Properties

Label 4.4.9792.1-9.1-d
Base field 4.4.9792.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{3} - 4w^{2} - w + 9]$
Dimension $2$
CM no
Base change no

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Base field 4.4.9792.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 2x + 7\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, w^{3} - 4w^{2} - w + 9]$
Dimension: $2$
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:

\(x^{2} + x - 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ $-3$
7 $[7, 7, w]$ $-e - 1$
7 $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ $\phantom{-}e$
9 $[9, 3, w^{3} - 4w^{2} - w + 9]$ $-1$
17 $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ $\phantom{-}7$
17 $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ $\phantom{-}e + 3$
17 $[17, 17, -w + 2]$ $-e + 2$
23 $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ $\phantom{-}2e - 1$
23 $[23, 23, -w^{2} + 2w + 3]$ $-2e - 3$
31 $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ $\phantom{-}2e + 3$
31 $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ $-2e + 1$
41 $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ $-3e - 1$
41 $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ $\phantom{-}3e + 2$
49 $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ $-7$
71 $[71, 71, w^{2} - 2w - 2]$ $-2e - 4$
71 $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ $\phantom{-}2e - 2$
73 $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ $-e + 10$
73 $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ $\phantom{-}e + 11$
79 $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ $-e - 7$
79 $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ $\phantom{-}e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w^{3} - 4w^{2} - w + 9]$ $1$