# 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-d Dimension 6 CM no Base change no

# Related objects

• L-function not available

## 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-d Dimension 6 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:
$$x^{6} - 9x^{4} + 20x^{2} - 11$$
Norm Prime Eigenvalue
2 $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ $\phantom{-}e$
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ $-e$
9 $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ $\phantom{-}1$
13 $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ $\phantom{-}e^{4} - 8e^{2} + 8$
13 $[13, 13, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ $\phantom{-}e^{4} - 8e^{2} + 8$
23 $[23, 23, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w]$ $\phantom{-}e^{3} - 3e$
23 $[23, 23, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 3]$ $-e^{3} + 3e$
37 $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w - 3]$ $-4e^{4} + 27e^{2} - 30$
37 $[37, 37, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 6]$ $-4e^{4} + 27e^{2} - 30$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{7}{2}w]$ $-3e^{5} + 23e^{3} - 33e$
59 $[59, 59, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 3]$ $\phantom{-}3e^{5} - 23e^{3} + 33e$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 7]$ $-2e^{2} + 5$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}e^{4} - 4e^{2} - 5$
61 $[61, 61, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}e^{4} - 4e^{2} - 5$
61 $[61, 61, w^{3} - w^{2} - 8w + 1]$ $-2e^{2} + 5$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 5]$ $\phantom{-}3e^{5} - 22e^{3} + 25e$
71 $[71, 71, -w^{3} + \frac{3}{2}w^{2} + \frac{15}{2}w - 6]$ $-3e^{5} + 22e^{3} - 25e$
83 $[83, 83, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 7]$ $\phantom{-}2e^{5} - 14e^{3} + 17e$
83 $[83, 83, \frac{1}{2}w^{3} - \frac{7}{2}w - 4]$ $-2e^{5} + 14e^{3} - 17e$
97 $[97, 97, 2w - 1]$ $-2e^{4} + 14e^{2} - 28$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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