# Properties

 Label 4.4.17069.1-9.1-e Base field 4.4.17069.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, w^{3} - 2w^{2} - 5w]$ Dimension $4$ CM no Base change yes

# 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: $[9, 3, w^{3} - 2w^{2} - 5w]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $15$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 11x^{3} + 29x^{2} + 8x - 8$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}1$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{15}{2}e + 3$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $-e^{2} + 6e$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e^{2} - \frac{7}{2}e$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $-e^{2} + 6e$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e^{2} - \frac{7}{2}e$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $-e^{3} + 7e^{2} - 8e$
25 $[25, 5, w^{2} - 2w - 7]$ $-e^{3} + 7e^{2} - 8e$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - \frac{3}{2}e - 2$
29 $[29, 29, w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - \frac{3}{2}e - 2$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $\phantom{-}e^{3} - 6e^{2} - e + 12$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $\phantom{-}e^{3} - 6e^{2} - e + 12$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $\phantom{-}e^{3} - 6e^{2} + e$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $\phantom{-}e^{3} - 6e^{2} + e$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $\phantom{-}e^{3} - 11e^{2} + 25e + 10$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $\phantom{-}4e^{2} - 24e + 2$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $\phantom{-}4e^{2} - 24e + 2$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}2e^{3} - 14e^{2} + 15e + 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $-1$
$3$ $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $-1$