# Properties

 Label 4.4.16609.1-9.1-d Base field 4.4.16609.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 9, w]$ Dimension $8$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16609.1

Generator $$w$$, with minimal polynomial $$x^{4} - 7x^{2} - x + 9$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 9, w]$ Dimension: $8$ CM: no Base change: no Newspace dimension: $15$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{8} - 16x^{6} + 82x^{4} - 148x^{2} + 73$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 4]$ $\phantom{-}e$
3 $[3, 3, -w^{2} + w + 3]$ $\phantom{-}0$
5 $[5, 5, w^{2} - 4]$ $-\frac{1}{4}e^{6} + \frac{13}{4}e^{4} - \frac{47}{4}e^{2} + \frac{43}{4}$
8 $[8, 2, w^{3} - w^{2} - 4w + 5]$ $\phantom{-}\frac{1}{2}e^{4} - 4e^{2} + \frac{13}{2}$
17 $[17, 17, -w^{2} + w + 5]$ $-\frac{1}{4}e^{6} + \frac{15}{4}e^{4} - \frac{59}{4}e^{2} + \frac{45}{4}$
27 $[27, 3, -w^{3} + 4w - 2]$ $-e^{3} + 5e$
29 $[29, 29, -w^{2} + w + 1]$ $-\frac{1}{4}e^{7} + \frac{13}{4}e^{5} - \frac{47}{4}e^{3} + \frac{35}{4}e$
29 $[29, 29, -w^{3} + 4w + 2]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{17}{4}e^{5} + \frac{83}{4}e^{3} - \frac{99}{4}e$
37 $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{15}{4}e^{5} + \frac{67}{4}e^{3} - \frac{85}{4}e$
41 $[41, 41, w^{3} - w^{2} - 5w + 2]$ $-\frac{1}{4}e^{7} + \frac{11}{4}e^{5} - \frac{23}{4}e^{3} - \frac{19}{4}e$
43 $[43, 43, -w^{3} + w^{2} + 3w - 4]$ $\phantom{-}2e$
61 $[61, 61, w^{2} - 2w - 2]$ $-\frac{3}{4}e^{7} + \frac{41}{4}e^{5} - \frac{161}{4}e^{3} + \frac{163}{4}e$
61 $[61, 61, 2w^{2} - w - 8]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{13}{4}e^{5} + \frac{51}{4}e^{3} - \frac{71}{4}e$
67 $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ $\phantom{-}e^{3} - 3e$
73 $[73, 73, -w^{2} - 2w + 2]$ $-\frac{1}{4}e^{6} + \frac{11}{4}e^{4} - \frac{35}{4}e^{2} + \frac{57}{4}$
79 $[79, 79, w^{2} - 2w - 4]$ $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - \frac{53}{2}e^{2} + \frac{61}{2}$
89 $[89, 89, w^{2} + w - 5]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{15}{4}e^{4} + \frac{55}{4}e^{2} - \frac{1}{4}$
89 $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ $-\frac{3}{4}e^{6} + \frac{41}{4}e^{4} - \frac{157}{4}e^{2} + \frac{127}{4}$
89 $[89, 89, w^{3} - 5w - 5]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{11}{4}e^{5} + \frac{19}{4}e^{3} + \frac{47}{4}e$
89 $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ $-\frac{1}{4}e^{6} + \frac{9}{4}e^{4} - \frac{15}{4}e^{2} - \frac{1}{4}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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