Base field 5.5.65657.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 5x^{3} + 2x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 2x^{3} - 7x^{2} + 18x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - \frac{10}{3}e + 4$ |
| 19 | $[19, 19, w^{4} - 2w^{3} - 4w^{2} + 5w + 4]$ | $-2e^{3} + e^{2} + 15e - 16$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 1]$ | $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + \frac{10}{3}e - 10$ |
| 29 | $[29, 29, 2w^{4} - 3w^{3} - 8w^{2} + 7w + 4]$ | $\phantom{-}\frac{10}{3}e^{3} - \frac{8}{3}e^{2} - \frac{85}{3}e + 31$ |
| 32 | $[32, 2, 2]$ | $-\frac{11}{3}e^{3} + \frac{7}{3}e^{2} + \frac{83}{3}e - 29$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{2}{3}e^{3} + \frac{7}{3}e^{2} + \frac{17}{3}e - 16$ |
| 41 | $[41, 41, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 6]$ | $-\frac{5}{3}e^{3} + \frac{1}{3}e^{2} + \frac{35}{3}e - 9$ |
| 43 | $[43, 43, -2w^{4} + 3w^{3} + 8w^{2} - 8w - 6]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{4}{3}e^{2} - \frac{20}{3}e + 11$ |
| 47 | $[47, 47, w^{4} - 2w^{3} - 5w^{2} + 6w + 5]$ | $-3e^{3} + 21e - 15$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ | $-1$ |
| 61 | $[61, 61, w^{2} - 2w - 3]$ | $\phantom{-}e^{3} + e^{2} - 7e - 3$ |
| 67 | $[67, 67, w^{4} - w^{3} - 4w^{2} + 3w]$ | $-\frac{2}{3}e^{3} - \frac{8}{3}e^{2} - \frac{4}{3}e + 15$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 2w - 2]$ | $\phantom{-}\frac{16}{3}e^{3} - \frac{8}{3}e^{2} - \frac{109}{3}e + 35$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 5]$ | $\phantom{-}\frac{14}{3}e^{3} - \frac{4}{3}e^{2} - \frac{92}{3}e + 28$ |
| 71 | $[71, 71, w^{4} - 2w^{3} - 3w^{2} + 5w + 3]$ | $\phantom{-}3e^{3} + e^{2} - 23e + 13$ |
| 71 | $[71, 71, 2w^{4} - 2w^{3} - 8w^{2} + 5w + 4]$ | $-\frac{2}{3}e^{3} - \frac{8}{3}e^{2} + \frac{14}{3}e + 6$ |
| 73 | $[73, 73, -2w^{4} + 2w^{3} + 9w^{2} - 5w - 6]$ | $\phantom{-}\frac{10}{3}e^{3} + \frac{1}{3}e^{2} - \frac{67}{3}e + 14$ |
| 81 | $[81, 3, -2w^{4} + 3w^{3} + 10w^{2} - 9w - 10]$ | $\phantom{-}\frac{16}{3}e^{3} - \frac{8}{3}e^{2} - \frac{112}{3}e + 30$ |
| 97 | $[97, 97, -2w^{4} + 3w^{3} + 7w^{2} - 5w - 4]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e^{2} - \frac{10}{3}e + 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53, 53, -w^{4} + w^{3} + 4w^{2} - w - 4]$ | $1$ |