Base field 3.3.229.1
Generator \(w\), with minimal polynomial \(x^{3} - 4x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[29, 29, -2w + 3]$ |
| 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:
| \(x^{6} - 12x^{4} + 35x^{2} - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + w + 3]$ | $-\frac{1}{4}e^{5} + \frac{5}{2}e^{3} - \frac{21}{4}e$ |
| 7 | $[7, 7, w^{2} - 2]$ | $-\frac{1}{2}e^{3} + \frac{5}{2}e$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-\frac{1}{4}e^{5} + 3e^{3} - \frac{27}{4}e$ |
| 23 | $[23, 23, -2w + 1]$ | $-e^{2} + 5$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 5$ |
| 29 | $[29, 29, -2w + 3]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -2w^{2} + 2w + 3]$ | $\phantom{-}\frac{3}{4}e^{5} - 8e^{3} + \frac{69}{4}e$ |
| 37 | $[37, 37, 4w^{2} - 2w - 13]$ | $\phantom{-}\frac{3}{4}e^{5} - 7e^{3} + \frac{41}{4}e$ |
| 37 | $[37, 37, -2w^{2} + 5]$ | $-\frac{1}{4}e^{5} + \frac{3}{2}e^{3} + \frac{3}{4}e$ |
| 37 | $[37, 37, 2w^{2} - w - 10]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{13}{2}e^{2} + 14$ |
| 41 | $[41, 41, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{4}e^{5} - 2e^{3} - \frac{9}{4}e$ |
| 47 | $[47, 47, w - 4]$ | $-\frac{3}{2}e^{4} + \frac{25}{2}e^{2} - 13$ |
| 49 | $[49, 7, 2w^{2} - w - 4]$ | $-e^{3} + 7e$ |
| 53 | $[53, 53, 2w^{2} - 2w - 7]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{19}{2}e$ |
| 53 | $[53, 53, 3w^{2} - 2w - 8]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 13e$ |
| 53 | $[53, 53, 2w + 5]$ | $-\frac{1}{2}e^{4} + \frac{5}{2}e^{2} + 2$ |
| 59 | $[59, 59, 2w^{2} - 2w - 9]$ | $-\frac{1}{2}e^{5} + 4e^{3} - \frac{7}{2}e$ |
| 67 | $[67, 67, 2w^{2} - 3]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{15}{2}e^{3} + \frac{43}{4}e$ |
| 73 | $[73, 73, 2w^{2} + w - 8]$ | $-\frac{3}{2}e^{4} + \frac{23}{2}e^{2} - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -2w + 3]$ | $-1$ |