Properties

Label 4.4.1600.1-41.2-a
Base field \(\Q(\sqrt{2}, \sqrt{5})\)
Weight $[2, 2, 2, 2]$
Level norm $41$
Level $[41,41,w^{3} + w^{2} - 5w - 3]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{2}, \sqrt{5})\)

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

Form

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

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 $[4, 2, \frac{1}{2}w^{3} - 2w]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 3]$ $-3e + 4$
9 $[9, 3, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 3]$ $\phantom{-}2e$
25 $[25, 5, w^{2} - 3]$ $-2e + 1$
31 $[31, 31, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w]$ $-3e - 2$
31 $[31, 31, -\frac{1}{2}w^{2} - w + 3]$ $\phantom{-}2e - 6$
31 $[31, 31, -\frac{1}{2}w^{2} + w + 3]$ $\phantom{-}2e - 6$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w]$ $-2e + 7$
41 $[41, 41, \frac{1}{2}w^{3} - w^{2} - w + 3]$ $\phantom{-}4e - 6$
41 $[41, 41, w^{3} + w^{2} - 5w - 3]$ $-1$
41 $[41, 41, -\frac{3}{2}w^{2} - w + 5]$ $-6e + 2$
41 $[41, 41, -\frac{1}{2}w^{3} - w^{2} + w + 3]$ $\phantom{-}7$
49 $[49, 7, -\frac{1}{2}w^{3} + 2w - 3]$ $-2e - 3$
49 $[49, 7, \frac{1}{2}w^{3} - 2w - 3]$ $\phantom{-}4e + 2$
71 $[71, 71, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 5]$ $-10e + 10$
71 $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 5]$ $-4e + 15$
71 $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 5]$ $\phantom{-}2$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 5]$ $\phantom{-}5e - 2$
79 $[79, 79, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 2w - 4]$ $\phantom{-}3e - 12$
79 $[79, 79, -w^{3} - \frac{1}{2}w^{2} + 6w]$ $-6e + 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41,41,w^{3} + w^{2} - 5w - 3]$ $1$