Properties

Label 4.4.18736.1-9.1-a
Base field 4.4.18736.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 9, w^{3} - 3w^{2} - 2w + 7]$
Dimension $1$
CM no
Base change no

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Base field 4.4.18736.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 9, w^{3} - 3w^{2} - 2w + 7]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w - 1]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}2$
5 $[5, 5, w]$ $\phantom{-}0$
7 $[7, 7, w - 2]$ $\phantom{-}2$
11 $[11, 11, w^{2} - 2w - 4]$ $-6$
23 $[23, 23, -w^{2} + 2w + 1]$ $\phantom{-}0$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}0$
27 $[27, 3, -w^{3} + w^{2} + 6w + 2]$ $\phantom{-}4$
31 $[31, 31, -w^{3} + 3w^{2} + w - 1]$ $-4$
31 $[31, 31, -w^{3} + 2w^{2} + 4w - 4]$ $-4$
37 $[37, 37, w^{2} - 2w - 6]$ $\phantom{-}2$
37 $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ $-10$
43 $[43, 43, w^{2} - 3w - 2]$ $-4$
61 $[61, 61, -w^{3} + 2w^{2} + 2w - 2]$ $\phantom{-}8$
73 $[73, 73, w^{3} - 3w^{2} - 2w + 3]$ $\phantom{-}2$
83 $[83, 83, -w - 3]$ $-6$
89 $[89, 89, -w^{3} + 3w^{2} + 2w - 2]$ $-6$
89 $[89, 89, 2w - 1]$ $-18$
101 $[101, 101, w^{3} - 4w^{2} + w + 7]$ $-18$
101 $[101, 101, 2w^{2} - 3w - 3]$ $-12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w - 1]$ $-1$