# Properties

 Label 4.4.8112.1-27.2-e Base field 4.4.8112.1 Weight $[2, 2, 2, 2]$ Level norm $27$ Level $[27, 9, -w^{3} + 3w]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8112.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[27, 9, -w^{3} + 3w]$ Dimension: $2$ 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:

 $$x^{2} + x - 3$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
4 $[4, 2, w^{2} - w - 1]$ $\phantom{-}e$
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}e + 2$
13 $[13, 13, w^{3} - 4w + 2]$ $\phantom{-}e + 3$
13 $[13, 13, -w^{3} + 4w + 2]$ $-2e$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}3$
17 $[17, 17, -w^{3} + 3w - 1]$ $\phantom{-}3$
29 $[29, 29, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}3$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}3$
43 $[43, 43, w^{2} + w - 4]$ $\phantom{-}2e - 5$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}2e + 4$
53 $[53, 53, w^{3} - 2w - 2]$ $\phantom{-}3e - 3$
53 $[53, 53, -w^{3} + 2w - 2]$ $-6e - 3$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}e + 3$
79 $[79, 79, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}7e$
101 $[101, 101, -w^{3} + w^{2} + 3w - 5]$ $-3e + 6$
101 $[101, 101, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}6e - 3$
103 $[103, 103, 2w^{2} - w - 4]$ $-6e - 4$
103 $[103, 103, 2w^{2} + w - 4]$ $\phantom{-}3e + 14$
107 $[107, 107, 2w^{2} + w - 5]$ $-6e - 9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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