Base field 3.3.1556.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -2w + 3]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} + 2x^{19} - 29x^{18} - 54x^{17} + 351x^{16} + 602x^{15} - 2301x^{14} - 3600x^{13} + 8866x^{12} + 12564x^{11} - 20352x^{10} - 26080x^{9} + 26748x^{8} + 31392x^{7} - 17864x^{6} - 20264x^{5} + 4336x^{4} + 5856x^{3} + 96x^{2} - 512x - 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 2]$ | $...$ |
| 9 | $[9, 3, w^{2} + w - 7]$ | $...$ |
| 11 | $[11, 11, w]$ | $...$ |
| 11 | $[11, 11, -2w + 3]$ | $-1$ |
| 11 | $[11, 11, -w^{2} + 3w - 1]$ | $...$ |
| 17 | $[17, 17, w + 2]$ | $...$ |
| 17 | $[17, 17, -2w + 5]$ | $...$ |
| 17 | $[17, 17, -w^{2} - w + 5]$ | $...$ |
| 23 | $[23, 23, w - 4]$ | $...$ |
| 29 | $[29, 29, w^{2} - 6]$ | $...$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $...$ |
| 37 | $[37, 37, -w^{2} - 2w + 6]$ | $...$ |
| 43 | $[43, 43, w^{2} - 3w + 3]$ | $...$ |
| 47 | $[47, 47, 3w^{2} - 28]$ | $...$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $...$ |
| 61 | $[61, 61, -5w + 6]$ | $...$ |
| 71 | $[71, 71, w^{2} - w - 7]$ | $...$ |
| 83 | $[83, 83, -2w^{2} - w + 14]$ | $...$ |
| 89 | $[89, 89, w^{2} + 3w - 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -2w + 3]$ | $1$ |