Properties

 Base field 4.4.17725.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.17725.1-16.1-d 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 $[16, 2, 2]$ Label 4.4.17725.1-16.1-d Dimension 1 Is CM no Is base change no Parent newspace dimension 30

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $-4$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}2$
16 $[16, 2, 2]$ $\phantom{-}1$
19 $[19, 19, w + 1]$ $\phantom{-}1$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}8$
19 $[19, 19, -w^{2} + 2w + 5]$ $-4$
19 $[19, 19, -w + 2]$ $\phantom{-}1$
25 $[25, 5, 2w^{2} - 2w - 13]$ $-2$
29 $[29, 29, -w^{2} + 9]$ $\phantom{-}0$
29 $[29, 29, -w^{2} + 2w + 6]$ $-6$
29 $[29, 29, w^{2} - 7]$ $\phantom{-}0$
29 $[29, 29, -w^{2} + 2w + 8]$ $-6$
31 $[31, 31, -2w^{2} + w + 12]$ $-7$
31 $[31, 31, 2w^{2} - 3w - 11]$ $\phantom{-}5$
41 $[41, 41, -w]$ $\phantom{-}0$
41 $[41, 41, -w + 1]$ $\phantom{-}0$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $\phantom{-}2$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $-4$
61 $[61, 61, 2w^{2} - 3w - 14]$ $\phantom{-}1$
61 $[61, 61, 2w^{2} - w - 15]$ $\phantom{-}13$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
16 $[16, 2, 2]$ $-1$