# Properties

 Base field 4.4.13968.1 Weight [2, 2, 2, 2] Level norm 9 Level $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ Label 4.4.13968.1-9.1-e Dimension 8 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.13968.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 7x^{2} + 8x + 4$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ Label 4.4.13968.1-9.1-e Dimension 8 Is CM no Is base change no Parent newspace dimension 22

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{8} - 14x^{6} + 57x^{4} - 56x^{2} + 4$$
Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ $\phantom{-}e$
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ $-\frac{1}{4}e^{7} + \frac{7}{2}e^{5} - \frac{55}{4}e^{3} + \frac{21}{2}e$
9 $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ $-1$
13 $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ $-\frac{1}{2}e^{6} + \frac{11}{2}e^{4} - 15e^{2} + 6$
13 $[13, 13, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e^{6} - 5e^{4} + \frac{23}{2}e^{2} - 1$
23 $[23, 23, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{7}{2}e^{3} + e$
23 $[23, 23, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 3]$ $-e^{3} + 7e$
37 $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{2}e^{6} - 4e^{4} + \frac{9}{2}e^{2} + 5$
37 $[37, 37, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 6]$ $-\frac{1}{2}e^{6} + \frac{13}{2}e^{4} - 22e^{2} + 12$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{7}{2}w]$ $\phantom{-}\frac{1}{2}e^{7} - 7e^{5} + \frac{59}{2}e^{3} - 39e$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 3]$ $\phantom{-}e^{7} - 15e^{5} + 62e^{3} - 46e$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 7]$ $-e^{4} + 5e^{2} + 8$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}\frac{1}{2}e^{6} - 6e^{4} + \frac{37}{2}e^{2} - 3$
61 $[61, 61, w^{3} - 2w^{2} - 5w + 3]$ $-\frac{1}{2}e^{6} + \frac{9}{2}e^{4} - 8e^{2} + 4$
61 $[61, 61, w^{3} - w^{2} - 8w + 1]$ $-e^{4} + 9e^{2} - 6$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 5]$ $-e^{5} + 11e^{3} - 26e$
71 $[71, 71, -w^{3} + \frac{3}{2}w^{2} + \frac{15}{2}w - 6]$ $-e^{7} + 12e^{5} - 39e^{3} + 24e$
83 $[83, 83, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 7]$ $\phantom{-}e^{7} - 14e^{5} + 56e^{3} - 47e$
83 $[83, 83, \frac{1}{2}w^{3} - \frac{7}{2}w - 4]$ $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - 24e^{3} + 16e$
97 $[97, 97, 2w - 1]$ $-\frac{3}{2}e^{4} + \frac{21}{2}e^{2} - 1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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