Properties

Label 4.4.17417.1-8.2-b
Base field 4.4.17417.1
Weight $[2, 2, 2, 2]$
Level norm $8$
Level $[8, 8, -w^{2} + w + 4]$
Dimension $4$
CM no
Base change no

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Base field 4.4.17417.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 3x + 4\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[8, 8, -w^{2} + w + 4]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $8$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} + 4x^{3} - 5x^{2} - 18x + 17\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 3w^{2} - w + 2]$ $\phantom{-}0$
5 $[5, 5, w^{2} - 2w - 3]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 3w^{2} - 3w + 5]$ $-e^{2} - 2e + 4$
8 $[8, 2, w^{3} - 2w^{2} - 3w + 3]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e + \frac{8}{3}$
13 $[13, 13, -w^{2} + w + 3]$ $-\frac{1}{3}e^{3} - 2e^{2} - \frac{1}{3}e + \frac{16}{3}$
17 $[17, 17, -w^{2} + 3w + 1]$ $\phantom{-}\frac{2}{3}e^{3} + 3e^{2} - \frac{4}{3}e - \frac{29}{3}$
23 $[23, 23, w^{2} - 3]$ $\phantom{-}2e^{2} + 4e - 12$
25 $[25, 5, -w^{2} + 2w + 1]$ $-\frac{1}{3}e^{3} + \frac{11}{3}e - \frac{8}{3}$
37 $[37, 37, w^{3} - 4w^{2} - 2w + 9]$ $-e^{3} - 2e^{2} + 3e - 4$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}\frac{4}{3}e^{3} + 2e^{2} - \frac{29}{3}e - \frac{4}{3}$
49 $[49, 7, -w^{3} + 2w^{2} + 2w - 1]$ $-e + 2$
49 $[49, 7, w^{2} + w - 3]$ $\phantom{-}2e^{2} + 3e - 12$
59 $[59, 59, w^{3} - 3w^{2} - 4w + 5]$ $\phantom{-}\frac{4}{3}e^{3} + 6e^{2} + \frac{4}{3}e - \frac{46}{3}$
67 $[67, 67, -w^{3} + 3w^{2} + w - 5]$ $-\frac{4}{3}e^{3} - 6e^{2} + \frac{2}{3}e + \frac{64}{3}$
71 $[71, 71, 2w - 3]$ $\phantom{-}\frac{8}{3}e^{3} + 10e^{2} - \frac{10}{3}e - \frac{68}{3}$
71 $[71, 71, w^{3} - 4w^{2} + 2w + 5]$ $-\frac{2}{3}e^{3} - 2e^{2} + \frac{10}{3}e - \frac{4}{3}$
79 $[79, 79, -w^{3} + 5w^{2} - 4w - 5]$ $\phantom{-}2e^{2} + 4e - 16$
79 $[79, 79, -2w^{3} + 7w^{2} + 5w - 15]$ $-\frac{4}{3}e^{3} - 6e^{2} + \frac{8}{3}e + \frac{58}{3}$
81 $[81, 3, -3]$ $\phantom{-}\frac{4}{3}e^{3} + 7e^{2} + \frac{4}{3}e - \frac{61}{3}$
83 $[83, 83, -2w^{3} + 6w^{2} + 2w - 5]$ $\phantom{-}\frac{4}{3}e^{3} + 4e^{2} - \frac{20}{3}e - \frac{46}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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