Base field 3.3.837.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, -2w - 5]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 3x^{4} - x^{3} - 5x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} - 2w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-e^{4} - 3e^{3} + 3e + 1$ |
| 4 | $[4, 2, w^{2} + w - 3]$ | $-e^{3} - 3e^{2} + e + 2$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e^{4} + 3e^{3} - e^{2} - 6e - 1$ |
| 13 | $[13, 13, -2w - 5]$ | $-1$ |
| 25 | $[25, 5, -w^{2} - 2w + 2]$ | $\phantom{-}3e^{3} + 7e^{2} - 6e - 7$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $-3e^{4} - 5e^{3} + 10e^{2} + 8e - 1$ |
| 31 | $[31, 31, -2w + 1]$ | $-6e^{4} - 16e^{3} + 7e^{2} + 16e - 3$ |
| 37 | $[37, 37, 2w + 3]$ | $\phantom{-}6e^{4} + 17e^{3} - 5e^{2} - 19e$ |
| 41 | $[41, 41, -w - 4]$ | $\phantom{-}e^{3} + 5e^{2} + 5e - 5$ |
| 43 | $[43, 43, 2w^{2} - 2w - 7]$ | $\phantom{-}2e^{4} + 5e^{3} - e^{2} - 5e - 9$ |
| 47 | $[47, 47, -2w^{2} - w + 8]$ | $\phantom{-}2e^{4} + 7e^{3} + 3e^{2} - 8e - 5$ |
| 53 | $[53, 53, 3w^{2} - 6w - 2]$ | $\phantom{-}e^{4} - 7e^{2} + 8$ |
| 53 | $[53, 53, -2w^{2} + 3w + 18]$ | $\phantom{-}2e^{4} + e^{3} - 12e^{2} - e + 4$ |
| 53 | $[53, 53, 2w - 3]$ | $\phantom{-}5e^{4} + 16e^{3} - 2e^{2} - 22e - 1$ |
| 59 | $[59, 59, 2w^{2} - 3w - 4]$ | $\phantom{-}4e^{4} + 14e^{3} + 4e^{2} - 14e - 7$ |
| 61 | $[61, 61, w^{2} - 2w - 4]$ | $\phantom{-}6e^{4} + 15e^{3} - 11e^{2} - 14e + 5$ |
| 71 | $[71, 71, 4w + 9]$ | $-e^{4} - 6e^{3} - 8e^{2} + 10e + 11$ |
| 73 | $[73, 73, 2w^{2} - 9]$ | $\phantom{-}6e^{4} + 15e^{3} - 12e^{2} - 22e + 5$ |
| 79 | $[79, 79, w^{2} - 4w + 2]$ | $-2e^{4} - 4e^{3} + 11e^{2} + 10e - 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -2w - 5]$ | $1$ |