Properties

Label 4.4.8000.1-41.1-a
Base field 4.4.8000.1
Weight $[2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$
Dimension $8$
CM no
Base change no

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Base field 4.4.8000.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} + 20\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$
Dimension: $8$
CM: no
Base change: no
Newspace dimension: $28$

Hecke eigenvalues ($q$-expansion)

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

\(x^{8} - 16x^{6} + 76x^{4} - 112x^{2} + 4\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ $-\frac{1}{4}e^{5} + 3e^{3} - \frac{15}{2}e$
5 $[5, 5, w^{2} - w - 5]$ $\phantom{-}e$
11 $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ $\phantom{-}e^{2} - 4$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $\phantom{-}\frac{1}{4}e^{4} - 3e^{2} + \frac{7}{2}$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{13}{4}e^{4} + \frac{17}{2}e^{2} + \frac{1}{2}$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ $-\frac{1}{4}e^{6} + \frac{13}{4}e^{4} - \frac{19}{2}e^{2} + \frac{3}{2}$
29 $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{13}{4}e^{5} + \frac{19}{2}e^{3} - \frac{7}{2}e$
29 $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{4}e^{5} - 2e^{3} - \frac{1}{2}e$
29 $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ $-\frac{3}{4}e^{7} + \frac{43}{4}e^{5} - \frac{83}{2}e^{3} + \frac{87}{2}e$
29 $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ $\phantom{-}\frac{1}{4}e^{5} - 4e^{3} + \frac{27}{2}e$
41 $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ $\phantom{-}1$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ $\phantom{-}\frac{3}{4}e^{6} - \frac{19}{2}e^{4} + \frac{55}{2}e^{2} - 11$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{2}e^{4} + \frac{23}{2}e^{2} - 5$
41 $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ $-\frac{1}{4}e^{6} + 3e^{4} - \frac{13}{2}e^{2} - 4$
79 $[79, 79, -w^{3} - w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{4}e^{7} - 4e^{5} + \frac{35}{2}e^{3} - 20e$
79 $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ $-\frac{1}{2}e^{7} + \frac{29}{4}e^{5} - 27e^{3} + \frac{39}{2}e$
79 $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ $-\frac{1}{4}e^{7} + \frac{9}{2}e^{5} - \frac{51}{2}e^{3} + 47e$
79 $[79, 79, w^{3} - w^{2} - 6w + 9]$ $\phantom{-}e^{7} - \frac{57}{4}e^{5} + 55e^{3} - \frac{119}{2}e$
81 $[81, 3, -3]$ $-\frac{3}{4}e^{6} + \frac{17}{2}e^{4} - \frac{33}{2}e^{2} - 13$
109 $[109, 109, w^{2} - w - 7]$ $\phantom{-}2e^{5} - 24e^{3} + 59e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ $-1$