Properties

Label 4.4.10889.1-22.1-a
Base field 4.4.10889.1
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 4.4.10889.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 2x + 1\); narrow class number \(2\) 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: $16$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}1$
7 $[7, 7, -w + 2]$ $\phantom{-}0$
8 $[8, 2, -w^{3} + 5w + 3]$ $\phantom{-}5$
11 $[11, 11, w^{3} - w^{2} - 5w + 4]$ $\phantom{-}1$
11 $[11, 11, w^{3} - w^{2} - 4w + 1]$ $-4$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-2$
25 $[25, 5, -w^{2} + w + 3]$ $\phantom{-}6$
25 $[25, 5, -w^{2} + 2]$ $\phantom{-}6$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $-6$
29 $[29, 29, -w^{3} + 4w + 2]$ $-2$
37 $[37, 37, 4w^{3} - 2w^{2} - 21w - 4]$ $\phantom{-}2$
43 $[43, 43, 4w^{3} - 2w^{2} - 20w - 3]$ $\phantom{-}4$
47 $[47, 47, -w^{3} + 6w]$ $\phantom{-}0$
53 $[53, 53, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}10$
81 $[81, 3, -3]$ $-2$
83 $[83, 83, 2w^{3} - w^{2} - 10w - 4]$ $-12$
89 $[89, 89, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}6$
89 $[89, 89, 2w - 3]$ $\phantom{-}6$
101 $[101, 101, 6w^{3} - 3w^{2} - 31w - 5]$ $\phantom{-}14$
107 $[107, 107, -w^{3} + w^{2} + 4w - 5]$ $-4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w + 1]$ $-1$
$11$ $[11, 11, w^{3} - w^{2} - 5w + 4]$ $-1$