Base field 4.4.16997.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 25, -w^{3} + 5w + 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $39$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 19x^{6} + 84x^{4} - 116x^{2} + 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{3}{17}e^{6} - \frac{49}{17}e^{4} + \frac{127}{17}e^{2} - \frac{49}{17}$ |
| 5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $-\frac{3}{34}e^{6} + \frac{49}{34}e^{4} - \frac{72}{17}e^{2} + \frac{67}{17}$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $\phantom{-}\frac{23}{102}e^{7} - \frac{202}{51}e^{5} + \frac{453}{34}e^{3} - \frac{389}{51}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{4}{51}e^{7} + \frac{125}{102}e^{5} - \frac{77}{34}e^{3} - \frac{133}{51}e$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $-\frac{5}{102}e^{7} + \frac{59}{102}e^{5} + \frac{28}{17}e^{3} - \frac{421}{51}e$ |
| 23 | $[23, 23, -w^{3} + 4w + 2]$ | $-\frac{4}{17}e^{6} + \frac{71}{17}e^{4} - \frac{243}{17}e^{2} + \frac{88}{17}$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 3w - 1]$ | $-\frac{2}{17}e^{7} + \frac{71}{34}e^{5} - \frac{243}{34}e^{3} + \frac{44}{17}e$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{17}e^{6} - \frac{22}{17}e^{4} + \frac{116}{17}e^{2} - \frac{124}{17}$ |
| 29 | $[29, 29, -w + 3]$ | $-\frac{3}{34}e^{6} + \frac{49}{34}e^{4} - \frac{55}{17}e^{2} - \frac{69}{17}$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}\frac{3}{34}e^{7} - \frac{49}{34}e^{5} + \frac{55}{17}e^{3} + \frac{35}{17}e$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $-\frac{8}{51}e^{7} + \frac{301}{102}e^{5} - \frac{443}{34}e^{3} + \frac{1009}{51}e$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $-\frac{7}{34}e^{6} + \frac{137}{34}e^{4} - \frac{321}{17}e^{2} + \frac{281}{17}$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 4w - 6]$ | $-\frac{49}{102}e^{7} + \frac{437}{51}e^{5} - \frac{1039}{34}e^{3} + \frac{1168}{51}e$ |
| 59 | $[59, 59, w^{2} + w - 4]$ | $\phantom{-}\frac{2}{51}e^{7} - \frac{44}{51}e^{5} + \frac{83}{17}e^{3} - \frac{367}{51}e$ |
| 61 | $[61, 61, -2w^{2} + w + 8]$ | $-\frac{67}{102}e^{7} + \frac{1219}{102}e^{5} - \frac{774}{17}e^{3} + \frac{1978}{51}e$ |
| 73 | $[73, 73, -w^{3} + 5w - 1]$ | $\phantom{-}\frac{13}{17}e^{7} - \frac{453}{34}e^{5} + \frac{1503}{34}e^{3} - \frac{609}{17}e$ |
| 79 | $[79, 79, 2w^{2} + w - 6]$ | $-\frac{8}{17}e^{6} + \frac{142}{17}e^{4} - \frac{486}{17}e^{2} + \frac{244}{17}$ |
| 79 | $[79, 79, 2w^{3} - w^{2} - 9w + 3]$ | $-\frac{1}{34}e^{6} + \frac{5}{34}e^{4} + \frac{78}{17}e^{2} - \frac{278}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^{2} + w + 2]$ | $-1$ |