# Properties

 Base field 4.4.17725.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19,19,-w + 2]$ Label 4.4.17725.1-19.4-b Dimension 1 CM no Base change no

# Related objects

## Base field 4.4.17725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 12x^{2} + 13x + 41$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[19,19,-w + 2]$ Label 4.4.17725.1-19.4-b Dimension 1 Is CM no Is base change no Parent newspace dimension 32

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $-6$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}3$
16 $[16, 2, 2]$ $\phantom{-}3$
19 $[19, 19, w + 1]$ $-7$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}1$
19 $[19, 19, -w^{2} + 2w + 5]$ $-5$
19 $[19, 19, -w + 2]$ $\phantom{-}1$
25 $[25, 5, 2w^{2} - 2w - 13]$ $\phantom{-}2$
29 $[29, 29, -w^{2} + 9]$ $-6$
29 $[29, 29, -w^{2} + 2w + 6]$ $\phantom{-}7$
29 $[29, 29, w^{2} - 7]$ $-2$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}9$
31 $[31, 31, -2w^{2} + w + 12]$ $\phantom{-}8$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-7$
41 $[41, 41, -w]$ $-11$
41 $[41, 41, -w + 1]$ $\phantom{-}1$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $-4$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $-1$
61 $[61, 61, 2w^{2} - 3w - 14]$ $\phantom{-}10$
61 $[61, 61, 2w^{2} - w - 15]$ $-8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,-w + 2]$ $-1$