Base field 5.5.70601.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[47, 47, w^{3} - w^{2} - 4w - 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 8x^{2} - 2x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{4} - 6w^{2} - 2w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{4} + w^{3} + 5w^{2} - w - 4]$ | $\phantom{-}e + 2$ |
| 11 | $[11, 11, -2w^{4} + w^{3} + 10w^{2} + w - 3]$ | $\phantom{-}e + 4$ |
| 11 | $[11, 11, w^{4} - 6w^{2} - 3w + 3]$ | $-\frac{1}{2}e^{3} - 3e^{2} - e + 8$ |
| 17 | $[17, 17, w^{2} - 2]$ | $\phantom{-}2e + 2$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w]$ | $-e^{3} - 3e^{2} + 4e + 6$ |
| 27 | $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w - 1]$ | $\phantom{-}\frac{3}{2}e^{3} + 4e^{2} - 9e - 4$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 3]$ | $\phantom{-}\frac{5}{2}e^{3} + 7e^{2} - 10e - 8$ |
| 32 | $[32, 2, -2]$ | $\phantom{-}2e^{3} + 7e^{2} - 6e - 11$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{3}{2}e^{3} - 6e^{2} + 4e + 18$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $\phantom{-}1$ |
| 53 | $[53, 53, -w^{4} + 7w^{2} - 3]$ | $-\frac{3}{2}e^{3} - 6e^{2} + 5e + 16$ |
| 53 | $[53, 53, 2w^{4} - 2w^{3} - 9w^{2} + 2w + 2]$ | $-\frac{1}{2}e^{3} - 2e^{2} - 3e + 2$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 16w^{2} + 8]$ | $\phantom{-}\frac{1}{2}e^{3} + 4e^{2} + 2e - 14$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 3e + 2$ |
| 73 | $[73, 73, 2w^{4} - 12w^{2} - 4w + 5]$ | $-3e^{3} - 9e^{2} + 13e + 12$ |
| 83 | $[83, 83, w^{4} - 5w^{2} - 3w + 3]$ | $\phantom{-}3e^{3} + 8e^{2} - 14e - 12$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}2e^{3} + 8e^{2} - 5e - 18$ |
| 103 | $[103, 103, 2w^{3} - 3w^{2} - 7w + 3]$ | $-\frac{9}{2}e^{3} - 15e^{2} + 15e + 28$ |
| 109 | $[109, 109, -3w^{4} + 2w^{3} + 14w^{2} + w - 6]$ | $-2e^{3} - 5e^{2} + 10e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $47$ | $[47, 47, w^{3} - w^{2} - 4w - 1]$ | $-1$ |