Base field \(\Q(\sqrt{13}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[79, 79, 5w - 4]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 4x^{4} - 4x^{3} + 28x^{2} - 20x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w]$ | $-2e^{4} + 2e^{3} + 15e^{2} - 12e - 4$ |
| 3 | $[3, 3, -w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}3e^{4} - 4e^{3} - 22e^{2} + 26e + 1$ |
| 13 | $[13, 13, -2w + 1]$ | $-e^{3} + 7e$ |
| 17 | $[17, 17, w + 4]$ | $\phantom{-}2e^{4} - e^{3} - 16e^{2} + 5e + 6$ |
| 17 | $[17, 17, -w + 5]$ | $-4e^{4} + 6e^{3} + 28e^{2} - 38e + 2$ |
| 23 | $[23, 23, 3w + 1]$ | $-2e^{4} + 4e^{3} + 14e^{2} - 26e$ |
| 23 | $[23, 23, -3w + 4]$ | $-2e^{4} + 2e^{3} + 14e^{2} - 13e + 6$ |
| 25 | $[25, 5, 5]$ | $-e^{4} + 8e^{2} - 6$ |
| 29 | $[29, 29, 3w - 2]$ | $-2e^{4} + 2e^{3} + 14e^{2} - 14e + 6$ |
| 29 | $[29, 29, -3w + 1]$ | $\phantom{-}4e^{4} - 5e^{3} - 28e^{2} + 29e - 2$ |
| 43 | $[43, 43, -4w - 1]$ | $-4e^{4} + 6e^{3} + 28e^{2} - 38e + 8$ |
| 43 | $[43, 43, 4w - 5]$ | $\phantom{-}4e^{4} - 4e^{3} - 30e^{2} + 22e + 8$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2e^{4} - 2e^{3} - 14e^{2} + 13e - 2$ |
| 53 | $[53, 53, -w - 7]$ | $-2e^{2} + 4e + 10$ |
| 53 | $[53, 53, w - 8]$ | $\phantom{-}6e^{4} - 8e^{3} - 43e^{2} + 50e - 2$ |
| 61 | $[61, 61, -3w - 8]$ | $\phantom{-}4e^{4} - 4e^{3} - 29e^{2} + 24e + 2$ |
| 61 | $[61, 61, 3w - 11]$ | $-2e^{4} + 2e^{3} + 16e^{2} - 12e - 2$ |
| 79 | $[79, 79, 5w - 4]$ | $-1$ |
| 79 | $[79, 79, 5w - 1]$ | $-2e^{3} + 2e^{2} + 15e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $79$ | $[79, 79, 5w - 4]$ | $1$ |