Base field 6.6.1541581.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 2x^{3} + 9x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - x^{2} + 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ | $-2e^{3} + 6e^{2} + 2e - 6$ |
| 11 | $[11, 11, w^{2} - w - 2]$ | $\phantom{-}3e^{3} - 11e^{2} + 3e + 6$ |
| 17 | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $\phantom{-}3e^{3} - 10e^{2} + 3e + 6$ |
| 27 | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ | $-2e^{3} + 3e^{2} + 7e - 5$ |
| 27 | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}e^{3} - 4e^{2} + 2e - 1$ |
| 37 | $[37, 37, -w^{2} + 2w + 2]$ | $-4e^{3} + 17e^{2} - 8e - 12$ |
| 47 | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ | $\phantom{-}e^{3} - 3e^{2} - 4e + 2$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ | $\phantom{-}1$ |
| 59 | $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ | $-6e^{3} + 16e^{2} + 6e - 13$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}e^{3} + e^{2} - 10e + 1$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}5e^{3} - 16e^{2} + 4$ |
| 67 | $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ | $\phantom{-}9e^{3} - 31e^{2} + 6e + 19$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-5e^{3} + 14e^{2} + e + 1$ |
| 71 | $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $\phantom{-}e^{3} + 2e^{2} - 8e - 9$ |
| 73 | $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ | $\phantom{-}e^{3} - e^{2} - 4e - 1$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ | $\phantom{-}8e^{3} - 26e^{2} + 3e + 17$ |
| 83 | $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ | $-6e^{3} + 18e^{2} + 4e - 6$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ | $\phantom{-}7e^{3} - 23e^{2} + 16$ |
| 97 | $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ | $-2e^{3} + 3e^{2} + 4e - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $53$ | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ | $-1$ |