# Properties

 Label 4.4.19429.1-9.1-d Base field 4.4.19429.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 9, -w^{3} + 2w^{2} + 4w - 2]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19429.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} - x + 5$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 9, -w^{3} + 2w^{2} + 4w - 2]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $13$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + 3x^{2} - 2x - 3$$
Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}0$
5 $[5, 5, w]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}e^{2} + e - 5$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}e^{2} + 2e - 5$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $-e^{2} - 3e - 1$
16 $[16, 2, 2]$ $\phantom{-}e^{2} + 3e - 2$
17 $[17, 17, -w + 2]$ $\phantom{-}e^{2} + 3e$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}e^{2} + 3e - 5$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $-e^{2} - e + 2$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $-1$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-2e^{2} - 6e + 4$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}3e^{2} + 8e - 3$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $-2e^{2} - 3e + 10$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $-3e^{2} - 9e + 6$
53 $[53, 53, -w - 3]$ $\phantom{-}2e^{2} + 3e$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $-3e^{2} - 8e + 6$
59 $[59, 59, 2w^{2} - 3w - 6]$ $-3e^{2} - 8e$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $-3e^{2} - 7e + 6$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $-3e^{2} - 9e + 2$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}3e^{2} + 9e - 7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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