Base field 3.3.404.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[29, 29, -2w + 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + x^{4} - 8x^{3} - 5x^{2} + 12x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{2} - 2w - 2]$ | $-e - 1$ |
| 7 | $[7, 7, -w + 2]$ | $-e^{4} - 2e^{3} + 7e^{2} + 11e - 8$ |
| 9 | $[9, 3, w^{2} - 2]$ | $\phantom{-}e^{4} + e^{3} - 7e^{2} - 6e + 5$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}e^{3} - e^{2} - 6e + 3$ |
| 29 | $[29, 29, -2w + 1]$ | $-1$ |
| 37 | $[37, 37, 2w^{2} - 4w - 3]$ | $-2e^{4} - e^{3} + 14e^{2} + 6e - 13$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}e^{4} + 3e^{3} - 7e^{2} - 16e + 4$ |
| 37 | $[37, 37, 2w^{2} - w - 8]$ | $-e^{4} - 4e^{3} + 8e^{2} + 21e - 14$ |
| 41 | $[41, 41, w^{2} - 4w + 2]$ | $\phantom{-}2e^{4} + 3e^{3} - 16e^{2} - 17e + 18$ |
| 43 | $[43, 43, -2w^{2} + 2w + 7]$ | $-e^{4} - e^{3} + 6e^{2} + 6e - 8$ |
| 43 | $[43, 43, -2w^{2} + 3w + 6]$ | $-e^{2} - e - 2$ |
| 43 | $[43, 43, -w^{2} + 6]$ | $\phantom{-}e + 2$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $\phantom{-}2e^{4} + 5e^{3} - 15e^{2} - 25e + 19$ |
| 53 | $[53, 53, 2w^{2} - 5w - 4]$ | $\phantom{-}3e^{4} + 3e^{3} - 20e^{2} - 18e + 15$ |
| 59 | $[59, 59, 2w - 3]$ | $\phantom{-}2e^{3} - 2e^{2} - 13e + 3$ |
| 61 | $[61, 61, -w - 4]$ | $\phantom{-}e^{4} + e^{3} - 5e^{2} - 3e - 5$ |
| 67 | $[67, 67, -2w^{2} - w + 2]$ | $-e^{2} - 2e + 5$ |
| 73 | $[73, 73, 2w^{2} - 3w - 12]$ | $-3e^{4} - 4e^{3} + 22e^{2} + 24e - 22$ |
| 83 | $[83, 83, -2w - 5]$ | $-3e^{4} - 2e^{3} + 21e^{2} + 14e - 21$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -2w + 1]$ | $1$ |