Base field 3.3.1492.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w^{2} - 2w - 8]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
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 |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $-\frac{1}{3}e^{2} + 3$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - 2w - 8]$ | $-1$ |
| 7 | $[7, 7, -2w^{2} + 3w + 16]$ | $\phantom{-}\frac{1}{9}e^{3} - e$ |
| 7 | $[7, 7, -w^{2} + 2w + 6]$ | $-\frac{1}{9}e^{3} + e$ |
| 11 | $[11, 11, w^{2} - 2w - 2]$ | $\phantom{-}\frac{2}{9}e^{3} - 3e$ |
| 19 | $[19, 19, -w + 2]$ | $-\frac{1}{9}e^{3}$ |
| 23 | $[23, 23, -w^{2} + 3w + 1]$ | $-\frac{1}{3}e^{2}$ |
| 25 | $[25, 5, w^{2} - w - 9]$ | $\phantom{-}\frac{2}{9}e^{3} - 5e$ |
| 27 | $[27, 3, 3]$ | $-2$ |
| 29 | $[29, 29, -w^{2} - w + 1]$ | $-\frac{2}{9}e^{3} + 4e$ |
| 29 | $[29, 29, w^{2} - 2w - 4]$ | $-\frac{1}{9}e^{3} + e$ |
| 29 | $[29, 29, -w^{2} + w + 11]$ | $\phantom{-}\frac{2}{3}e^{2} - 12$ |
| 43 | $[43, 43, 2w^{2} - 3w - 18]$ | $\phantom{-}\frac{1}{3}e^{2} - 8$ |
| 47 | $[47, 47, -2w + 7]$ | $\phantom{-}e$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $-\frac{5}{9}e^{3} + 6e$ |
| 61 | $[61, 61, w^{2} + 2w + 2]$ | $-8$ |
| 67 | $[67, 67, -2w^{2} + 5w + 8]$ | $-\frac{2}{3}e^{3} + 9e$ |
| 79 | $[79, 79, w^{2} - 3w - 9]$ | $-\frac{4}{3}e^{2} + 16$ |
| 97 | $[97, 97, -w^{2} - 2w + 2]$ | $\phantom{-}\frac{4}{9}e^{3} - 8e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w^{2} - 2w - 8]$ | $1$ |