Base field 3.3.1708.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[2, 2, w^{2} - 2w - 5]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 6x^{3} - 11x^{2} + 4x + 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w^{2} - 2w - 5]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{2} + 3w + 1]$ | $\phantom{-}e^{2} - 3$ |
| 7 | $[7, 7, -2w^{2} + 2w + 17]$ | $-e^{4} - e^{3} + 6e^{2} + 4e - 4$ |
| 7 | $[7, 7, -w^{2} + w + 9]$ | $-e^{4} - e^{3} + 6e^{2} + 4e - 4$ |
| 13 | $[13, 13, 2w + 1]$ | $-e^{4} - e^{3} + 7e^{2} + 4e - 7$ |
| 25 | $[25, 5, -3w^{2} + 5w + 19]$ | $-e^{4} - e^{3} + 7e^{2} + 8e - 7$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}e^{4} - 7e^{2} + 10$ |
| 29 | $[29, 29, w^{2} + w - 1]$ | $\phantom{-}2e^{3} + e^{2} - 10e - 3$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $-e^{3} - e^{2} + 4e + 2$ |
| 37 | $[37, 37, 2w^{2} + 6w + 3]$ | $-e^{3} + 4e - 1$ |
| 41 | $[41, 41, -6w^{2} - 14w - 3]$ | $\phantom{-}e^{4} - 7e^{2} + 4e + 12$ |
| 53 | $[53, 53, -4w^{2} + 6w + 27]$ | $\phantom{-}2e^{4} - 13e^{2} + 9$ |
| 59 | $[59, 59, 2w^{2} - 4w - 11]$ | $\phantom{-}e^{4} - 3e^{2} + 4e - 6$ |
| 61 | $[61, 61, w^{2} - w - 3]$ | $\phantom{-}e^{4} - e^{3} - 7e^{2} + 4e + 5$ |
| 61 | $[61, 61, -2w^{2} + 2w + 13]$ | $-3e^{4} - 4e^{3} + 18e^{2} + 16e - 13$ |
| 73 | $[73, 73, w^{2} + 3w + 3]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 6e + 11$ |
| 97 | $[97, 97, w^{2} + w - 15]$ | $\phantom{-}e^{4} + e^{3} - 7e^{2} - 6e + 17$ |
| 101 | $[101, 101, w^{2} + 3w - 1]$ | $\phantom{-}e^{4} + 4e^{3} - 3e^{2} - 20e$ |
| 101 | $[101, 101, w^{2} - w - 11]$ | $\phantom{-}3e^{4} + 2e^{3} - 20e^{2} - 10e + 15$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{2} - 2w - 5]$ | $-1$ |