Properties

Label 2.2.357.1-3.1-i
Base field \(\Q(\sqrt{357}) \)
Weight $[2, 2]$
Level norm $3$
Level $[3, 3, w + 1]$
Dimension $10$
CM no
Base change no

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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 $[61, 61, w + 16]$ $-\frac{21541}{28077064}e^{8} + \frac{373771}{7019266}e^{6} - \frac{31724689}{28077064}e^{4} + \frac{101665269}{14038532}e^{2} - \frac{27410957}{3509633}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $-1$