Properties

Label 4.4.8768.1-7.4-c
Base field 4.4.8768.1
Weight $[2, 2, 2, 2]$
Level norm $7$
Level $[7,7,-w + 1]$
Dimension $2$
CM no
Base change no

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Base field 4.4.8768.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[7,7,-w + 1]$
Dimension: $2$
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:

\(x^{2} - 2x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
7 $[7, 7, w]$ $\phantom{-}e + 2$
7 $[7, 7, -w^{2} + 2w + 1]$ $-2e$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}3$
7 $[7, 7, w - 1]$ $-1$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $-2e + 6$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}4e - 2$
31 $[31, 31, w^{2} - 5]$ $-4e + 3$
31 $[31, 31, -w^{2} + 2w + 4]$ $\phantom{-}4e - 2$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $-4e$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $\phantom{-}6$
47 $[47, 47, w^{2} - 2w - 5]$ $-3e + 6$
47 $[47, 47, w^{2} - 6]$ $\phantom{-}2$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $-6e + 2$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}3e - 10$
79 $[79, 79, -w - 3]$ $\phantom{-}6e - 14$
79 $[79, 79, w - 4]$ $-5e + 12$
81 $[81, 3, -3]$ $-e - 6$
89 $[89, 89, w^{2} - 3w - 2]$ $-10e + 10$
89 $[89, 89, w^{2} + w - 4]$ $-4e + 2$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7,7,-w + 1]$ $1$