# Properties

 Base field 4.4.725.1 Weight [2, 2, 2, 2] Level norm 81 Level $[81, 3, -3]$ Label 4.4.725.1-81.1-a Dimension 2 CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.725.1

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

## Form

 Weight [2, 2, 2, 2] Level $[81, 3, -3]$ Label 4.4.725.1-81.1-a Dimension 2 Is CM no Is base change yes Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 2x$$ $$\mathstrut -\mathstrut 4$$
Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 3w]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-2e$
19 $[19, 19, -w^{3} + 2w + 2]$ $-\frac{3}{2}e - 3$
19 $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ $-\frac{3}{2}e - 3$
25 $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}\frac{3}{2}e + 8$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $-4e - 4$
31 $[31, 31, w^{3} - 4w + 1]$ $\phantom{-}\frac{5}{2}e + 2$
31 $[31, 31, -w^{2} + 2w + 3]$ $\phantom{-}\frac{5}{2}e + 2$
41 $[41, 41, 2w^{2} - w - 3]$ $\phantom{-}3e + 6$
41 $[41, 41, -w^{3} + 3w^{2} + w - 4]$ $\phantom{-}3e + 6$
49 $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ $-\frac{5}{2}e - 2$
49 $[49, 7, w^{2} + w - 3]$ $-\frac{5}{2}e - 2$
61 $[61, 61, 2w^{3} - 3w^{2} - 4w]$ $-\frac{9}{2}e - 7$
61 $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ $-\frac{9}{2}e - 7$
79 $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}\frac{7}{2}e - 3$
79 $[79, 79, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}\frac{7}{2}e - 3$
81 $[81, 3, -3]$ $-1$
89 $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ $\phantom{-}e - 4$
89 $[89, 89, 3w^{3} - 2w^{2} - 7w]$ $\phantom{-}e - 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
81 $[81, 3, -3]$ $1$