Base field 5.5.24217.1
Generator \(w\), with minimal polynomial \(x^{5} - 5 x^{3} - x^{2} + 3 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[83, 83, -2 w^{4} + 9 w^{2} + 2 w - 4]$ |
| 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:
| \(x^{5} + x^{4} - 20 x^{3} - 12 x^{2} + 48 x - 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2 w^{4} + w^{3} + 9 w^{2} - 2 w - 3]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -2 w^{4} + w^{3} + 9 w^{2} - 3 w - 5]$ | $-\frac{1}{4} e^{4} - \frac{1}{2} e^{3} + \frac{19}{4} e^{2} + 7 e - 9$ |
| 17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}\frac{1}{4} e^{4} + \frac{1}{4} e^{3} - 5 e^{2} - 4 e + 8$ |
| 23 | $[23, 23, w^{3} - 3 w]$ | $\phantom{-}\frac{1}{4} e^{4} + \frac{1}{2} e^{3} - \frac{19}{4} e^{2} - 7 e + 10$ |
| 29 | $[29, 29, 2 w^{4} - w^{3} - 10 w^{2} + 2 w + 4]$ | $-\frac{1}{4} e^{4} - \frac{1}{4} e^{3} + 4 e^{2} + 3 e$ |
| 32 | $[32, 2, 2]$ | $-\frac{3}{8} e^{4} - \frac{3}{8} e^{3} + 7 e^{2} + 5 e - 10$ |
| 37 | $[37, 37, -w^{4} + w^{3} + 4 w^{2} - 2 w]$ | $\phantom{-}\frac{3}{8} e^{4} + \frac{7}{8} e^{3} - 7 e^{2} - \frac{23}{2} e + 12$ |
| 41 | $[41, 41, -3 w^{4} + 2 w^{3} + 14 w^{2} - 5 w - 7]$ | $\phantom{-}\frac{3}{8} e^{4} + \frac{3}{8} e^{3} - \frac{15}{2} e^{2} - \frac{7}{2} e + 12$ |
| 43 | $[43, 43, -3 w^{4} + w^{3} + 14 w^{2} - 3 w - 6]$ | $\phantom{-}\frac{1}{4} e^{4} + \frac{3}{4} e^{3} - 5 e^{2} - \frac{23}{2} e + 12$ |
| 47 | $[47, 47, -3 w^{4} + 2 w^{3} + 14 w^{2} - 7 w - 6]$ | $-\frac{3}{8} e^{4} - \frac{3}{8} e^{3} + \frac{15}{2} e^{2} + \frac{9}{2} e - 10$ |
| 53 | $[53, 53, 2 w^{4} - w^{3} - 8 w^{2} + 2 w + 1]$ | $\phantom{-}\frac{1}{4} e^{4} + \frac{1}{4} e^{3} - 4 e^{2} - 3 e + 2$ |
| 53 | $[53, 53, -2 w^{4} + w^{3} + 10 w^{2} - 4 w - 6]$ | $\phantom{-}\frac{1}{4} e^{4} + \frac{1}{2} e^{3} - \frac{19}{4} e^{2} - 9 e + 11$ |
| 59 | $[59, 59, -w^{4} + 4 w^{2} + 1]$ | $-\frac{3}{4} e^{4} - \frac{5}{4} e^{3} + 14 e^{2} + \frac{41}{2} e - 22$ |
| 59 | $[59, 59, -3 w^{4} + 2 w^{3} + 14 w^{2} - 6 w - 8]$ | $-\frac{1}{4} e^{4} - \frac{1}{4} e^{3} + \frac{7}{2} e^{2} + \frac{7}{2} e + 4$ |
| 61 | $[61, 61, 4 w^{4} - 2 w^{3} - 18 w^{2} + 5 w + 7]$ | $\phantom{-}\frac{1}{4} e^{4} - \frac{17}{4} e^{2} + e + 8$ |
| 61 | $[61, 61, 3 w^{4} - w^{3} - 15 w^{2} + 2 w + 7]$ | $\phantom{-}\frac{1}{4} e^{4} - \frac{17}{4} e^{2} + e + 8$ |
| 73 | $[73, 73, -4 w^{4} + 2 w^{3} + 18 w^{2} - 7 w - 6]$ | $-\frac{1}{4} e^{4} - \frac{3}{4} e^{3} + \frac{9}{2} e^{2} + 12 e - 2$ |
| 83 | $[83, 83, -2 w^{4} + 9 w^{2} + 2 w - 4]$ | $\phantom{-}1$ |
| 83 | $[83, 83, -2 w^{4} + 2 w^{3} + 10 w^{2} - 7 w - 6]$ | $\phantom{-}\frac{1}{4} e^{4} + \frac{3}{4} e^{3} - \frac{9}{2} e^{2} - 13 e + 2$ |
| 97 | $[97, 97, -2 w^{4} + w^{3} + 8 w^{2} - 3 w + 1]$ | $\phantom{-}\frac{3}{8} e^{4} + \frac{7}{8} e^{3} - 7 e^{2} - \frac{31}{2} e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $83$ | $[83, 83, -2 w^{4} + 9 w^{2} + 2 w - 4]$ | $-1$ |