3e + 1$ |
43 | $[43, 43, -w^{3} + 4w - 2]$ | $\phantom{-}e^{3} + 2e^{2} - 8e - 1$ |
53 | $[53, 53, w^{4} - 3w^{2} - 1]$ | $-2e^{3} + 3e^{2} + 1$ |
53 | $[53, 53, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-3e^{3} - e^{2} + 15e + 3$ |
53 | $[53, 53, -w^{3} - w^{2} + 3w + 4]$ | $-e^{3} + 3e^{2} + 5e - 9$ |
61 | $[61, 61, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}4e^{3} - 6e^{2} - 7e + 5$ |
61 | $[61, 61, w^{4} - 4w^{2} + w + 1]$ | $\phantom{-}3e^{3} - 7e^{2} - 8e + 12$ |
61 | $[61, 61, w^{3} + w^{2} - 4w - 3]$ | $-e^{3} + 8e^{2} - 4e - 11$ |
67 | $[67, 67, -2w^{3} + w^{2} + 6w - 2]$ | $-3e^{2} - e + 10$ |
71 | $[71, 71, -2w^{3} + w^{2} + 7w - 3]$ | $\phantom{-}e^{3} + 3e^{2} - 7e - 9$ |
71 | $[71, 71, 2w^{4} - 4w^{3} - 7w^{2} + 13w - 1]$ | $\phantom{-}4e^{3} - 7e^{2} - 4e + 7$ |
73 | $[73, 73, -w^{4} + 2w^{3} + 3w^{2} - 7w]$ | $-e^{3} - 3e^{2} + 9e + 5$ |
73 | $[73, 73, w^{4} + w^{3} - 3w^{2} - 4w - 2]$ | $-3e^{3} + 2e^{2} + 10e + 3$ |
79 | $[79, 79, w^{4} - w^{3} - 5w^{2} + 4w + 6]$ | $\phantom{-}4e^{3} - 12e^{2} - 3e + 17$ |
83 | $[83, 83, -2w^{4} + w^{3} + 9w^{2} - 3w - 6]$ | $-3e^{3} + 5e^{2} + 2e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{3} + w^{2} + 3w - 4]$ | $-1$ |