Base field 5.5.157457.1
Generator \(w\), with minimal polynomial \(x^{5} - 2x^{4} - 4x^{3} + 5x^{2} + 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[27, 27, w^{3} - 2w^{2} - 2w + 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 12x^{3} + 9x^{2} + 33x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{4} - 2w^{3} - 3w^{2} + 4w + 2]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{2}{3}e^{3} - 2e^{2} - 5e$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}\frac{1}{3}e^{4} - \frac{1}{3}e^{3} - 3e^{2} + 2e + 6$ |
| 29 | $[29, 29, -w^{4} + 3w^{3} + 2w^{2} - 7w - 1]$ | $-e^{4} - e^{3} + 8e^{2} + 6e - 6$ |
| 29 | $[29, 29, -w^{2} + 2w + 3]$ | $-e^{4} - 2e^{3} + 8e^{2} + 13e - 3$ |
| 31 | $[31, 31, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{2}{3}e^{3} - e^{2} - 4e - 6$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 2]$ | $-\frac{2}{3}e^{4} - \frac{4}{3}e^{3} + 4e^{2} + 9e + 4$ |
| 32 | $[32, 2, 2]$ | $-e^{4} - e^{3} + 6e^{2} + 7e + 6$ |
| 43 | $[43, 43, -w^{2} - w + 4]$ | $\phantom{-}\frac{4}{3}e^{4} + \frac{5}{3}e^{3} - 10e^{2} - 12e + 6$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 6w^{2} - 2w - 5]$ | $\phantom{-}e^{4} + 2e^{3} - 9e^{2} - 13e + 12$ |
| 53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $\phantom{-}e^{4} - e^{3} - 9e^{2} + 5e + 12$ |
| 73 | $[73, 73, w^{4} - w^{3} - 6w^{2} + 2w + 6]$ | $-\frac{2}{3}e^{4} - \frac{7}{3}e^{3} + 4e^{2} + 18e + 9$ |
| 73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $-\frac{5}{3}e^{4} - \frac{4}{3}e^{3} + 14e^{2} + 10e - 9$ |
| 81 | $[81, 3, 2w^{4} - 5w^{3} - 4w^{2} + 9w + 2]$ | $-\frac{10}{3}e^{4} - \frac{14}{3}e^{3} + 27e^{2} + 31e - 22$ |
| 83 | $[83, 83, w^{3} - w^{2} - 5w]$ | $-e^{3} + 6e + 3$ |
| 89 | $[89, 89, -w^{4} + 2w^{3} + 4w^{2} - 4w - 2]$ | $-2e^{4} - 2e^{3} + 15e^{2} + 16e - 3$ |
| 97 | $[97, 97, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ | $\phantom{-}\frac{10}{3}e^{4} + \frac{8}{3}e^{3} - 25e^{2} - 18e + 12$ |
| 101 | $[101, 101, -w^{4} + 3w^{3} + 3w^{2} - 7w - 3]$ | $-e^{4} + e^{3} + 8e^{2} - 6e - 9$ |
| 103 | $[103, 103, -w^{4} + w^{3} + 6w^{2} - w - 7]$ | $\phantom{-}\frac{10}{3}e^{4} + \frac{14}{3}e^{3} - 27e^{2} - 31e + 19$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $-1$ |