Properties

Label 4.4.11661.1-9.1-a
Base field 4.4.11661.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{3} - 2w^{2} - 3w + 3]$
Dimension $3$
CM no
Base change no

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Base field 4.4.11661.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, w^{3} - 2w^{2} - 3w + 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} - 2x^{2} - 5x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
3 $[3, 3, w - 2]$ $-1$
3 $[3, 3, w - 1]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}e^{2} - e - 3$
23 $[23, 23, -w^{3} + 4w + 1]$ $\phantom{-}e^{2} - 2e$
25 $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ $-2e + 2$
25 $[25, 5, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}e^{2} - 6$
29 $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ $-e + 2$
29 $[29, 29, w^{3} - w^{2} - 5w + 1]$ $-2e - 2$
43 $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}2e^{2} - 4e - 4$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $-2e^{2} + e + 8$
61 $[61, 61, -w^{2} + 2w + 4]$ $-e^{2} + 4e + 6$
61 $[61, 61, w^{2} - 5]$ $\phantom{-}2e^{2} - 5e - 6$
79 $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ $\phantom{-}3e^{2} - 6e - 8$
79 $[79, 79, -w^{3} + w^{2} + 6w - 4]$ $\phantom{-}2e$
101 $[101, 101, -w^{3} + 3w^{2} + w - 7]$ $-3e^{2} + 6e + 6$
101 $[101, 101, w^{3} - 4w - 4]$ $-4e^{2} + 4e + 14$
103 $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ $\phantom{-}2e^{2} - e - 4$
103 $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ $-2e^{2} + 4e + 8$
107 $[107, 107, 2w^{2} - 3w - 4]$ $-2e^{2} + 4e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$
$3$ $[3, 3, w - 2]$ $1$