Base field 5.5.149169.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} - 3x^{2} + 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[21, 21, w^{3} - 5w - 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 5x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 4w^{2} + 1]$ | $-1$ |
| 7 | $[7, 7, w^{4} - w^{3} - 5w^{2} + w + 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{4} + 5w^{2} + 3w + 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, w^{4} - w^{3} - 4w^{2} + w - 1]$ | $\phantom{-}e - 3$ |
| 19 | $[19, 19, w^{4} - 6w^{2} - 2w + 3]$ | $\phantom{-}4$ |
| 19 | $[19, 19, -w^{2} + w + 2]$ | $-6$ |
| 27 | $[27, 3, -w^{3} + w^{2} + 3w - 1]$ | $-e + 6$ |
| 29 | $[29, 29, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $\phantom{-}e - 3$ |
| 29 | $[29, 29, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}e - 5$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}3$ |
| 37 | $[37, 37, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $\phantom{-}2e - 5$ |
| 41 | $[41, 41, w^{4} - w^{3} - 4w^{2} - 1]$ | $\phantom{-}2e - 5$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ | $-2$ |
| 67 | $[67, 67, w^{3} - 2w^{2} - 3w]$ | $\phantom{-}4e - 10$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 3w - 5]$ | $\phantom{-}4e - 8$ |
| 97 | $[97, 97, -w^{4} + 2w^{3} + 3w^{2} - 6w + 1]$ | $\phantom{-}2e - 3$ |
| 107 | $[107, 107, w^{3} - 2w^{2} - 4w + 1]$ | $\phantom{-}2e + 6$ |
| 109 | $[109, 109, -w^{4} + 6w^{2} + 3w - 1]$ | $\phantom{-}2e - 5$ |
| 121 | $[121, 11, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $\phantom{-}5e - 13$ |
| 121 | $[121, 11, -2w^{4} + w^{3} + 11w^{2} - 5]$ | $\phantom{-}3e - 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{4} - w^{3} - 4w^{2} + 1]$ | $1$ |
| $7$ | $[7, 7, w^{4} - w^{3} - 5w^{2} + w + 3]$ | $-1$ |