Base field 4.4.4400.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29,29,-w^{3} - 2w^{2} + 3w + 7]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 15x^{4} + 32x^{2} - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{2} + w + 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{15}{4}e^{3} + 7e$ |
| 5 | $[5, 5, -w^{3} + w^{2} + 4w - 4]$ | $-\frac{3}{8}e^{5} + \frac{41}{8}e^{3} - \frac{9}{2}e$ |
| 11 | $[11, 11, w]$ | $-\frac{5}{8}e^{5} + \frac{71}{8}e^{3} - \frac{25}{2}e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ | $\phantom{-}e^{4} - 14e^{2} + 18$ |
| 29 | $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ | $-1$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{41}{4}e^{3} + 11e$ |
| 31 | $[31, 31, -w^{3} - w^{2} + 4w + 2]$ | $-\frac{3}{8}e^{5} + \frac{41}{8}e^{3} - \frac{15}{2}e$ |
| 41 | $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{41}{4}e^{3} + 11e$ |
| 41 | $[41, 41, w^{3} - 5w + 2]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{41}{4}e^{3} + 11e$ |
| 49 | $[49, 7, -w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{41}{2}e^{3} + 24e$ |
| 49 | $[49, 7, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{19}{4}e^{3} + 17e$ |
| 59 | $[59, 59, -3w^{2} - w + 10]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{15}{2}e^{2} + 20$ |
| 59 | $[59, 59, -3w^{2} + w + 10]$ | $\phantom{-}2e^{4} - 27e^{2} + 28$ |
| 61 | $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ | $-\frac{3}{2}e^{5} + \frac{41}{2}e^{3} - 22e$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ | $\phantom{-}\frac{3}{8}e^{5} - \frac{41}{8}e^{3} + \frac{9}{2}e$ |
| 71 | $[71, 71, 2w^{2} + w - 9]$ | $\phantom{-}2e^{2} - 12$ |
| 71 | $[71, 71, 2w^{2} - w - 9]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{43}{2}e^{2} + 28$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{4} - 15e^{2} + 18$ |
| 101 | $[101, 101, 2w^{2} - w - 10]$ | $-\frac{3}{2}e^{4} + \frac{41}{2}e^{2} - 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29,29,-w^{3} - 2w^{2} + 3w + 7]$ | $1$ |