Base field 4.4.5744.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{2} + 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 2x^{2} - 9x + 19\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{3} + 4w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e^{2} - 5$ |
| 7 | $[7, 7, -w^{2} + w + 2]$ | $-e^{2} - e + 10$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w]$ | $-e^{2} + 4$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $-1$ |
| 17 | $[17, 17, -w^{2} + 2]$ | $-3e^{2} + 23$ |
| 19 | $[19, 19, -w^{3} + 5w]$ | $\phantom{-}5e^{2} + 2e - 38$ |
| 31 | $[31, 31, -w^{2} + 2w + 3]$ | $\phantom{-}e^{2} + 3e - 8$ |
| 37 | $[37, 37, -2w^{3} + w^{2} + 8w - 1]$ | $-3e^{2} - 3e + 23$ |
| 43 | $[43, 43, -w - 3]$ | $\phantom{-}7e^{2} + 4e - 53$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 3w - 2]$ | $-5e^{2} - 5e + 43$ |
| 53 | $[53, 53, w^{3} - 6w - 2]$ | $-2e^{2} + 13$ |
| 59 | $[59, 59, 2w^{3} - w^{2} - 10w - 2]$ | $-10e^{2} - 5e + 76$ |
| 61 | $[61, 61, 2w^{3} - w^{2} - 10w]$ | $-e^{2} - 3e + 11$ |
| 61 | $[61, 61, 2w^{3} - w^{2} - 8w]$ | $-e^{2} - e + 15$ |
| 71 | $[71, 71, 2w^{3} - 9w - 2]$ | $-3e^{2} + 28$ |
| 73 | $[73, 73, -w^{3} - w^{2} + 6w + 3]$ | $-3e + 5$ |
| 81 | $[81, 3, -3]$ | $-9e^{2} - 4e + 68$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}8e^{2} + e - 58$ |
| 101 | $[101, 101, 2w^{3} - 8w - 3]$ | $-6e^{2} - 5e + 53$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{2} + 3]$ | $1$ |