# Properties

 Label 4.4.12725.1-29.3-a Base field 4.4.12725.1 Weight $[2, 2, 2, 2]$ Level norm $29$ Level $[29,29,2w^{2} - 3w - 9]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.12725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 10x^{2} + 11x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[29,29,2w^{2} - 3w - 9]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $30$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + 3x - 5$$
Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $-1$
11 $[11, 11, w^{2} - 5]$ $-3$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}1$
11 $[11, 11, w - 2]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-e$
19 $[19, 19, w^{2} - 2w - 5]$ $\phantom{-}1$
19 $[19, 19, -w^{2} + 6]$ $-7$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}e - 1$
29 $[29, 29, w]$ $-3$
29 $[29, 29, 2w^{2} - w - 10]$ $\phantom{-}2e + 3$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-1$
29 $[29, 29, w - 1]$ $-2e - 8$
31 $[31, 31, w^{3} - 6w - 6]$ $\phantom{-}e$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $\phantom{-}5$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $-3e - 8$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $-2$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}0$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}2e + 6$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $-e - 1$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $-e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$29$ $[29,29,2w^{2} - 3w - 9]$ $1$