Base field 5.5.89417.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} - x^{2} + 8x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[33, 33, w^{4} - w^{3} - 4w^{2} + 4w + 3]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} - 5x^{2} + 2x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{2} - 3]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{4} - 5w^{2} + 4]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $-1$ |
| 17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $\phantom{-}e^{2} - 4e - 2$ |
| 32 | $[32, 2, 2]$ | $-2e^{2} + 8e + 1$ |
| 37 | $[37, 37, -w^{4} + 2w^{3} + 5w^{2} - 7w - 5]$ | $-2e^{2} + 7e + 4$ |
| 37 | $[37, 37, -w^{3} + 4w - 1]$ | $\phantom{-}e^{2} - 3e - 4$ |
| 41 | $[41, 41, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}e^{2} - 5e$ |
| 41 | $[41, 41, -w^{3} + 2w + 2]$ | $\phantom{-}2e^{2} - 10e + 2$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}0$ |
| 49 | $[49, 7, w^{4} - 5w^{2} + 2]$ | $\phantom{-}2e^{2} - 7e$ |
| 53 | $[53, 53, w^{4} - w^{3} - 5w^{2} + 2w + 5]$ | $\phantom{-}2e - 2$ |
| 59 | $[59, 59, w^{4} - w^{3} - 4w^{2} + 3w - 1]$ | $-3e^{2} + 10e$ |
| 67 | $[67, 67, -w^{4} + 3w^{2} + 2w + 2]$ | $-e^{2} + 4e + 8$ |
| 79 | $[79, 79, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}2e^{2} - 4e - 8$ |
| 81 | $[81, 3, -w^{4} + 6w^{2} + w - 8]$ | $-2e^{2} + 7e + 8$ |
| 83 | $[83, 83, w^{4} + w^{3} - 5w^{2} - 4w + 1]$ | $-e^{2} + 4e$ |
| 89 | $[89, 89, -w^{4} + 5w^{2} + w - 1]$ | $-e^{2} + e + 12$ |
| 97 | $[97, 97, -w^{4} + 2w^{3} + 5w^{2} - 5w - 5]$ | $-2e + 10$ |
| 101 | $[101, 101, 2w^{2} - w - 2]$ | $\phantom{-}3e^{2} - 11e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{2} - 3]$ | $-1$ |
| $11$ | $[11, 11, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $1$ |