Base field 4.4.17600.1
Generator \(w\), with minimal polynomial \(x^{4} - 14x^{2} + 44\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 41x^{6} + 591x^{4} - 3440x^{2} + 6400\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ | $-\frac{7}{320}e^{7} + \frac{207}{320}e^{5} - \frac{1817}{320}e^{3} + \frac{27}{2}e$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ | $-1$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $\phantom{-}\frac{1}{80}e^{7} - \frac{21}{80}e^{5} + \frac{91}{80}e^{3} + \frac{3}{4}e$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ | $\phantom{-}\frac{9}{320}e^{7} - \frac{209}{320}e^{5} + \frac{1319}{320}e^{3} - \frac{29}{4}e$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ | $-e^{2} + 10$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{25}{16}e^{4} + \frac{191}{16}e^{2} - 30$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ | $-\frac{3}{80}e^{7} + \frac{83}{80}e^{5} - \frac{693}{80}e^{3} + \frac{45}{2}e$ |
| 25 | $[25, 5, \frac{1}{2}w^{2} - 1]$ | $\phantom{-}\frac{1}{16}e^{6} - \frac{25}{16}e^{4} + \frac{175}{16}e^{2} - 19$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ | $-\frac{7}{160}e^{7} + \frac{207}{160}e^{5} - \frac{1817}{160}e^{3} + 26e$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ | $-\frac{9}{160}e^{7} + \frac{249}{160}e^{5} - \frac{1999}{160}e^{3} + \frac{105}{4}e$ |
| 31 | $[31, 31, -w - 1]$ | $-\frac{13}{160}e^{7} + \frac{373}{160}e^{5} - \frac{3203}{160}e^{3} + \frac{95}{2}e$ |
| 31 | $[31, 31, w - 1]$ | $-\frac{13}{320}e^{7} + \frac{373}{320}e^{5} - \frac{3043}{320}e^{3} + \frac{73}{4}e$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ | $\phantom{-}\frac{1}{320}e^{7} - \frac{41}{320}e^{5} + \frac{591}{320}e^{3} - \frac{31}{4}e$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ | $-\frac{1}{40}e^{7} + \frac{31}{40}e^{5} - \frac{301}{40}e^{3} + \frac{85}{4}e$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ | $\phantom{-}\frac{1}{32}e^{7} - \frac{25}{32}e^{5} + \frac{191}{32}e^{3} - 16e$ |
| 49 | $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ | $-\frac{3}{40}e^{7} + \frac{83}{40}e^{5} - \frac{693}{40}e^{3} + 43e$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ | $\phantom{-}\frac{1}{8}e^{6} - \frac{25}{8}e^{4} + \frac{167}{8}e^{2} - 30$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ | $\phantom{-}\frac{3}{16}e^{6} - \frac{75}{16}e^{4} + \frac{541}{16}e^{2} - 70$ |
| 61 | $[61, 61, \frac{1}{2}w^{2} + w - 6]$ | $\phantom{-}\frac{5}{16}e^{6} - \frac{141}{16}e^{4} + \frac{1195}{16}e^{2} - 177$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ | $1$ |