Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 4x^{4} - 4x^{3} - 21x^{2} - x + 20\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{3} + 2w^{2} + 3w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}2e^{4} + 5e^{3} - 15e^{2} - 17e + 23$ |
| 11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $-e^{2} - 2e + 4$ |
| 13 | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $-1$ |
| 16 | $[16, 2, 2]$ | $-2e^{4} - 5e^{3} + 14e^{2} + 16e - 19$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ | $-3e^{4} - 7e^{3} + 24e^{2} + 25e - 34$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 5w]$ | $-e^{2} - e + 4$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}e^{4} + 3e^{3} - 6e^{2} - 10e + 9$ |
| 19 | $[19, 19, w^{2} - w - 2]$ | $-2e^{4} - 5e^{3} + 15e^{2} + 20e - 20$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w]$ | $-e^{4} - 2e^{3} + 9e^{2} + 6e - 16$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}2e^{4} + 4e^{3} - 18e^{2} - 12e + 31$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ | $-2e^{4} - 5e^{3} + 14e^{2} + 17e - 17$ |
| 43 | $[43, 43, 2w^{3} - 3w^{2} - 11w]$ | $\phantom{-}e^{4} + 2e^{3} - 9e^{2} - 7e + 12$ |
| 47 | $[47, 47, w^{3} - 7w - 4]$ | $\phantom{-}3e^{4} + 7e^{3} - 24e^{2} - 22e + 40$ |
| 53 | $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ | $\phantom{-}3e^{4} + 7e^{3} - 25e^{2} - 25e + 44$ |
| 61 | $[61, 61, -w - 3]$ | $-3e^{4} - 6e^{3} + 29e^{2} + 21e - 54$ |
| 73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $\phantom{-}3e^{4} + 8e^{3} - 20e^{2} - 25e + 32$ |
| 73 | $[73, 73, w^{3} - w^{2} - 7w - 1]$ | $\phantom{-}e^{4} + 3e^{3} - 8e^{2} - 14e + 14$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}5e^{4} + 11e^{3} - 40e^{2} - 35e + 65$ |
| 83 | $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ | $-4e^{4} - 8e^{3} + 35e^{2} + 27e - 54$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ | $1$ |