# Properties

 Label 4.4.17069.1-9.2-a Base field 4.4.17069.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17069.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $19$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 2x^{3} - 8x^{2} - 12x + 6$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 3e - 2$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $-1$
16 $[16, 2, 2]$ $\phantom{-}\frac{2}{3}e^{3} + \frac{2}{3}e^{2} - 4e - 3$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $\phantom{-}e^{2} + e - 4$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 4e - 2$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 3e + 4$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 4e + 4$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $-e^{3} - e^{2} + 6e + 2$
25 $[25, 5, w^{2} - 2w - 7]$ $-e^{3} - e^{2} + 6e + 2$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 4e$
29 $[29, 29, w - 2]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{2}{3}e^{2} - 4e + 6$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $\phantom{-}\frac{4}{3}e^{3} + \frac{1}{3}e^{2} - 12e - 2$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $\phantom{-}e^{2} + 4e - 4$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 2e + 4$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $\phantom{-}\frac{1}{3}e^{3} + \frac{1}{3}e^{2} - 2e + 4$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $-\frac{2}{3}e^{3} - \frac{2}{3}e^{2} + 4e + 6$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}\frac{5}{3}e^{3} + \frac{11}{3}e^{2} - 14e - 14$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{5}{3}e^{2} + 2e + 14$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}\frac{4}{3}e^{3} + \frac{4}{3}e^{2} - 11e - 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $1$