Properties

Label 4.4.19773.1-9.2-c
Base field 4.4.19773.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, -w^{3} + 3w^{2} + 7w - 3]$
Dimension $1$
CM no
Base change yes

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Base field 4.4.19773.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} - 9x + 3\); narrow class number \(4\) and class number \(1\).

Form

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

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w^{3} - 2w^{2} - 8w - 3]$ $-1$
3 $[3, 3, w^{3} - 3w^{2} - 5w + 2]$ $-1$
13 $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ $-2$
16 $[16, 2, 2]$ $-7$
17 $[17, 17, -2w^{3} + 5w^{2} + 14w - 1]$ $\phantom{-}6$
17 $[17, 17, -w^{3} + 3w^{2} + 5w - 4]$ $\phantom{-}6$
17 $[17, 17, -w^{3} + 2w^{2} + 8w + 1]$ $\phantom{-}6$
17 $[17, 17, w - 1]$ $\phantom{-}6$
23 $[23, 23, 2w^{3} - 6w^{2} - 11w + 7]$ $\phantom{-}0$
23 $[23, 23, w^{3} - 3w^{2} - 7w + 4]$ $\phantom{-}0$
23 $[23, 23, -w^{2} + 2w + 5]$ $\phantom{-}0$
23 $[23, 23, 3w^{3} - 8w^{2} - 20w + 5]$ $\phantom{-}0$
61 $[61, 61, -w^{3} + 2w^{2} + 9w + 1]$ $-2$
61 $[61, 61, -2w^{3} + 5w^{2} + 13w - 2]$ $-2$
61 $[61, 61, w^{3} - 2w^{2} - 9w - 2]$ $-2$
61 $[61, 61, 2w^{3} - 5w^{2} - 13w + 1]$ $-2$
79 $[79, 79, 4w^{3} - 10w^{2} - 28w + 5]$ $-8$
79 $[79, 79, w^{3} - 3w^{2} - 4w + 4]$ $-8$
79 $[79, 79, w^{3} - 4w^{2} - 2w + 10]$ $-8$
79 $[79, 79, 2w^{3} - 6w^{2} - 10w + 5]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w^{3} - 2w^{2} - 8w - 3]$ $1$
$3$ $[3, 3, w^{3} - 3w^{2} - 5w + 2]$ $1$