Base field 3.3.1101.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[12, 6, w^{2} + w - 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 5x^{2} - x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 3]$ | $-e^{3} - e^{2} + 4e$ |
| 3 | $[3, 3, w - 1]$ | $-1$ |
| 4 | $[4, 2, w^{2} + w - 7]$ | $-1$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}2e^{3} + 2e^{2} - 10e$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $-e^{3} - e^{2} + 6e - 1$ |
| 31 | $[31, 31, -2w^{2} + 19]$ | $-e^{3} - 3e^{2} + 2e + 5$ |
| 31 | $[31, 31, -w^{2} + 5]$ | $\phantom{-}e^{3} + e^{2} - 8e - 4$ |
| 31 | $[31, 31, -3w + 5]$ | $-2e^{3} + 12e - 2$ |
| 41 | $[41, 41, w^{2} + 2w - 7]$ | $-3e^{3} - 3e^{2} + 16e + 6$ |
| 43 | $[43, 43, w^{2} - 11]$ | $\phantom{-}e^{3} + 3e^{2} - 10$ |
| 47 | $[47, 47, 3w - 7]$ | $-e^{3} - 3e^{2} + 4e + 9$ |
| 53 | $[53, 53, -3w^{2} - 6w + 11]$ | $-2e^{3} + 8e - 4$ |
| 59 | $[59, 59, 2w - 1]$ | $\phantom{-}2e^{3} - 12e$ |
| 67 | $[67, 67, 2w^{2} + w - 19]$ | $\phantom{-}2e^{3} - 14e - 2$ |
| 67 | $[67, 67, 3w^{2} + 2w - 25]$ | $\phantom{-}3e^{3} + 3e^{2} - 12e - 1$ |
| 67 | $[67, 67, w - 5]$ | $\phantom{-}5e^{3} + 7e^{2} - 24e - 5$ |
| 73 | $[73, 73, -4w^{2} - 3w + 29]$ | $\phantom{-}7e^{3} + 9e^{2} - 30e - 4$ |
| 73 | $[73, 73, 2w^{2} - w - 11]$ | $-2e^{3} - 2e^{2} + 12e$ |
| 73 | $[73, 73, w^{2} + 2w - 11]$ | $\phantom{-}4e^{3} + 2e^{2} - 24e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $1$ |
| $4$ | $[4, 2, w^{2} + w - 7]$ | $1$ |