Properties

Label 4.4.9792.1-7.2-a
Base field 4.4.9792.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7,7,w^{3} - 3w^{2} - 4w + 5]$
Dimension $4$
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: $[7,7,w^{3} - 3w^{2} - 4w + 5]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $4$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 6x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ $-e^{2} + 3$
7 $[7, 7, w]$ $-e^{2} + 4$
7 $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ $-1$
9 $[9, 3, w^{3} - 4w^{2} - w + 9]$ $\phantom{-}e$
17 $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ $\phantom{-}e^{3} - 3e$
17 $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ $\phantom{-}2e^{3} - 9e$
17 $[17, 17, -w + 2]$ $-e^{3} + 8e$
23 $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ $-2e$
23 $[23, 23, -w^{2} + 2w + 3]$ $\phantom{-}2e^{3} - 7e$
31 $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ $\phantom{-}4$
31 $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ $\phantom{-}4$
41 $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ $-3e^{3} + 11e$
41 $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ $-e^{3} + 6e$
49 $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ $-6$
71 $[71, 71, w^{2} - 2w - 2]$ $-e^{3} + 3e$
71 $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ $-2e^{3} + 15e$
73 $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ $-5e^{2} + 14$
73 $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ $\phantom{-}3e^{2} - 6$
79 $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ $\phantom{-}3e^{2} - 4$
79 $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ $\phantom{-}3e^{2} - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7,7,w^{3} - 3w^{2} - 4w + 5]$ $1$