Base field 4.4.11344.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 4x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 17x^{8} + 93x^{6} - 175x^{4} + 98x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 7e$ |
| 5 | $[5, 5, -w + 2]$ | $-\frac{1}{4}e^{9} + 4e^{7} - \frac{81}{4}e^{5} + \frac{67}{2}e^{3} - 14e$ |
| 11 | $[11, 11, w + 2]$ | $-1$ |
| 27 | $[27, 3, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{1}{2}e^{9} + \frac{17}{2}e^{7} - \frac{91}{2}e^{5} + \frac{157}{2}e^{3} - 33e$ |
| 29 | $[29, 29, -w^{2} + 3w + 1]$ | $-\frac{1}{4}e^{9} + 4e^{7} - \frac{79}{4}e^{5} + 30e^{3} - 13e$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 2w + 2]$ | $-\frac{1}{4}e^{9} + \frac{9}{2}e^{7} - \frac{107}{4}e^{5} + \frac{115}{2}e^{3} - 36e$ |
| 31 | $[31, 31, -w^{2} + 2w + 4]$ | $-\frac{1}{2}e^{7} + 5e^{5} - \frac{23}{2}e^{3} + 7e$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w + 1]$ | $-\frac{1}{4}e^{8} + \frac{7}{2}e^{6} - \frac{63}{4}e^{4} + \frac{51}{2}e^{2} - 6$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 8w - 1]$ | $-\frac{1}{2}e^{9} + \frac{17}{2}e^{7} - \frac{93}{2}e^{5} + \frac{171}{2}e^{3} - 35e$ |
| 49 | $[49, 7, w^{3} - w^{2} - 3w - 2]$ | $\phantom{-}2e$ |
| 53 | $[53, 53, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}\frac{3}{2}e^{6} - \frac{31}{2}e^{4} + 35e^{2} - 6$ |
| 53 | $[53, 53, w^{3} - 5w - 5]$ | $-\frac{1}{2}e^{9} + \frac{17}{2}e^{7} - \frac{91}{2}e^{5} + \frac{157}{2}e^{3} - 35e$ |
| 61 | $[61, 61, 2w - 1]$ | $\phantom{-}e^{5} - 7e^{3} + 2e$ |
| 61 | $[61, 61, -w^{3} + 4w^{2} - 4]$ | $-\frac{1}{4}e^{8} + 5e^{6} - \frac{113}{4}e^{4} + \frac{81}{2}e^{2} - 8$ |
| 67 | $[67, 67, 3w^{3} - 3w^{2} - 13w - 4]$ | $-e^{9} + \frac{33}{2}e^{7} - \frac{171}{2}e^{5} + 141e^{3} - 56e$ |
| 73 | $[73, 73, -w^{3} + 4w^{2} - 10]$ | $\phantom{-}\frac{1}{2}e^{9} - \frac{17}{2}e^{7} + \frac{87}{2}e^{5} - \frac{121}{2}e^{3} + 9e$ |
| 73 | $[73, 73, w^{2} - w + 1]$ | $\phantom{-}\frac{1}{2}e^{8} - 8e^{6} + \frac{77}{2}e^{4} - 49e^{2} + 2$ |
| 83 | $[83, 83, -4w^{3} + 5w^{2} + 17w + 1]$ | $\phantom{-}\frac{3}{2}e^{6} - \frac{31}{2}e^{4} + 37e^{2} - 8$ |
| 83 | $[83, 83, 3w^{3} - 3w^{2} - 14w - 5]$ | $\phantom{-}\frac{1}{4}e^{8} - \frac{3}{2}e^{6} - \frac{17}{4}e^{4} + \frac{37}{2}e^{2} - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w + 2]$ | $1$ |