Properties

Label 4.4.12725.1-11.2-e
Base field 4.4.12725.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, w^{2} - 5]$
Dimension $2$
CM no
Base change no

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Base field 4.4.12725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 10x^{2} + 11x + 29\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, w^{2} - 5]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{2} - 9x + 19\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w - 1]$ $\phantom{-}e$
11 $[11, 11, w^{2} - 5]$ $-1$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}3e - 15$
11 $[11, 11, w - 2]$ $\phantom{-}2e - 12$
16 $[16, 2, 2]$ $-4e + 19$
19 $[19, 19, w^{2} - 2w - 5]$ $-2e + 14$
19 $[19, 19, -w^{2} + 6]$ $-4e + 16$
25 $[25, 5, -2w^{2} + 2w + 11]$ $\phantom{-}3e - 18$
29 $[29, 29, w]$ $-e + 10$
29 $[29, 29, 2w^{2} - w - 10]$ $-4e + 24$
29 $[29, 29, -2w^{2} + 3w + 9]$ $-e + 10$
29 $[29, 29, w - 1]$ $\phantom{-}e - 3$
31 $[31, 31, w^{3} - 6w - 6]$ $-3e + 16$
31 $[31, 31, -w^{3} + 3w^{2} + 3w - 11]$ $\phantom{-}5e - 25$
41 $[41, 41, w^{3} - 4w^{2} - 2w + 16]$ $-4e + 14$
41 $[41, 41, w^{3} - 5w^{2} - 2w + 24]$ $-2e + 12$
59 $[59, 59, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}4e - 8$
59 $[59, 59, 2w^{2} - w - 13]$ $\phantom{-}5e - 31$
61 $[61, 61, w^{3} - w^{2} - 6w + 3]$ $\phantom{-}2e - 4$
61 $[61, 61, -w^{3} + 2w^{2} + 5w - 3]$ $-3e + 23$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, w^{2} - 5]$ $1$