Properties

Label 4.4.4400.1-25.3-c
Base field 4.4.4400.1
Weight $[2, 2, 2, 2]$
Level norm $25$
Level $[25, 5, -2w^{2} + 7]$
Dimension $3$
CM no
Base change yes

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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: $[25, 5, -2w^{2} + 7]$
Dimension: $3$
CM: no
Base change: yes
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 2x^{2} - 7x + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
5 $[5, 5, w + 1]$ $-1$
5 $[5, 5, -w^{3} + w^{2} + 4w - 4]$ $-1$
11 $[11, 11, w]$ $\phantom{-}2e - 2$
29 $[29, 29, w^{3} - 2w^{2} - 3w + 7]$ $-e^{2} + 3e + 2$
29 $[29, 29, -w^{3} - 2w^{2} + 3w + 7]$ $-e^{2} + 3e + 2$
31 $[31, 31, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}e^{2} - 3e - 4$
31 $[31, 31, -w^{3} - w^{2} + 4w + 2]$ $\phantom{-}e^{2} - 3e - 4$
41 $[41, 41, w^{3} + 2w^{2} - 4w - 6]$ $\phantom{-}e^{2} - e - 4$
41 $[41, 41, w^{3} - 5w + 2]$ $\phantom{-}e^{2} - e - 4$
49 $[49, 7, -w^{3} + w^{2} + 4w - 1]$ $-2e^{2} + 2e + 10$
49 $[49, 7, w^{3} + w^{2} - 4w - 1]$ $-2e^{2} + 2e + 10$
59 $[59, 59, -3w^{2} - w + 10]$ $-e^{2} - e + 12$
59 $[59, 59, -3w^{2} + w + 10]$ $-e^{2} - e + 12$
61 $[61, 61, -2w^{3} + 2w^{2} + 7w - 5]$ $-2e^{2} + 4e + 8$
61 $[61, 61, 2w^{3} + w^{2} - 8w - 6]$ $-2e^{2} + 4e + 8$
71 $[71, 71, 2w^{2} + w - 9]$ $\phantom{-}2e^{2} - 6e - 8$
71 $[71, 71, 2w^{2} - w - 9]$ $\phantom{-}2e^{2} - 6e - 8$
81 $[81, 3, -3]$ $-2e^{2} + 4e + 16$
101 $[101, 101, 2w^{2} - w - 10]$ $\phantom{-}6e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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