Base field \(\Q(\sqrt{71}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 71\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, -14w + 118]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 57x^{8} + 1120x^{6} - 8848x^{4} + 23232x^{2} - 8192\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -7w + 59]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -2w - 17]$ | $\phantom{-}\frac{57}{51776}e^{8} - \frac{2293}{51776}e^{6} + \frac{5721}{12944}e^{4} - \frac{1359}{3236}e^{2} - \frac{506}{809}$ |
| 5 | $[5, 5, 2w - 17]$ | $\phantom{-}\frac{57}{51776}e^{8} - \frac{2293}{51776}e^{6} + \frac{5721}{12944}e^{4} - \frac{1359}{3236}e^{2} - \frac{506}{809}$ |
| 7 | $[7, 7, -w - 8]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 8]$ | $-e$ |
| 9 | $[9, 3, 3]$ | $-\frac{5}{51776}e^{8} + \frac{485}{51776}e^{6} - \frac{1507}{6472}e^{4} + \frac{1552}{809}e^{2} - \frac{4838}{809}$ |
| 11 | $[11, 11, -5w - 42]$ | $-\frac{135}{207104}e^{9} + \frac{6623}{207104}e^{7} - \frac{6187}{12944}e^{5} + \frac{27659}{12944}e^{3} - \frac{377}{3236}e$ |
| 11 | $[11, 11, -5w + 42]$ | $\phantom{-}\frac{135}{207104}e^{9} - \frac{6623}{207104}e^{7} + \frac{6187}{12944}e^{5} - \frac{27659}{12944}e^{3} + \frac{377}{3236}e$ |
| 23 | $[23, 23, -12w + 101]$ | $-\frac{23}{103552}e^{9} + \frac{2231}{103552}e^{7} - \frac{7903}{12944}e^{5} + \frac{38103}{6472}e^{3} - \frac{22093}{1618}e$ |
| 23 | $[23, 23, 47w - 396]$ | $\phantom{-}\frac{23}{103552}e^{9} - \frac{2231}{103552}e^{7} + \frac{7903}{12944}e^{5} - \frac{38103}{6472}e^{3} + \frac{22093}{1618}e$ |
| 29 | $[29, 29, -w - 10]$ | $\phantom{-}\frac{61}{51776}e^{8} - \frac{2681}{51776}e^{6} + \frac{7485}{12944}e^{4} - \frac{493}{1618}e^{2} - \frac{4402}{809}$ |
| 29 | $[29, 29, w - 10]$ | $\phantom{-}\frac{61}{51776}e^{8} - \frac{2681}{51776}e^{6} + \frac{7485}{12944}e^{4} - \frac{493}{1618}e^{2} - \frac{4402}{809}$ |
| 31 | $[31, 31, -19w + 160]$ | $\phantom{-}\frac{75}{51776}e^{9} - \frac{4039}{51776}e^{7} + \frac{18513}{12944}e^{5} - \frac{16627}{1618}e^{3} + \frac{16749}{809}e$ |
| 31 | $[31, 31, 40w - 337]$ | $-\frac{75}{51776}e^{9} + \frac{4039}{51776}e^{7} - \frac{18513}{12944}e^{5} + \frac{16627}{1618}e^{3} - \frac{16749}{809}e$ |
| 37 | $[37, 37, -3w + 26]$ | $-\frac{5}{51776}e^{8} + \frac{485}{51776}e^{6} - \frac{1507}{6472}e^{4} + \frac{743}{809}e^{2} + \frac{4870}{809}$ |
| 37 | $[37, 37, 3w + 26]$ | $-\frac{5}{51776}e^{8} + \frac{485}{51776}e^{6} - \frac{1507}{6472}e^{4} + \frac{743}{809}e^{2} + \frac{4870}{809}$ |
| 47 | $[47, 47, 4w + 33]$ | $-\frac{149}{103552}e^{9} + \frac{7981}{103552}e^{7} - \frac{1118}{809}e^{5} + \frac{59927}{6472}e^{3} - \frac{23955}{1618}e$ |
| 47 | $[47, 47, -4w + 33]$ | $\phantom{-}\frac{149}{103552}e^{9} - \frac{7981}{103552}e^{7} + \frac{1118}{809}e^{5} - \frac{59927}{6472}e^{3} + \frac{23955}{1618}e$ |
| 59 | $[59, 59, 2w - 15]$ | $-\frac{141}{207104}e^{9} + \frac{7205}{207104}e^{7} - \frac{4031}{6472}e^{5} + \frac{67145}{12944}e^{3} - \frac{64107}{3236}e$ |
| 59 | $[59, 59, -2w - 15]$ | $\phantom{-}\frac{141}{207104}e^{9} - \frac{7205}{207104}e^{7} + \frac{4031}{6472}e^{5} - \frac{67145}{12944}e^{3} + \frac{64107}{3236}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -7w + 59]$ | $1$ |