Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[3, 3, w + 1]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 92x^{8} + 2906x^{6} - 35776x^{4} + 136605x^{2} - 19612\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
4 | $[4, 2, 2]$ | $-\frac{3567}{56154128}e^{8} + \frac{280973}{56154128}e^{6} - \frac{7939361}{56154128}e^{4} + \frac{87766583}{56154128}e^{2} - \frac{57439469}{14038532}$ |
7 | $[7, 7, w + 3]$ | $-\frac{1799}{56154128}e^{8} - \frac{19655}{56154128}e^{6} + \frac{5000631}{56154128}e^{4} - \frac{86836405}{56154128}e^{2} + \frac{50523315}{14038532}$ |
11 | $[11, 11, w + 3]$ | $\phantom{-}e$ |
11 | $[11, 11, w + 7]$ | $-e$ |
17 | $[17, 17, w + 8]$ | $\phantom{-}0$ |
23 | $[23, 23, w + 4]$ | $-\frac{8119}{56154128}e^{9} + \frac{800897}{56154128}e^{7} - \frac{26391121}{56154128}e^{5} + \frac{321967835}{56154128}e^{3} - \frac{275632073}{14038532}e$ |
23 | $[23, 23, w + 18]$ | $\phantom{-}\frac{8119}{56154128}e^{9} - \frac{800897}{56154128}e^{7} + \frac{26391121}{56154128}e^{5} - \frac{321967835}{56154128}e^{3} + \frac{275632073}{14038532}e$ |
25 | $[25, 5, 5]$ | $-\frac{749}{3303184}e^{8} + \frac{40015}{3303184}e^{6} - \frac{527155}{3303184}e^{4} + \frac{1958253}{3303184}e^{2} - \frac{7925699}{825796}$ |
29 | $[29, 29, w + 1]$ | $\phantom{-}\frac{8119}{56154128}e^{9} - \frac{800897}{56154128}e^{7} + \frac{26391121}{56154128}e^{5} - \frac{321967835}{56154128}e^{3} + \frac{261593541}{14038532}e$ |
29 | $[29, 29, w + 27]$ | $-\frac{8119}{56154128}e^{9} + \frac{800897}{56154128}e^{7} - \frac{26391121}{56154128}e^{5} + \frac{321967835}{56154128}e^{3} - \frac{261593541}{14038532}e$ |
31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{3493}{7019266}e^{8} - \frac{898873}{28077064}e^{6} + \frac{8808489}{14038532}e^{4} - \frac{108858193}{28077064}e^{2} - \frac{5771661}{7019266}$ |
31 | $[31, 31, w + 17]$ | $\phantom{-}\frac{3493}{7019266}e^{8} - \frac{898873}{28077064}e^{6} + \frac{8808489}{14038532}e^{4} - \frac{108858193}{28077064}e^{2} - \frac{5771661}{7019266}$ |
43 | $[43, 43, -w - 11]$ | $-\frac{18503}{28077064}e^{8} + \frac{1296121}{28077064}e^{6} - \frac{28069977}{28077064}e^{4} + \frac{186521987}{28077064}e^{2} - \frac{21237261}{7019266}$ |
43 | $[43, 43, w - 12]$ | $-\frac{18503}{28077064}e^{8} + \frac{1296121}{28077064}e^{6} - \frac{28069977}{28077064}e^{4} + \frac{186521987}{28077064}e^{2} - \frac{21237261}{7019266}$ |
47 | $[47, 47, -w - 6]$ | $-\frac{939}{3303184}e^{9} + \frac{88203}{3303184}e^{7} - \frac{2743561}{3303184}e^{5} + \frac{31187525}{3303184}e^{3} - \frac{24863947}{825796}e$ |
47 | $[47, 47, w - 7]$ | $\phantom{-}\frac{939}{3303184}e^{9} - \frac{88203}{3303184}e^{7} + \frac{2743561}{3303184}e^{5} - \frac{31187525}{3303184}e^{3} + \frac{24863947}{825796}e$ |
59 | $[59, 59, -w - 5]$ | $\phantom{-}\frac{8881}{28077064}e^{9} - \frac{369949}{14038532}e^{7} + \frac{20819953}{28077064}e^{5} - \frac{27709470}{3509633}e^{3} + \frac{79002414}{3509633}e$ |
59 | $[59, 59, w - 6]$ | $-\frac{8881}{28077064}e^{9} + \frac{369949}{14038532}e^{7} - \frac{20819953}{28077064}e^{5} + \frac{27709470}{3509633}e^{3} - \frac{79002414}{3509633}e$ |
61 | $[61, 61, w + 16]$ | $-\frac{21541}{28077064}e^{8} + \frac{373771}{7019266}e^{6} - \frac{31724689}{28077064}e^{4} + \frac{101665269}{14038532}e^{2} - \frac{27410957}{3509633}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $-1$ |