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: | $[85, 85, w^{4} - 5 w^{2} - 2 w + 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 4 x^{2} - 20 x + 24\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2 w^{4} + w^{3} + 9 w^{2} - 2 w - 3]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -2 w^{4} + w^{3} + 9 w^{2} - 3 w - 5]$ | $-1$ |
| 17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}e$ |
| 23 | $[23, 23, w^{3} - 3 w]$ | $\phantom{-}0$ |
| 29 | $[29, 29, 2 w^{4} - w^{3} - 10 w^{2} + 2 w + 4]$ | $\phantom{-}\frac{1}{2} e^{2} - 2 e - 6$ |
| 32 | $[32, 2, 2]$ | $-\frac{1}{2} e^{2} + e + 9$ |
| 37 | $[37, 37, -w^{4} + w^{3} + 4 w^{2} - 2 w]$ | $\phantom{-}2$ |
| 41 | $[41, 41, -3 w^{4} + 2 w^{3} + 14 w^{2} - 5 w - 7]$ | $\phantom{-}e$ |
| 43 | $[43, 43, -3 w^{4} + w^{3} + 14 w^{2} - 3 w - 6]$ | $-e + 2$ |
| 47 | $[47, 47, -3 w^{4} + 2 w^{3} + 14 w^{2} - 7 w - 6]$ | $\phantom{-}\frac{1}{2} e^{2} - e - 6$ |
| 53 | $[53, 53, 2 w^{4} - w^{3} - 8 w^{2} + 2 w + 1]$ | $-2 e + 6$ |
| 53 | $[53, 53, -2 w^{4} + w^{3} + 10 w^{2} - 4 w - 6]$ | $-e$ |
| 59 | $[59, 59, -w^{4} + 4 w^{2} + 1]$ | $-\frac{1}{2} e^{2} + 3 e + 6$ |
| 59 | $[59, 59, -3 w^{4} + 2 w^{3} + 14 w^{2} - 6 w - 8]$ | $\phantom{-}\frac{1}{2} e^{2} - 2 e - 12$ |
| 61 | $[61, 61, 4 w^{4} - 2 w^{3} - 18 w^{2} + 5 w + 7]$ | $-\frac{1}{2} e^{2} + e + 8$ |
| 61 | $[61, 61, 3 w^{4} - w^{3} - 15 w^{2} + 2 w + 7]$ | $\phantom{-}\frac{1}{2} e^{2} - 10$ |
| 73 | $[73, 73, -4 w^{4} + 2 w^{3} + 18 w^{2} - 7 w - 6]$ | $-2 e + 2$ |
| 83 | $[83, 83, -2 w^{4} + 9 w^{2} + 2 w - 4]$ | $-e^{2} + 4 e + 12$ |
| 83 | $[83, 83, -2 w^{4} + 2 w^{3} + 10 w^{2} - 7 w - 6]$ | $\phantom{-}2 e$ |
| 97 | $[97, 97, -2 w^{4} + w^{3} + 8 w^{2} - 3 w + 1]$ | $\phantom{-}2 e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -2 w^{4} + w^{3} + 9 w^{2} - 2 w - 3]$ | $-1$ |
| $17$ | $[17, 17, -2 w^{4} + w^{3} + 9 w^{2} - 3 w - 5]$ | $1$ |