Properties

Label 4.4.3981.1-41.1-c
Base field 4.4.3981.1
Weight $[2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, w^{3} - 5w + 1]$
Dimension $2$
CM no
Base change no

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Base field 4.4.3981.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[41, 41, w^{3} - 5w + 1]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $9$

Hecke eigenvalues ($q$-expansion)

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

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

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} - w^{2} - 3w + 1]$ $-2$
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}e - 2$
13 $[13, 13, -w^{3} + w^{2} + 4w]$ $\phantom{-}e + 2$
16 $[16, 2, 2]$ $-2e - 1$
23 $[23, 23, w^{2} - 2w - 2]$ $-4e - 4$
37 $[37, 37, w^{3} - 4w + 1]$ $\phantom{-}2e - 2$
37 $[37, 37, w^{3} - w^{2} - 5w + 1]$ $-e - 4$
41 $[41, 41, w^{3} - 5w + 1]$ $\phantom{-}1$
43 $[43, 43, 2w^{3} - w^{2} - 7w]$ $\phantom{-}e - 2$
53 $[53, 53, 2w - 3]$ $-4e - 4$
59 $[59, 59, -2w^{3} + w^{2} + 9w - 1]$ $\phantom{-}4$
67 $[67, 67, -w - 3]$ $\phantom{-}e - 10$
67 $[67, 67, w^{3} + w^{2} - 5w - 4]$ $\phantom{-}6e + 8$
71 $[71, 71, 2w^{3} - 3w^{2} - 7w + 5]$ $\phantom{-}0$
73 $[73, 73, w^{3} - 6w]$ $-e - 12$
73 $[73, 73, -w^{3} - w^{2} + 5w + 3]$ $-6$
79 $[79, 79, w^{3} - 3w - 4]$ $\phantom{-}2e + 4$
83 $[83, 83, w^{3} - 2w^{2} - 3w + 1]$ $\phantom{-}6$
83 $[83, 83, -2w^{3} + 2w^{2} + 6w - 3]$ $-3e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, w^{3} - 5w + 1]$ $-1$