Properties

Label 4.4.2000.1-41.2-a
Base field \(\Q(\zeta_{20})^+\)
Weight $[2, 2, 2, 2]$
Level norm $41$
Level $[41,41,-w^{3} + 3w + 3]$
Dimension $4$
CM no
Base change no

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Base field \(\Q(\zeta_{20})^+\)

Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[41,41,-w^{3} + 3w + 3]$
Dimension: $4$
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:

\(x^{4} - 10x^{2} + 17\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{3} - w^{2} + 3w + 4]$ $\phantom{-}e$
5 $[5, 5, w]$ $-\frac{1}{2}e^{2} + \frac{9}{2}$
19 $[19, 19, -w^{2} + w + 4]$ $-\frac{1}{2}e^{3} + \frac{5}{2}e$
19 $[19, 19, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}e^{3} - 7e$
19 $[19, 19, -w^{3} - w^{2} + 3w + 1]$ $-\frac{1}{2}e^{3} + \frac{5}{2}e$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}e^{3} - 7e$
41 $[41, 41, w + 3]$ $-\frac{7}{2}e^{2} + \frac{35}{2}$
41 $[41, 41, -w^{3} + 3w + 3]$ $-1$
41 $[41, 41, -w^{3} + 3w - 3]$ $\phantom{-}2e^{2} - 8$
41 $[41, 41, w - 3]$ $\phantom{-}2e^{2} - 8$
59 $[59, 59, 2w^{2} + w - 7]$ $-e^{3} + 9e$
59 $[59, 59, -w^{3} - 2w^{2} + 3w + 3]$ $-2e$
59 $[59, 59, 2w^{3} - w^{2} - 7w + 2]$ $-\frac{3}{2}e^{3} + \frac{15}{2}e$
59 $[59, 59, w^{3} - w^{2} - w + 3]$ $-e^{3} + 9e$
61 $[61, 61, 3w^{2} - w - 8]$ $\phantom{-}e^{2} - 5$
61 $[61, 61, w^{3} + 3w^{2} - 3w - 7]$ $\phantom{-}e^{2} - 5$
61 $[61, 61, -w^{3} + 3w^{2} + 3w - 7]$ $\phantom{-}e^{2} - 5$
61 $[61, 61, -3w^{2} - w + 8]$ $\phantom{-}e^{2} - 5$
79 $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ $-e^{3} + 13e$
79 $[79, 79, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}e^{3} - 9e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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