Properties

 Label 4.4.16448.1-22.1-b Base field 4.4.16448.1 Weight $[2, 2, 2, 2]$ Level norm $22$ Level $[22, 22, -w + 2]$ Dimension $1$ CM no Base change no

Related objects

Base field 4.4.16448.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 6x^{2} + 2$$; narrow class number $$2$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2]$ Level: $[22, 22, -w + 2]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $-1$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $-1$
5 $[5, 5, w - 1]$ $\phantom{-}1$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $-1$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}6$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $\phantom{-}2$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $-6$
25 $[25, 5, -w^{2} + 3w + 1]$ $-6$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $\phantom{-}0$
31 $[31, 31, -w^{2} + 2w + 1]$ $-7$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $\phantom{-}9$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $-4$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $\phantom{-}5$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $-4$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $\phantom{-}10$
81 $[81, 3, -3]$ $\phantom{-}2$
83 $[83, 83, -w - 3]$ $\phantom{-}9$
83 $[83, 83, w^{2} - 3w - 7]$ $-1$
89 $[89, 89, w^{2} - 2w - 7]$ $-15$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $-2$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $1$
$11$ $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $1$