Properties

Label 4.4.8957.1-9.2-a
Base field 4.4.8957.1
Weight $[2, 2, 2, 2]$
Level norm $9$
Level $[9, 3, w^{3} - w^{2} - 4w]$
Dimension $2$
CM no
Base change no

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Base field 4.4.8957.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[9, 3, w^{3} - w^{2} - 4w]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 2x - 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + w^{2} + 5w]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $-e + 2$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $-1$
13 $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ $\phantom{-}e - 2$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ $-e$
16 $[16, 2, 2]$ $-1$
23 $[23, 23, -w^{2} + 2]$ $-2e + 4$
23 $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}2e$
49 $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}2e + 6$
49 $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ $-2e + 10$
53 $[53, 53, w^{3} - 3w^{2} + 3]$ $\phantom{-}2$
53 $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ $\phantom{-}2$
53 $[53, 53, -w^{3} + w^{2} + 6w - 1]$ $\phantom{-}4$
61 $[61, 61, -w - 3]$ $\phantom{-}4e - 10$
61 $[61, 61, -w^{3} + w^{2} + 5w - 4]$ $-4e - 2$
79 $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}2e - 6$
79 $[79, 79, w^{2} - 5]$ $-2e - 2$
101 $[101, 101, w^{3} - 6w]$ $\phantom{-}4e - 6$
101 $[101, 101, w^{2} - 2w - 4]$ $-4e + 2$
103 $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ $-6e + 12$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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