Properties

Base field 5.5.160801.1
Weight [2, 2, 2, 2, 2]
Level norm 27
Level $[27, 27, w^{4} - w^{3} - 5w^{2} + 4w + 1]$
Label 5.5.160801.1-27.3-i
Dimension 8
CM no
Base change no

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Base field 5.5.160801.1

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

Form

Weight [2, 2, 2, 2, 2]
Level $[27, 27, w^{4} - w^{3} - 5w^{2} + 4w + 1]$
Label 5.5.160801.1-27.3-i
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 24

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 48x^{6} \) \(\mathstrut +\mathstrut 716x^{4} \) \(\mathstrut -\mathstrut 3952x^{2} \) \(\mathstrut +\mathstrut 6400\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}0$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $-\frac{5}{272}e^{6} + \frac{12}{17}e^{4} - \frac{441}{68}e^{2} + \frac{231}{17}$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $\phantom{-}e$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-\frac{49}{5440}e^{7} + \frac{259}{680}e^{5} - \frac{5811}{1360}e^{3} + \frac{4093}{340}e$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $-\frac{1}{272}e^{6} + \frac{13}{68}e^{4} - \frac{197}{68}e^{2} + \frac{206}{17}$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{21}{5440}e^{7} - \frac{111}{680}e^{5} + \frac{2539}{1360}e^{3} - \frac{1827}{340}e$
23 $[23, 23, -w^{2} + 3]$ $-\frac{43}{5440}e^{7} + \frac{203}{680}e^{5} - \frac{3337}{1360}e^{3} + \frac{511}{340}e$
31 $[31, 31, w^{3} - 4w + 2]$ $\phantom{-}\frac{3}{136}e^{6} - \frac{61}{68}e^{4} + \frac{319}{34}e^{2} - \frac{335}{17}$
32 $[32, 2, 2]$ $\phantom{-}\frac{19}{5440}e^{7} - \frac{8}{85}e^{5} - \frac{99}{1360}e^{3} + \frac{2257}{340}e$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}\frac{1}{136}e^{6} - \frac{13}{34}e^{4} + \frac{197}{34}e^{2} - \frac{344}{17}$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $\phantom{-}\frac{5}{1088}e^{7} - \frac{3}{17}e^{5} + \frac{475}{272}e^{3} - \frac{333}{68}e$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-\frac{43}{2720}e^{7} + \frac{203}{340}e^{5} - \frac{3677}{680}e^{3} + \frac{1871}{170}e$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-\frac{11}{2720}e^{7} + \frac{23}{170}e^{5} - \frac{569}{680}e^{3} - \frac{63}{170}e$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $\phantom{-}\frac{21}{1360}e^{7} - \frac{111}{170}e^{5} + \frac{2539}{340}e^{3} - \frac{1827}{85}e$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $\phantom{-}\frac{3}{136}e^{6} - \frac{61}{68}e^{4} + \frac{151}{17}e^{2} - \frac{216}{17}$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}\frac{11}{5440}e^{7} - \frac{23}{340}e^{5} + \frac{229}{1360}e^{3} + \frac{913}{340}e$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $\phantom{-}\frac{1}{16}e^{6} - \frac{5}{2}e^{4} + \frac{103}{4}e^{2} - 64$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{1}{272}e^{7} + \frac{13}{68}e^{5} - \frac{107}{34}e^{3} + \frac{497}{34}e$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{5440}e^{7} + \frac{19}{680}e^{5} - \frac{1401}{1360}e^{3} + \frac{1953}{340}e$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-\frac{1}{68}e^{6} + \frac{13}{17}e^{4} - \frac{197}{17}e^{2} + \frac{722}{17}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $-1$