Base field 5.5.81589.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[32, 2, 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 7x^{4} - 7x^{3} + 100x^{2} - 96x + 24\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} - 3]$ | $-1$ |
| 11 | $[11, 11, -w^{4} + 5w^{2} + w - 4]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{1}{2}e^{4} + 3e^{3} + 6e^{2} - \frac{87}{2}e + 17$ |
| 16 | $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{3} + \frac{9}{2}e^{2} - 52e + 30$ |
| 31 | $[31, 31, w^{4} - 4w^{2} - w + 3]$ | $-\frac{1}{4}e^{4} + \frac{7}{4}e^{3} + \frac{11}{4}e^{2} - 28e + 11$ |
| 43 | $[43, 43, -w^{3} + 4w - 2]$ | $-e + 2$ |
| 53 | $[53, 53, w^{4} - 3w^{2} - 1]$ | $-\frac{3}{2}e^{4} + \frac{19}{2}e^{3} + \frac{31}{2}e^{2} - 137e + 72$ |
| 53 | $[53, 53, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-\frac{3}{2}e^{4} + 10e^{3} + 15e^{2} - \frac{295}{2}e + 75$ |
| 53 | $[53, 53, -w^{3} - w^{2} + 3w + 4]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{19}{2}e^{3} - \frac{31}{2}e^{2} + 137e - 72$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 5w - 2]$ | $-2e^{4} + 13e^{3} + 21e^{2} - 191e + 92$ |
| 61 | $[61, 61, w^{4} - 4w^{2} + w + 1]$ | $-\frac{7}{4}e^{4} + \frac{45}{4}e^{3} + \frac{73}{4}e^{2} - 163e + 83$ |
| 61 | $[61, 61, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{7}{4}e^{3} - \frac{11}{4}e^{2} + 24e - 1$ |
| 67 | $[67, 67, -2w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{3} - \frac{9}{2}e^{2} + 50e - 22$ |
| 71 | $[71, 71, -2w^{3} + w^{2} + 7w - 3]$ | $-2e^{4} + 13e^{3} + 21e^{2} - 191e + 90$ |
| 71 | $[71, 71, 2w^{4} - 4w^{3} - 7w^{2} + 13w - 1]$ | $\phantom{-}\frac{7}{4}e^{4} - \frac{45}{4}e^{3} - \frac{73}{4}e^{2} + 163e - 81$ |
| 73 | $[73, 73, -w^{4} + 2w^{3} + 3w^{2} - 7w]$ | $-\frac{3}{2}e^{4} + 10e^{3} + 15e^{2} - \frac{293}{2}e + 71$ |
| 73 | $[73, 73, w^{4} + w^{3} - 3w^{2} - 4w - 2]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{19}{2}e^{3} - \frac{31}{2}e^{2} + 138e - 76$ |
| 79 | $[79, 79, w^{4} - w^{3} - 5w^{2} + 4w + 6]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{19}{2}e^{3} - \frac{31}{2}e^{2} + 137e - 70$ |
| 83 | $[83, 83, -2w^{4} + w^{3} + 9w^{2} - 3w - 6]$ | $-\frac{7}{4}e^{4} + \frac{45}{4}e^{3} + \frac{73}{4}e^{2} - 162e + 81$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{2} - 3]$ | $1$ |
| $16$ | $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ | $-1$ |