# Properties

 Label 4.4.16225.1-36.1-b Base field 4.4.16225.1 Weight $[2, 2, 2, 2]$ Level norm $36$ Level $[36, 6, -w]$ Dimension $11$ 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: $[36, 6, -w]$ Dimension: $11$ CM: no Base change: no Newspace dimension: $52$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{11} + 4x^{10} - 16x^{9} - 80x^{8} + 7x^{7} + 334x^{6} + 215x^{5} - 362x^{4} - 283x^{3} + 81x^{2} + 81x + 10$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ $\phantom{-}1$
4 $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ $-1$
9 $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ $...$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ $-\frac{10372}{78891}e^{10} - \frac{12590}{26297}e^{9} + \frac{168082}{78891}e^{8} + \frac{747907}{78891}e^{7} - \frac{128567}{78891}e^{6} - \frac{2995244}{78891}e^{5} - \frac{612225}{26297}e^{4} + \frac{2883101}{78891}e^{3} + \frac{1865534}{78891}e^{2} - \frac{574004}{78891}e - \frac{230272}{78891}$
19 $[19, 19, w + 1]$ $-\frac{7454}{26297}e^{10} - \frac{30440}{26297}e^{9} + \frac{123320}{26297}e^{8} + \frac{616310}{26297}e^{7} - \frac{133262}{26297}e^{6} - \frac{2694502}{26297}e^{5} - \frac{1237753}{26297}e^{4} + \frac{3348313}{26297}e^{3} + \frac{1624790}{26297}e^{2} - \frac{1175850}{26297}e - \frac{432860}{26297}$
19 $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ $...$
25 $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ $...$
29 $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ $-\frac{9097}{78891}e^{10} - \frac{2204}{26297}e^{9} + \frac{214978}{78891}e^{8} + \frac{153499}{78891}e^{7} - \frac{1451894}{78891}e^{6} - \frac{863120}{78891}e^{5} + \frac{1220666}{26297}e^{4} + \frac{1684232}{78891}e^{3} - \frac{2987068}{78891}e^{2} - \frac{1034231}{78891}e + \frac{248045}{78891}$
29 $[29, 29, w - 1]$ $...$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ $...$
31 $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ $-\frac{13862}{78891}e^{10} - \frac{13794}{26297}e^{9} + \frac{261848}{78891}e^{8} + \frac{857771}{78891}e^{7} - \frac{885817}{78891}e^{6} - \frac{3993691}{78891}e^{5} + \frac{24437}{26297}e^{4} + \frac{5707762}{78891}e^{3} + \frac{1213717}{78891}e^{2} - \frac{2204131}{78891}e - \frac{371342}{78891}$
41 $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ $...$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ $...$
59 $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ $-\frac{7037}{26297}e^{10} - \frac{20002}{26297}e^{9} + \frac{138534}{26297}e^{8} + \frac{423203}{26297}e^{7} - \frac{561489}{26297}e^{6} - \frac{2095430}{26297}e^{5} + \frac{503340}{26297}e^{4} + \frac{3389525}{26297}e^{3} + \frac{153658}{26297}e^{2} - \frac{1552278}{26297}e - \frac{207060}{26297}$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ $...$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ $...$
79 $[79, 79, w^{2} - 11]$ $...$
79 $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ $...$
89 $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ $-1$
$9$ $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ $1$