Properties

Label 4.4.4400.1-25.1-a
Base field 4.4.4400.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25,5,-2w^{2} - w + 8]$
Dimension $2$
CM no
Base change no

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Base field 4.4.4400.1

Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[25,5,-2w^{2} - w + 8]$
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:

\(x^{2} - 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $\phantom{-}2e$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $\phantom{-}0$
11 $[11, 11, w]$ $-e$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $\phantom{-}6$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $\phantom{-}6$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $-2e$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $-2e$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $-e$
41 $[41, 41, w^{3} - 5w + 2]$ $\phantom{-}4e$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $-e$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $-e$
59 $[59, 59, -3w^{2} - w + 10]$ $-3$
59 $[59, 59, -3w^{2} + w + 10]$ $-3$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $-2e$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $\phantom{-}8e$
71 $[71, 71, 2w^{2} + w - 9]$ $-6$
71 $[71, 71, 2w^{2} - w - 9]$ $-6$
81 $[81, 3, -3]$ $-1$
101 $[101, 101, 2w^{2} - w - 10]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5,5,-w + 1]$ $1$