# Properties

 Base field 4.4.6125.1 Weight [2, 2, 2, 2] Level norm 11 Level $[11,11,-w^{3} - w^{2} + 7w + 4]$ Label 4.4.6125.1-11.3-a Dimension 4 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.6125.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 9x^{2} + 9x + 11$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[11,11,-w^{3} - w^{2} + 7w + 4]$ Label 4.4.6125.1-11.3-a Dimension 4 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 6x^{2} + 4$$
Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $\phantom{-}e$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $-2e^{2} + 8$
11 $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ $\phantom{-}e^{2}$
11 $[11, 11, w^{3} + w^{2} - 7w - 4]$ $-1$
11 $[11, 11, w - 1]$ $\phantom{-}e^{2}$
16 $[16, 2, 2]$ $-e^{2} + 3$
19 $[19, 19, -w^{2} + 4]$ $-2e^{3} + 8e$
19 $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ $\phantom{-}2e^{3} - 10e$
19 $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ $-e$
19 $[19, 19, -w^{3} - w^{2} + 5w + 3]$ $-e^{3} + 9e$
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $\phantom{-}3e^{3} - 15e$
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $\phantom{-}3e^{3} - 11e$
59 $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ $-3e$
59 $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ $\phantom{-}2e^{3} - 12e$
59 $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ $-4e^{3} + 15e$
71 $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ $\phantom{-}2e^{2} - 4$
71 $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ $\phantom{-}5e^{2} - 12$
71 $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ $-4e^{2} + 12$
71 $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ $-4e^{2} + 12$
81 $[81, 3, -3]$ $\phantom{-}2e^{2} - 14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11,11,-w^{3} - w^{2} + 7w + 4]$ $1$