# Properties

 Base field $$\Q(\zeta_{15})^+$$ Weight [2, 2, 2, 2] Level norm 81 Level $[81, 3, -3]$ Label 4.4.1125.1-81.1-c Dimension 2 CM no Base change yes

# Related objects

• L-function not available

## Base field $$\Q(\zeta_{15})^+$$

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

## Form

 Weight [2, 2, 2, 2] Level $[81, 3, -3]$ Label 4.4.1125.1-81.1-c Dimension 2 Is CM no Is base change yes Parent newspace dimension 5

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut -\mathstrut 18$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + 1]$ $\phantom{-}e$
9 $[9, 3, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}0$
16 $[16, 2, 2]$ $-1$
29 $[29, 29, -w^{3} - w^{2} + 2w + 3]$ $-e$
29 $[29, 29, -w^{2} + w + 3]$ $-e$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $-e$
29 $[29, 29, 2w^{3} + w^{2} - 7w]$ $-e$
31 $[31, 31, -2w + 1]$ $-4$
31 $[31, 31, 2w^{2} - 5]$ $-4$
31 $[31, 31, 2w^{3} + 2w^{2} - 6w - 3]$ $-4$
31 $[31, 31, 2w^{3} - 8w + 1]$ $-4$
59 $[59, 59, w^{3} + w^{2} - 2w - 5]$ $-2e$
59 $[59, 59, -w^{3} + 2w^{2} + 4w - 5]$ $-2e$
59 $[59, 59, -3w^{3} + 10w - 4]$ $-2e$
59 $[59, 59, -2w^{3} - w^{2} + 7w - 2]$ $-2e$
61 $[61, 61, 4w^{3} + w^{2} - 13w - 1]$ $\phantom{-}8$
61 $[61, 61, 2w^{3} - w^{2} - 5w + 2]$ $\phantom{-}8$
61 $[61, 61, -3w^{3} - w^{2} + 8w]$ $\phantom{-}8$
61 $[61, 61, 3w^{3} - w^{2} - 10w + 5]$ $\phantom{-}8$
89 $[89, 89, w^{3} + w^{2} - w - 4]$ $\phantom{-}3e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, w^{3} + w^{2} - 4w - 3]$ $1$