Base field 5.5.160801.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 4x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[27, 3, -w^{3} + w^{2} + 3w - 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 7x^{4} + 6x^{3} + 35x^{2} - 40x - 20\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{4} + 5w^{2} - 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $-1$ |
| 13 | $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $\phantom{-}\frac{2}{5}e^{4} - \frac{7}{5}e^{3} - 2e^{2} + 5e + 2$ |
| 17 | $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ | $\phantom{-}\frac{3}{10}e^{4} - \frac{13}{10}e^{3} - 2e^{2} + \frac{15}{2}e + 4$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{5}e^{4} - \frac{6}{5}e^{3} + 7e - 1$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{2}{5}e^{4} + \frac{7}{5}e^{3} + 3e^{2} - 8e - 4$ |
| 31 | $[31, 31, w^{3} - 4w + 2]$ | $\phantom{-}\frac{1}{10}e^{4} - \frac{1}{10}e^{3} - e^{2} - \frac{3}{2}e + 4$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{1}{10}e^{4} - \frac{1}{10}e^{3} - e^{2} - \frac{1}{2}e$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $\phantom{-}e^{2} - 3e - 2$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - 5e^{2} + \frac{17}{2}e + 14$ |
| 59 | $[59, 59, -w^{4} + 5w^{2} + w - 4]$ | $-\frac{1}{5}e^{4} + \frac{6}{5}e^{3} - 2e^{2} - 2e + 11$ |
| 61 | $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ | $-\frac{1}{5}e^{4} + \frac{1}{5}e^{3} + 2e^{2} + 2e - 2$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ | $\phantom{-}\frac{3}{5}e^{4} - \frac{18}{5}e^{3} + e^{2} + 16e - 5$ |
| 71 | $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ | $-e^{3} + 4e^{2} + e - 8$ |
| 79 | $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ | $\phantom{-}\frac{3}{5}e^{4} - \frac{13}{5}e^{3} - e^{2} + 7e + 2$ |
| 83 | $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ | $\phantom{-}\frac{3}{5}e^{4} - \frac{13}{5}e^{3} - e^{2} + 8e - 4$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ | $-\frac{2}{5}e^{4} + \frac{2}{5}e^{3} + 5e^{2} - 4$ |
| 83 | $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ | $-e^{4} + 4e^{3} + 3e^{2} - 16e + 9$ |
| 83 | $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ | $-\frac{1}{5}e^{4} + \frac{6}{5}e^{3} - 2e^{2} - 2e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-1$ |
| $9$ | $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ | $1$ |