# Properties

 Label 4.4.9792.1-31.1-a Base field 4.4.9792.1 Weight $[2, 2, 2, 2]$ Level norm $31$ Level $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ Dimension $8$ CM no Base change no

# Related objects

• L-function not available

## 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:

 $$x^{8} - 38x^{6} + 455x^{4} - 1696x^{2} + 256$$
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 $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ $\phantom{-}\frac{1}{58}e^{6} - \frac{38}{87}e^{4} + \frac{673}{174}e^{2} - \frac{1201}{87}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ $-1$