Base field 4.4.9909.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^{2} + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 18x^{2} + 54\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}2$ |
| 11 | $[11, 11, -w^{2} + w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} - 4e$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 3w - 1]$ | $-e^{2} + 8$ |
| 16 | $[16, 2, 2]$ | $-e^{2} + 11$ |
| 17 | $[17, 17, -w^{3} + 5w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} - 3e$ |
| 29 | $[29, 29, -w^{2} + w + 1]$ | $-e$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}e^{2} - 4$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w + 1]$ | $-\frac{1}{3}e^{3} + 7e$ |
| 41 | $[41, 41, w^{2} - 5]$ | $-\frac{2}{3}e^{3} + 7e$ |
| 47 | $[47, 47, w^{3} - w^{2} - 5w - 2]$ | $-\frac{1}{3}e^{3} + 2e$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}\frac{1}{3}e^{3} - 4e$ |
| 53 | $[53, 53, w^{3} - 4w - 4]$ | $\phantom{-}3e$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ | $-\frac{1}{3}e^{3} + 3e$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}e^{2} - 10$ |
| 71 | $[71, 71, w^{3} - w^{2} - 6w - 2]$ | $-\frac{1}{3}e^{3} + 6e$ |
| 103 | $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ | $-10$ |
| 103 | $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ | $\phantom{-}2e^{2} - 10$ |
| 109 | $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ | $-2e^{2} + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $1$ |