Base field 5.5.24217.1
Generator \(w\), with minimal polynomial \(x^{5} - 5x^{3} - x^{2} + 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + x^{4} - 20x^{3} - 12x^{2} + 48x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2w^{4} + w^{3} + 9w^{2} - 2w - 3]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -2w^{4} + w^{3} + 9w^{2} - 3w - 5]$ | $-\frac{1}{4}e^{4} - \frac{1}{2}e^{3} + \frac{19}{4}e^{2} + 7e - 9$ |
| 17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - 5e^{2} - 4e + 8$ |
| 23 | $[23, 23, w^{3} - 3w]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{19}{4}e^{2} - 7e + 10$ |
| 29 | $[29, 29, 2w^{4} - w^{3} - 10w^{2} + 2w + 4]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + 4e^{2} + 3e$ |
| 32 | $[32, 2, 2]$ | $-\frac{3}{8}e^{4} - \frac{3}{8}e^{3} + 7e^{2} + 5e - 10$ |
| 37 | $[37, 37, -w^{4} + w^{3} + 4w^{2} - 2w]$ | $\phantom{-}\frac{3}{8}e^{4} + \frac{7}{8}e^{3} - 7e^{2} - \frac{23}{2}e + 12$ |
| 41 | $[41, 41, -3w^{4} + 2w^{3} + 14w^{2} - 5w - 7]$ | $\phantom{-}\frac{3}{8}e^{4} + \frac{3}{8}e^{3} - \frac{15}{2}e^{2} - \frac{7}{2}e + 12$ |
| 43 | $[43, 43, -3w^{4} + w^{3} + 14w^{2} - 3w - 6]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - 5e^{2} - \frac{23}{2}e + 12$ |
| 47 | $[47, 47, -3w^{4} + 2w^{3} + 14w^{2} - 7w - 6]$ | $-\frac{3}{8}e^{4} - \frac{3}{8}e^{3} + \frac{15}{2}e^{2} + \frac{9}{2}e - 10$ |
| 53 | $[53, 53, 2w^{4} - w^{3} - 8w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{4}e^{3} - 4e^{2} - 3e + 2$ |
| 53 | $[53, 53, -2w^{4} + w^{3} + 10w^{2} - 4w - 6]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{1}{2}e^{3} - \frac{19}{4}e^{2} - 9e + 11$ |
| 59 | $[59, 59, -w^{4} + 4w^{2} + 1]$ | $-\frac{3}{4}e^{4} - \frac{5}{4}e^{3} + 14e^{2} + \frac{41}{2}e - 22$ |
| 59 | $[59, 59, -3w^{4} + 2w^{3} + 14w^{2} - 6w - 8]$ | $-\frac{1}{4}e^{4} - \frac{1}{4}e^{3} + \frac{7}{2}e^{2} + \frac{7}{2}e + 4$ |
| 61 | $[61, 61, 4w^{4} - 2w^{3} - 18w^{2} + 5w + 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{17}{4}e^{2} + e + 8$ |
| 61 | $[61, 61, 3w^{4} - w^{3} - 15w^{2} + 2w + 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{17}{4}e^{2} + e + 8$ |
| 73 | $[73, 73, -4w^{4} + 2w^{3} + 18w^{2} - 7w - 6]$ | $-\frac{1}{4}e^{4} - \frac{3}{4}e^{3} + \frac{9}{2}e^{2} + 12e - 2$ |
| 83 | $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ | $\phantom{-}1$ |
| 83 | $[83, 83, -2w^{4} + 2w^{3} + 10w^{2} - 7w - 6]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{3}{4}e^{3} - \frac{9}{2}e^{2} - 13e + 2$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 8w^{2} - 3w + 1]$ | $\phantom{-}\frac{3}{8}e^{4} + \frac{7}{8}e^{3} - 7e^{2} - \frac{31}{2}e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $83$ | $[83, 83, -2w^{4} + 9w^{2} + 2w - 4]$ | $-1$ |