Properties

Label 4.4.15529.1-9.2-a
Base field 4.4.15529.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$
Dimension $1$
CM no
Base change no

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Base field 4.4.15529.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}1$
5 $[5, 5, w - 1]$ $-2$
8 $[8, 2, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}3$
9 $[9, 3, -w^{3} + w^{2} + 5w + 1]$ $\phantom{-}6$
9 $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$ $-1$
19 $[19, 19, -w^{3} + 2w^{2} + 4w - 1]$ $\phantom{-}4$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}0$
29 $[29, 29, w^{2} - 3w - 1]$ $-6$
29 $[29, 29, -w^{2} + w + 3]$ $-2$
37 $[37, 37, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}10$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}4$
47 $[47, 47, -w^{2} + 2w + 5]$ $\phantom{-}8$
47 $[47, 47, 2w^{3} - 2w^{2} - 11w - 5]$ $\phantom{-}8$
53 $[53, 53, -w^{3} + 2w^{2} + 2w + 1]$ $\phantom{-}6$
59 $[59, 59, -w - 3]$ $-4$
73 $[73, 73, w^{2} - w + 1]$ $-6$
73 $[73, 73, 2w^{3} - 2w^{2} - 12w - 5]$ $-2$
79 $[79, 79, 4w^{3} - 4w^{2} - 22w - 7]$ $-8$
97 $[97, 97, 2w^{3} - 3w^{2} - 9w + 1]$ $\phantom{-}14$
101 $[101, 101, 2w^{2} - 2w - 9]$ $-2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, -w^{3} + 2w^{2} + 3w - 1]$ $1$