Properties

Label 5.5.81589.1-17.1-a
Base field 5.5.81589.1
Weight $[2, 2, 2, 2, 2]$
Level norm $17$
Level $[17, 17, w^{4} - 4w^{2} + 2]$
Dimension $12$
CM no
Base change no

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Base field 5.5.81589.1

Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 8x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2]$
Level: $[17, 17, w^{4} - 4w^{2} + 2]$
Dimension: $12$
CM: no
Base change: no
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{12} - 22x^{10} + 178x^{8} - 644x^{6} + 1006x^{4} - 543x^{2} + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2} - 3]$ $\phantom{-}e$
11 $[11, 11, -w^{4} + 5w^{2} + w - 4]$ $-\frac{1}{3}e^{6} + \frac{11}{3}e^{4} - 10e^{2} + \frac{16}{3}$
13 $[13, 13, -w^{3} + w^{2} + 3w - 4]$ $-\frac{1}{3}e^{7} + \frac{14}{3}e^{5} - 19e^{3} + \frac{58}{3}e$
16 $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{12}e^{11} - \frac{11}{6}e^{9} + \frac{89}{6}e^{7} - \frac{160}{3}e^{5} + \frac{487}{6}e^{3} - \frac{165}{4}e$
17 $[17, 17, w^{4} - 4w^{2} + 2]$ $\phantom{-}1$
31 $[31, 31, w^{4} - 4w^{2} - w + 3]$ $\phantom{-}\frac{1}{6}e^{11} - \frac{10}{3}e^{9} + \frac{71}{3}e^{7} - 70e^{5} + 75e^{3} - \frac{97}{6}e$
43 $[43, 43, -w^{3} + 4w - 2]$ $\phantom{-}\frac{1}{3}e^{7} - \frac{14}{3}e^{5} + 19e^{3} - \frac{64}{3}e$
53 $[53, 53, w^{4} - 3w^{2} - 1]$ $-\frac{1}{6}e^{11} + \frac{11}{3}e^{9} - \frac{89}{3}e^{7} + \frac{320}{3}e^{5} - \frac{481}{3}e^{3} + \frac{145}{2}e$
53 $[53, 53, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{3}e^{6} - \frac{11}{3}e^{4} + 10e^{2} - \frac{10}{3}$
53 $[53, 53, -w^{3} - w^{2} + 3w + 4]$ $-2e^{2} + 8$
61 $[61, 61, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}\frac{1}{3}e^{9} - 6e^{7} + \frac{110}{3}e^{5} - \frac{262}{3}e^{3} + \frac{199}{3}e$
61 $[61, 61, w^{4} - 4w^{2} + w + 1]$ $\phantom{-}\frac{1}{12}e^{11} - \frac{11}{6}e^{9} + \frac{89}{6}e^{7} - \frac{163}{3}e^{5} + \frac{535}{6}e^{3} - \frac{197}{4}e$
61 $[61, 61, w^{3} + w^{2} - 4w - 3]$ $\phantom{-}\frac{1}{3}e^{8} - \frac{14}{3}e^{6} + 18e^{4} - \frac{37}{3}e^{2} - 6$
67 $[67, 67, -2w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{1}{3}e^{8} - \frac{16}{3}e^{6} + \frac{82}{3}e^{4} - \frac{139}{3}e^{2} + \frac{44}{3}$
71 $[71, 71, -2w^{3} + w^{2} + 7w - 3]$ $-\frac{1}{3}e^{10} + \frac{19}{3}e^{8} - 42e^{6} + \frac{338}{3}e^{4} - \frac{305}{3}e^{2} + \frac{35}{3}$
71 $[71, 71, 2w^{4} - 4w^{3} - 7w^{2} + 13w - 1]$ $-\frac{1}{12}e^{11} + \frac{11}{6}e^{9} - \frac{89}{6}e^{7} + \frac{163}{3}e^{5} - \frac{535}{6}e^{3} + \frac{205}{4}e$
73 $[73, 73, -w^{4} + 2w^{3} + 3w^{2} - 7w]$ $-\frac{1}{4}e^{11} + \frac{11}{2}e^{9} - \frac{263}{6}e^{7} + \frac{455}{3}e^{5} - \frac{427}{2}e^{3} + \frac{1141}{12}e$
73 $[73, 73, w^{4} + w^{3} - 3w^{2} - 4w - 2]$ $\phantom{-}\frac{1}{12}e^{11} - \frac{11}{6}e^{9} + \frac{89}{6}e^{7} - \frac{163}{3}e^{5} + \frac{547}{6}e^{3} - \frac{253}{4}e$
79 $[79, 79, w^{4} - w^{3} - 5w^{2} + 4w + 6]$ $-\frac{1}{4}e^{11} + \frac{31}{6}e^{9} - \frac{77}{2}e^{7} + \frac{373}{3}e^{5} - \frac{997}{6}e^{3} + \frac{929}{12}e$
83 $[83, 83, -2w^{4} + w^{3} + 9w^{2} - 3w - 6]$ $-2e^{4} + 14e^{2} - 8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, w^{4} - 4w^{2} + 2]$ $-1$