Base field 4.4.9792.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 2x + 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 38x^{6} + 455x^{4} - 1696x^{2} + 256\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ | $-\frac{1}{464}e^{6} + \frac{3}{232}e^{4} + \frac{201}{464}e^{2} - \frac{72}{29}$ |
7 | $[7, 7, w]$ | $\phantom{-}\frac{1}{1392}e^{6} - \frac{1}{232}e^{4} - \frac{665}{1392}e^{2} + \frac{188}{87}$ |
7 | $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ | $-\frac{11}{696}e^{6} + \frac{149}{348}e^{4} - \frac{655}{232}e^{2} + \frac{98}{87}$ |
9 | $[9, 3, w^{3} - 4w^{2} - w + 9]$ | $\phantom{-}e$ |
17 | $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ | $-\frac{91}{5568}e^{7} + \frac{1433}{2784}e^{5} - \frac{26717}{5568}e^{3} + \frac{1441}{116}e$ |
17 | $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ | $-\frac{7}{5568}e^{7} + \frac{253}{2784}e^{5} - \frac{2779}{1856}e^{3} + \frac{2135}{348}e$ |
17 | $[17, 17, -w + 2]$ | $\phantom{-}\frac{1}{2784}e^{7} - \frac{1}{464}e^{5} - \frac{665}{2784}e^{3} + \frac{94}{87}e$ |
23 | $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ | $\phantom{-}\frac{37}{2784}e^{7} - \frac{575}{1392}e^{5} + \frac{9731}{2784}e^{3} - \frac{165}{29}e$ |
23 | $[23, 23, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{59}{5568}e^{7} - \frac{1105}{2784}e^{5} + \frac{26653}{5568}e^{3} - \frac{545}{29}e$ |
31 | $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ | $\phantom{-}1$ |
31 | $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ | $-\frac{1}{1392}e^{6} + \frac{1}{232}e^{4} + \frac{665}{1392}e^{2} - \frac{536}{87}$ |
41 | $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ | $\phantom{-}\frac{25}{2784}e^{7} - \frac{539}{1392}e^{5} + \frac{14927}{2784}e^{3} - \frac{686}{29}e$ |
41 | $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ | $-\frac{7}{464}e^{7} + \frac{353}{696}e^{5} - \frac{7147}{1392}e^{3} + \frac{5639}{348}e$ |
49 | $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ | $\phantom{-}\frac{85}{1392}e^{6} - \frac{1183}{696}e^{4} + \frac{5441}{464}e^{2} - \frac{956}{87}$ |
71 | $[71, 71, w^{2} - 2w - 2]$ | $\phantom{-}\frac{121}{5568}e^{7} - \frac{585}{928}e^{5} + \frac{28111}{5568}e^{3} - \frac{1415}{174}e$ |
71 | $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ | $\phantom{-}\frac{13}{696}e^{7} - \frac{121}{174}e^{5} + \frac{5159}{696}e^{3} - \frac{2347}{116}e$ |
73 | $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ | $\phantom{-}\frac{3}{116}e^{6} - \frac{85}{174}e^{4} + \frac{395}{348}e^{2} - \frac{163}{87}$ |
73 | $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ | $\phantom{-}\frac{43}{696}e^{6} - \frac{593}{348}e^{4} + \frac{8525}{696}e^{2} - \frac{372}{29}$ |
79 | $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ | $-\frac{1}{58}e^{6} + \frac{3}{29}e^{4} + \frac{143}{58}e^{2} + \frac{4}{29}$ |
79 | $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ | $\phantom{-}\frac{1}{58}e^{6} - \frac{38}{87}e^{4} + \frac{673}{174}e^{2} - \frac{1201}{87}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ | $-1$ |