Properties

Label 4.4.6809.1-22.1-d
Base field 4.4.6809.1
Weight $[2, 2, 2, 2]$
Level norm $22$
Level $[22, 22, -w^{2} + 3]$
Dimension $1$
CM no
Base change no

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Base field 4.4.6809.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[22, 22, -w^{2} + 3]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}1$
5 $[5, 5, w^{3} - 4w]$ $-2$
8 $[8, 2, w^{3} - w^{2} - 4w + 3]$ $-3$
11 $[11, 11, w^{3} - 5w + 1]$ $-1$
17 $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $\phantom{-}2$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}0$
29 $[29, 29, -w^{2} - w + 3]$ $-10$
31 $[31, 31, -w^{3} + 6w + 2]$ $\phantom{-}0$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}4$
47 $[47, 47, 2w^{3} - 9w]$ $-8$
47 $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ $-8$
53 $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ $\phantom{-}6$
59 $[59, 59, w^{2} - w - 5]$ $-4$
59 $[59, 59, 3w^{3} - 15w - 5]$ $-4$
71 $[71, 71, w^{3} - 3w - 3]$ $\phantom{-}8$
81 $[81, 3, -3]$ $\phantom{-}2$
83 $[83, 83, -2w^{3} + 8w + 3]$ $-12$
89 $[89, 89, -2w^{3} + 11w - 2]$ $-6$
101 $[101, 101, 2w^{3} - w^{2} - 10w]$ $-10$
101 $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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