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: | $[11, 11, w^{2} - w - 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 7x^{2} + 8x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w + 1]$ | $-e$ |
| 11 | $[11, 11, w^{2} - w - 2]$ | $-1$ |
| 17 | $[17, 17, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 3w - 3]$ | $-e^{3} + 4e^{2} + e - 6$ |
| 27 | $[27, 3, w^{5} - w^{4} - 5w^{3} + w^{2} + 6w + 1]$ | $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{7}{2}e - 4$ |
| 27 | $[27, 3, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-2e^{3} + 8e^{2} + 6e - 16$ |
| 37 | $[37, 37, -w^{2} + 2w + 2]$ | $\phantom{-}e^{3} - 5e^{2} - e + 10$ |
| 47 | $[47, 47, -w^{5} + 2w^{4} + 3w^{3} - 3w^{2} - 2w - 1]$ | $-2e^{3} + 8e^{2} + 3e - 18$ |
| 53 | $[53, 53, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} + 3]$ | $-e^{3} + 7e^{2} - 5e - 18$ |
| 59 | $[59, 59, w^{4} - 2w^{3} - 2w^{2} + 3w - 2]$ | $\phantom{-}e^{3} - 6e^{2} + 5e + 18$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{13}{2}e^{2} + \frac{3}{2}e + 16$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 3w^{3} + 4w^{2} + w - 2]$ | $-2e^{3} + 9e^{2} + 2e - 23$ |
| 67 | $[67, 67, -w^{5} + 3w^{4} + w^{3} - 7w^{2} + 3w + 2]$ | $\phantom{-}3e^{3} - 11e^{2} - 6e + 19$ |
| 71 | $[71, 71, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $\phantom{-}2e^{3} - 7e^{2} - 6e + 18$ |
| 71 | $[71, 71, w^{4} - w^{3} - 5w^{2} + 2w + 4]$ | $-e^{3} + 7e^{2} - 5e - 18$ |
| 73 | $[73, 73, 2w^{5} - 4w^{4} - 7w^{3} + 10w^{2} + 5w - 3]$ | $\phantom{-}2e^{3} - 8e^{2} - 5e + 19$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 5w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{7}{2}e^{2} - \frac{3}{2}e + 18$ |
| 83 | $[83, 83, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 3]$ | $\phantom{-}e^{3} - 7e^{2} + 3e + 24$ |
| 89 | $[89, 89, -w^{5} + w^{4} + 6w^{3} - 2w^{2} - 8w + 1]$ | $-\frac{3}{2}e^{3} + \frac{13}{2}e^{2} + \frac{1}{2}e - 12$ |
| 97 | $[97, 97, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 7w]$ | $\phantom{-}2e^{2} - 8e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w^{2} - w - 2]$ | $1$ |