Base field 3.3.1373.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[12, 6, w^{2} - w - 9]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 8x^{3} - x^{2} + 11x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-1$ |
| 4 | $[4, 2, w^{2} - w - 7]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e + 1$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $-e^{3} + e^{2} + 5e - 3$ |
| 13 | $[13, 13, -w + 2]$ | $-e^{4} + 7e^{2} - 4$ |
| 25 | $[25, 5, w^{2} - 8]$ | $\phantom{-}e^{2} - 3$ |
| 29 | $[29, 29, 2w + 3]$ | $-e^{4} + e^{3} + 7e^{2} - 5e - 4$ |
| 37 | $[37, 37, w + 4]$ | $\phantom{-}e^{4} - 8e^{2} + e + 8$ |
| 37 | $[37, 37, -3w^{2} + 2w + 24]$ | $-e^{4} + e^{3} + 8e^{2} - 7e - 11$ |
| 37 | $[37, 37, w^{2} + 2w - 2]$ | $-e^{3} + 6e + 1$ |
| 47 | $[47, 47, w^{2} - 2]$ | $-e^{4} + e^{3} + 6e^{2} - 5e - 5$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $-e^{3} + 3e$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $-2e^{4} + e^{3} + 13e^{2} - 10$ |
| 71 | $[71, 71, 2w - 1]$ | $-3e^{2} + 15$ |
| 71 | $[71, 71, -w^{2} + 4w + 2]$ | $-e^{4} + 4e^{2} + 5$ |
| 71 | $[71, 71, -w^{2} + 4w - 2]$ | $\phantom{-}e^{4} - e^{3} - 4e^{2} + 3e - 3$ |
| 73 | $[73, 73, -w^{2} + 4w + 4]$ | $\phantom{-}e^{4} - 6e^{2} - 2e + 1$ |
| 79 | $[79, 79, -2w + 7]$ | $-3e^{3} + 15e$ |
| 83 | $[83, 83, -2w^{2} + 13]$ | $\phantom{-}2e^{4} - 3e^{3} - 14e^{2} + 12e + 15$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 2]$ | $1$ |
| $4$ | $[4, 2, w^{2} - w - 7]$ | $-1$ |