Base field 4.4.15952.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[6, 6, w - 1]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} - 5x^{2} - 15x + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $-1$ |
| 3 | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $-1$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w + 2]$ | $-\frac{1}{3}e^{2} + \frac{2}{3}e + 6$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}e - 2$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $-e + 1$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}e - 1$ |
| 23 | $[23, 23, w^{3} - 6w]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - 1$ |
| 27 | $[27, 3, w^{3} + w^{2} - 5w - 4]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e - 3$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w]$ | $\phantom{-}e + 1$ |
| 41 | $[41, 41, 2w^{3} - 11w - 4]$ | $-\frac{2}{3}e^{2} + \frac{4}{3}e + 8$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ | $-\frac{2}{3}e^{2} + \frac{7}{3}e + 8$ |
| 59 | $[59, 59, 2w^{3} - 11w - 2]$ | $-\frac{1}{3}e^{2} - \frac{1}{3}e + 11$ |
| 67 | $[67, 67, w^{3} - 7w - 1]$ | $-e - 6$ |
| 71 | $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}e - 4$ |
| 79 | $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{13}{3}e - 11$ |
| 89 | $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e - 3$ |
| 101 | $[101, 101, -2w^{3} + 13w + 6]$ | $-\frac{2}{3}e^{2} + \frac{1}{3}e + 16$ |
| 101 | $[101, 101, w^{3} + w^{2} - 6w - 3]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{5}{3}e + 3$ |
| 101 | $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ | $-\frac{1}{3}e^{2} + \frac{2}{3}e + 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $1$ |
| $3$ | $[3, 3, -w^{3} + w^{2} + 5w - 2]$ | $1$ |