Properties

Label 4.4.16448.1-20.2-a
Base field 4.4.16448.1
Weight $[2, 2, 2, 2]$
Level norm $20$
Level $[20, 10, -w^{2} + 2w + 4]$
Dimension $1$
CM no
Base change no

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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: $[20, 10, -w^{2} + 2w + 4]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
5 $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ $\phantom{-}0$
5 $[5, 5, w - 1]$ $-1$
11 $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ $\phantom{-}4$
13 $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ $\phantom{-}0$
17 $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ $-4$
23 $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ $-8$
25 $[25, 5, -w^{2} + 3w + 1]$ $-4$
29 $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ $\phantom{-}8$
31 $[31, 31, -w^{2} + 2w + 1]$ $-8$
43 $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ $\phantom{-}4$
43 $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ $\phantom{-}12$
59 $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ $\phantom{-}12$
73 $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ $-4$
79 $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ $-8$
81 $[81, 3, -3]$ $-2$
83 $[83, 83, -w - 3]$ $-12$
83 $[83, 83, w^{2} - 3w - 7]$ $\phantom{-}4$
89 $[89, 89, w^{2} - 2w - 7]$ $-10$
101 $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$
$5$ $[5, 5, w - 1]$ $1$