Base field 4.4.10309.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 8x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25,5,w^{3} + w^{2} - 5w - 1]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 8x^{8} - 8x^{7} - 187x^{6} - 269x^{5} + 759x^{4} + 1333x^{3} - 1034x^{2} - 1212x + 747\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, w^{3} - 5w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 5w + 2]$ | $...$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{630845}{27565779}e^{8} - \frac{4813717}{27565779}e^{7} + \frac{5770441}{27565779}e^{6} + \frac{108127904}{27565779}e^{5} + \frac{143786632}{27565779}e^{4} - \frac{118649196}{9188593}e^{3} - \frac{586918364}{27565779}e^{2} + \frac{243515152}{27565779}e + \frac{99143464}{9188593}$ |
| 13 | $[13, 13, w^{3} - 6w + 4]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, w^{2} + w - 2]$ | $...$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $...$ |
| 23 | $[23, 23, w^{3} - w^{2} - 6w + 6]$ | $...$ |
| 23 | $[23, 23, w^{3} + w^{2} - 4w - 1]$ | $...$ |
| 25 | $[25, 5, -w^{2} + 3]$ | $...$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 5w + 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^{2} - 2w + 3]$ | $\phantom{-}\frac{323048}{27565779}e^{8} + \frac{2442367}{27565779}e^{7} - \frac{2688991}{27565779}e^{6} - \frac{52907012}{27565779}e^{5} - \frac{79700656}{27565779}e^{4} + \frac{44068070}{9188593}e^{3} + \frac{328324511}{27565779}e^{2} + \frac{109447256}{27565779}e - \frac{97106767}{9188593}$ |
| 29 | $[29, 29, -w^{3} + w^{2} + 7w - 7]$ | $...$ |
| 43 | $[43, 43, 2w^{3} + w^{2} - 10w + 3]$ | $-\frac{5432691}{174583267}e^{8} - \frac{36575614}{174583267}e^{7} + \frac{72619091}{174583267}e^{6} + \frac{815365004}{174583267}e^{5} + \frac{721281808}{174583267}e^{4} - \frac{132654783}{9188593}e^{3} - \frac{3276250775}{174583267}e^{2} + \frac{165114321}{174583267}e + \frac{2022149679}{174583267}$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 5w - 7]$ | $...$ |
| 53 | $[53, 53, w^{3} - w^{2} - 7w + 5]$ | $...$ |
| 53 | $[53, 53, w^{2} + 2w - 5]$ | $...$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 10w]$ | $...$ |
| 61 | $[61, 61, w^{3} - 7w + 3]$ | $...$ |
| 61 | $[61, 61, 2w^{3} + w^{2} - 9w + 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25,5,w^{3} + w^{2} - 5w - 1]$ | $-1$ |