Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{2} + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 7x^{3} + 9x^{2} + 23x - 43\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $-e^{3} + 4e^{2} + 4e - 16$ |
| 5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e^{3} - 4e^{2} - 3e + 17$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $-1$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $\phantom{-}0$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}2e - 2$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $\phantom{-}2e^{3} - 9e^{2} - 3e + 35$ |
| 23 | $[23, 23, -w^{3} + 4w + 2]$ | $-2e^{3} + 8e^{2} + 4e - 24$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}4e^{3} - 18e^{2} - 8e + 68$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}3e^{3} - 12e^{2} - 7e + 38$ |
| 29 | $[29, 29, -w + 3]$ | $\phantom{-}2$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}2e^{3} - 10e^{2} - e + 36$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $-5e^{3} + 21e^{2} + 15e - 85$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $-3e^{2} + 6e + 12$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $-5e^{3} + 22e^{2} + 9e - 76$ |
| 59 | $[59, 59, w^{2} + w - 4]$ | $-4e^{3} + 17e^{2} + 11e - 62$ |
| 61 | $[61, 61, -2w^{2} + w + 8]$ | $\phantom{-}4e^{3} - 18e^{2} - 8e + 62$ |
| 73 | $[73, 73, -w^{3} + 5w - 1]$ | $\phantom{-}2e^{3} - 8e^{2} - 10e + 32$ |
| 79 | $[79, 79, 2w^{2} + w - 6]$ | $-3e^{3} + 14e^{2} + 5e - 51$ |
| 79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $\phantom{-}e^{3} - 6e^{2} - 3e + 28$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{2} + 3]$ | $1$ |