Base field 3.3.1524.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + 2w + 4]$ |
| Dimension: | $24$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $38$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{24} + x^{23} - 41x^{22} - 37x^{21} + 732x^{20} + 591x^{19} - 7471x^{18} - 5345x^{17} + 48105x^{16} + 30136x^{15} - 203446x^{14} - 109742x^{13} + 570608x^{12} + 258072x^{11} - 1047721x^{10} - 379546x^{9} + 1215918x^{8} + 324663x^{7} - 836387x^{6} - 140861x^{5} + 302718x^{4} + 23865x^{3} - 43734x^{2} - 1413x + 1134\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 3w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{2} - w + 3]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 7 | $[7, 7, 2w^{2} - 6w - 1]$ | $...$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{2} + 4w - 2]$ | $...$ |
| 19 | $[19, 19, w^{2} - 6]$ | $...$ |
| 19 | $[19, 19, -w^{2} - 3w - 1]$ | $...$ |
| 19 | $[19, 19, 3w^{2} - 9w - 1]$ | $...$ |
| 41 | $[41, 41, w^{2} - 8]$ | $...$ |
| 43 | $[43, 43, -2w^{2} - 3w + 4]$ | $...$ |
| 47 | $[47, 47, -2w - 3]$ | $...$ |
| 49 | $[49, 7, -9w^{2} + 29w - 3]$ | $...$ |
| 67 | $[67, 67, 2w - 3]$ | $...$ |
| 71 | $[71, 71, 4w^{2} - 14w + 5]$ | $...$ |
| 79 | $[79, 79, w^{2} - 3w - 3]$ | $...$ |
| 79 | $[79, 79, -w^{2} + 5w - 5]$ | $...$ |
| 79 | $[79, 79, 6w^{2} - 3w - 38]$ | $...$ |
| 97 | $[97, 97, 3w^{2} - 10w]$ | $...$ |
| 103 | $[103, 103, 3w^{2} - 4w - 24]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + 2w + 4]$ | $-1$ |