Properties

 Label 4.4.8112.1-4.1-b Base field 4.4.8112.1 Weight $[2, 2, 2, 2]$ Level norm $4$ Level $[4, 2, w^{2} - w - 1]$ Dimension $1$ CM no Base change yes

Related objects

Base field 4.4.8112.1

Generator $$w$$, with minimal polynomial $$x^{4} - 5x^{2} + 3$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[4, 2, w^{2} - w - 1]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $2$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
4 $[4, 2, w^{2} - w - 1]$ $-1$
9 $[9, 3, -w^{2} + 2]$ $-5$
13 $[13, 13, w^{3} - 4w + 2]$ $\phantom{-}4$
13 $[13, 13, -w^{3} + 4w + 2]$ $\phantom{-}4$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}3$
17 $[17, 17, -w^{3} + 3w - 1]$ $\phantom{-}3$
29 $[29, 29, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}0$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}0$
43 $[43, 43, w^{2} + w - 4]$ $-1$
43 $[43, 43, w^{2} - w - 4]$ $-1$
53 $[53, 53, w^{3} - 2w - 2]$ $-6$
53 $[53, 53, -w^{3} + 2w - 2]$ $-6$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}10$
79 $[79, 79, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}10$
101 $[101, 101, -w^{3} + w^{2} + 3w - 5]$ $\phantom{-}12$
101 $[101, 101, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}12$
103 $[103, 103, 2w^{2} - w - 4]$ $\phantom{-}14$
103 $[103, 103, 2w^{2} + w - 4]$ $\phantom{-}14$
107 $[107, 107, 2w^{2} + w - 5]$ $-12$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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