Base field 4.4.19664.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[10, 10, w + 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 18x^{8} + 113x^{6} - 292x^{4} + 268x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}\frac{1}{4}e^{9} - 4e^{7} + \frac{81}{4}e^{5} - \frac{67}{2}e^{3} + 9e$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{8} + 8e^{6} - \frac{79}{2}e^{4} + 58e^{2}$ |
| 29 | $[29, 29, 2w^{3} - 5w^{2} - 7w + 9]$ | $-e^{4} + 7e^{2} - 4$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $-\frac{1}{4}e^{9} + 4e^{7} - \frac{81}{4}e^{5} + \frac{65}{2}e^{3} - 4e$ |
| 41 | $[41, 41, -w^{3} + 4w^{2} - w - 3]$ | $-e^{8} + 15e^{6} - 69e^{4} + 93e^{2} + 4$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $-\frac{1}{4}e^{9} + 3e^{7} - \frac{25}{4}e^{5} - \frac{51}{2}e^{3} + 65e$ |
| 47 | $[47, 47, w^{2} - 3w - 3]$ | $\phantom{-}\frac{1}{2}e^{9} - 8e^{7} + \frac{85}{2}e^{5} - 86e^{3} + 55e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}e^{8} - 15e^{6} + 69e^{4} - 95e^{2} + 6$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $-\frac{1}{4}e^{9} + 4e^{7} - \frac{85}{4}e^{5} + \frac{87}{2}e^{3} - 30e$ |
| 61 | $[61, 61, 5w^{3} - 12w^{2} - 19w + 17]$ | $\phantom{-}\frac{1}{2}e^{8} - 8e^{6} + \frac{81}{2}e^{4} - 63e^{2} + 4$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 7w + 5]$ | $\phantom{-}\frac{1}{2}e^{9} - 7e^{7} + \frac{53}{2}e^{5} - 8e^{3} - 56e$ |
| 67 | $[67, 67, w^{3} - 4w^{2} + w + 5]$ | $\phantom{-}e^{7} - 15e^{5} + 68e^{3} - 86e$ |
| 67 | $[67, 67, 3w^{3} - 7w^{2} - 12w + 11]$ | $\phantom{-}\frac{1}{4}e^{9} - 4e^{7} + \frac{85}{4}e^{5} - \frac{83}{2}e^{3} + 20e$ |
| 67 | $[67, 67, -2w^{3} + 4w^{2} + 8w - 5]$ | $-e^{5} + 10e^{3} - 21e$ |
| 71 | $[71, 71, -3w^{3} + 8w^{2} + 9w - 9]$ | $-\frac{3}{4}e^{9} + 12e^{7} - \frac{251}{4}e^{5} + \frac{243}{2}e^{3} - 74e$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $-\frac{1}{4}e^{9} + 4e^{7} - \frac{81}{4}e^{5} + \frac{63}{2}e^{3} + e$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 14w + 15]$ | $-\frac{3}{4}e^{9} + 12e^{7} - \frac{243}{4}e^{5} + \frac{201}{2}e^{3} - 27e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $5$ | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $-1$ |