Base field \(\Q(\zeta_{11})^+\)
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[199,199,-2w^{4} + 2w^{3} + 7w^{2} - 3w - 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 46x^{2} - 66x + 431\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $\phantom{-}2$ |
| 23 | $[23, 23, -w^{4} + 3w^{2} + 1]$ | $-\frac{2}{71}e^{3} + \frac{46}{71}e^{2} + \frac{78}{71}e - \frac{966}{71}$ |
| 23 | $[23, 23, -w^{4} + 3w^{2} + w - 2]$ | $\phantom{-}e$ |
| 23 | $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ | $\phantom{-}\frac{4}{71}e^{3} - \frac{21}{71}e^{2} - \frac{156}{71}e + \frac{228}{71}$ |
| 23 | $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ | $-\frac{6}{71}e^{3} - \frac{4}{71}e^{2} + \frac{92}{71}e + \frac{84}{71}$ |
| 23 | $[23, 23, -w^{2} + w + 3]$ | $-\frac{5}{71}e^{3} + \frac{44}{71}e^{2} + \frac{124}{71}e - \frac{1066}{71}$ |
| 32 | $[32, 2, 2]$ | $\phantom{-}\frac{10}{71}e^{3} - \frac{17}{71}e^{2} - \frac{248}{71}e + \frac{712}{71}$ |
| 43 | $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ | $-\frac{8}{71}e^{3} + \frac{42}{71}e^{2} + \frac{170}{71}e - \frac{1166}{71}$ |
| 43 | $[43, 43, -w^{4} + 2w^{2} + w + 1]$ | $\phantom{-}\frac{8}{71}e^{3} - \frac{42}{71}e^{2} - \frac{241}{71}e + \frac{1308}{71}$ |
| 43 | $[43, 43, w^{3} + w^{2} - 4w - 2]$ | $-1$ |
| 43 | $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ | $-\frac{6}{71}e^{3} - \frac{4}{71}e^{2} + \frac{234}{71}e + \frac{226}{71}$ |
| 43 | $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ | $-\frac{14}{71}e^{3} + \frac{38}{71}e^{2} + \frac{404}{71}e - \frac{869}{71}$ |
| 67 | $[67, 67, 2w^{4} - 7w^{2} + 2]$ | $-\frac{16}{71}e^{3} + \frac{13}{71}e^{2} + \frac{482}{71}e - \frac{344}{71}$ |
| 67 | $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ | $-\frac{4}{71}e^{3} - \frac{50}{71}e^{2} + \frac{14}{71}e + \frac{1263}{71}$ |
| 67 | $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ | $\phantom{-}\frac{2}{71}e^{3} - \frac{46}{71}e^{2} - \frac{78}{71}e + \frac{1108}{71}$ |
| 67 | $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ | $\phantom{-}\frac{23}{71}e^{3} - \frac{32}{71}e^{2} - \frac{684}{71}e + \frac{814}{71}$ |
| 67 | $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}\frac{17}{71}e^{3} - \frac{36}{71}e^{2} - \frac{521}{71}e + \frac{1040}{71}$ |
| 89 | $[89, 89, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}\frac{2}{71}e^{3} - \frac{46}{71}e^{2} + \frac{64}{71}e + \frac{1037}{71}$ |
| 89 | $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ | $-\frac{20}{71}e^{3} + \frac{34}{71}e^{2} + \frac{638}{71}e - \frac{856}{71}$ |
| 89 | $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ | $\phantom{-}\frac{2}{71}e^{3} - \frac{46}{71}e^{2} - \frac{78}{71}e + \frac{1250}{71}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $199$ | $[199,199,-2w^{4} + 2w^{3} + 7w^{2} - 3w - 4]$ | $-1$ |