# Properties

 Label 4.4.16225.1-16.3-b Base field 4.4.16225.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16,4,-\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w + 1]$ Dimension $10$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16225.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 13x^{2} + 6x + 36$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16,4,-\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w + 1]$ Dimension: $10$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{10} - 28x^{8} + 283x^{6} - 1275x^{4} + 2478x^{2} - 1587$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ $\phantom{-}0$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ $-\frac{3}{2}e^{8} + \frac{65}{2}e^{6} - 218e^{4} + \frac{1037}{2}e^{2} - \frac{721}{2}$
9 $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ $\phantom{-}\frac{5}{6}e^{8} - \frac{109}{6}e^{6} + 123e^{4} - \frac{591}{2}e^{2} + \frac{411}{2}$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ $\phantom{-}\frac{37}{69}e^{9} - \frac{806}{69}e^{7} + \frac{1819}{23}e^{5} - \frac{4386}{23}e^{3} + \frac{3054}{23}e$
19 $[19, 19, w + 1]$ $-\frac{61}{69}e^{9} + \frac{1340}{69}e^{7} - \frac{3071}{23}e^{5} + \frac{7617}{23}e^{3} - \frac{5605}{23}e$
19 $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ $\phantom{-}\frac{25}{69}e^{9} - \frac{539}{69}e^{7} + \frac{1193}{23}e^{5} - \frac{2782}{23}e^{3} + \frac{1905}{23}e$
25 $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ $-\frac{7}{3}e^{8} + \frac{152}{3}e^{6} - 341e^{4} + 815e^{2} - 571$
29 $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ $\phantom{-}\frac{93}{46}e^{9} - \frac{2029}{46}e^{7} + \frac{6892}{23}e^{5} - \frac{33567}{46}e^{3} + \frac{24305}{46}e$
29 $[29, 29, w - 1]$ $-\frac{107}{138}e^{9} + \frac{2329}{138}e^{7} - \frac{2628}{23}e^{5} + \frac{12769}{46}e^{3} - \frac{9377}{46}e$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ $\phantom{-}\frac{197}{69}e^{9} - \frac{4297}{69}e^{7} + \frac{9721}{23}e^{5} - \frac{23580}{23}e^{3} + \frac{16833}{23}e$
31 $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ $-\frac{74}{69}e^{9} + \frac{1612}{69}e^{7} - \frac{3638}{23}e^{5} + \frac{8795}{23}e^{3} - \frac{6269}{23}e$
41 $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ $\phantom{-}\frac{3}{46}e^{9} - \frac{61}{46}e^{7} + \frac{183}{23}e^{5} - \frac{743}{46}e^{3} + \frac{649}{46}e$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ $-\frac{427}{138}e^{9} + \frac{9311}{138}e^{7} - \frac{10530}{23}e^{5} + \frac{51111}{46}e^{3} - \frac{36613}{46}e$
59 $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $\phantom{-}e^{8} - 22e^{6} + 151e^{4} - 370e^{2} + 264$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ $-\frac{23}{3}e^{8} + \frac{502}{3}e^{6} - 1137e^{4} + 2764e^{2} - 1972$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ $-\frac{7}{3}e^{8} + \frac{152}{3}e^{6} - 341e^{4} + 816e^{2} - 578$
79 $[79, 79, w^{2} - 11]$ $\phantom{-}\frac{13}{3}e^{8} - \frac{284}{3}e^{6} + 644e^{4} - 1567e^{2} + 1128$
79 $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ $\phantom{-}\frac{35}{3}e^{8} - \frac{763}{3}e^{6} + 1725e^{4} - 4184e^{2} + 2999$
89 $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ $-\frac{157}{138}e^{9} + \frac{3407}{138}e^{7} - \frac{3821}{23}e^{5} + \frac{18333}{46}e^{3} - \frac{13095}{46}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,\frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{10}{3}w - 7]$ $1$