# Properties

 Label 4.4.16357.1-9.1-a Base field 4.4.16357.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 9, w - 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16357.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 9, w - 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 5x^{2} + 2$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}0$
5 $[5, 5, -w^{3} + 5w + 2]$ $\phantom{-}e$
5 $[5, 5, w - 1]$ $\phantom{-}e^{2} - 4$
11 $[11, 11, -w^{3} + 5w]$ $-2e$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-2e^{3} + 9e$
16 $[16, 2, 2]$ $-2e^{2} + 3$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $\phantom{-}2e^{3} - 8e$
25 $[25, 5, -w^{2} + w + 3]$ $\phantom{-}0$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $-4e$
31 $[31, 31, -w - 3]$ $-6$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $-e^{3} + 8e$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}e^{3} - 3e$
43 $[43, 43, w^{3} - 7w - 2]$ $\phantom{-}2e^{2} - 2$
47 $[47, 47, -2w^{3} + 11w + 2]$ $\phantom{-}5e^{3} - 19e$
61 $[61, 61, w^{2} - 3]$ $-e^{3} + 3e$
67 $[67, 67, w^{2} + w - 4]$ $-6e^{2} + 18$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $-7e^{3} + 27e$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $-e^{2} - 10$
97 $[97, 97, -w^{3} + 6w - 3]$ $\phantom{-}e^{2} - 4$
97 $[97, 97, -3w^{3} + 16w]$ $\phantom{-}2e^{3} - 6e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $-1$