Properties

Label 4.4.8000.1-41.3-b
Base field 4.4.8000.1
Weight $[2, 2, 2, 2]$
Level norm $41$
Level $[41,41,\frac{1}{2}w^{2} - 2w + 1]$
Dimension $20$
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: $[41,41,\frac{1}{2}w^{2} - 2w + 1]$
Dimension: $20$
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:

\(x^{20} - 50x^{18} + 1023x^{16} - 11172x^{14} + 71111x^{12} - 269554x^{10} + 592673x^{8} - 688600x^{6} + 323688x^{4} - 6208x^{2} + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ $\phantom{-}e$
5 $[5, 5, w^{2} - w - 5]$ $...$
11 $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ $...$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $...$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ $...$
29 $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ $...$
29 $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ $...$
29 $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ $...$
29 $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ $...$
41 $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ $...$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ $...$
41 $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ $-1$
41 $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ $...$
79 $[79, 79, -w^{3} - w^{2} + 4w - 1]$ $...$
79 $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ $...$
79 $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ $...$
79 $[79, 79, w^{3} - w^{2} - 6w + 9]$ $...$
81 $[81, 3, -3]$ $...$
109 $[109, 109, w^{2} - w - 7]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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