Properties

Base field 6.6.300125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 139
Level $[139, 139, -w^{5} - w^{4} + 8w^{3} + 12w^{2} - 3w - 5]$
Label 6.6.300125.1-139.1-b
Dimension 8
CM no
Base change no

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Base field 6.6.300125.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[139, 139, -w^{5} - w^{4} + 8w^{3} + 12w^{2} - 3w - 5]$
Label 6.6.300125.1-139.1-b
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 4x^{7} \) \(\mathstrut -\mathstrut 86x^{6} \) \(\mathstrut +\mathstrut 230x^{5} \) \(\mathstrut +\mathstrut 1887x^{4} \) \(\mathstrut -\mathstrut 3026x^{3} \) \(\mathstrut -\mathstrut 13513x^{2} \) \(\mathstrut +\mathstrut 5886x \) \(\mathstrut +\mathstrut 23413\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
29 $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ $\phantom{-}e$
29 $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ $-\frac{10420688}{36415534529}e^{7} + \frac{54924961}{36415534529}e^{6} + \frac{745145019}{36415534529}e^{5} - \frac{3441133101}{36415534529}e^{4} - \frac{7670573816}{36415534529}e^{3} + \frac{60147393495}{36415534529}e^{2} - \frac{59252990171}{36415534529}e - \frac{309187269012}{36415534529}$
29 $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ $...$
29 $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ $...$
29 $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ $...$
29 $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ $...$
41 $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ $\phantom{-}\frac{1340189}{72831069058}e^{7} - \frac{12874567}{36415534529}e^{6} + \frac{33295425}{36415534529}e^{5} + \frac{341839435}{36415534529}e^{4} - \frac{2959790593}{36415534529}e^{3} + \frac{25497428116}{36415534529}e^{2} + \frac{13115236197}{36415534529}e - \frac{454974466191}{72831069058}$
41 $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ $-\frac{124291177}{72831069058}e^{7} + \frac{873640349}{72831069058}e^{6} + \frac{8595282343}{72831069058}e^{5} - \frac{57007763399}{72831069058}e^{4} - \frac{54252602000}{36415534529}e^{3} + \frac{412446500759}{36415534529}e^{2} + \frac{102227077341}{72831069058}e - \frac{2051383296939}{72831069058}$
41 $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ $...$
41 $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ $...$
41 $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ $-\frac{40842897}{72831069058}e^{7} + \frac{18146599}{36415534529}e^{6} + \frac{3393452025}{72831069058}e^{5} + \frac{1153559839}{36415534529}e^{4} - \frac{55331778757}{72831069058}e^{3} - \frac{112307558857}{72831069058}e^{2} + \frac{166606413165}{72831069058}e + \frac{805386731443}{72831069058}$
41 $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ $...$
49 $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ $...$
64 $[64, 2, -2]$ $...$
71 $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ $-\frac{2337387}{1776367538}e^{7} + \frac{8351281}{888183769}e^{6} + \frac{176713919}{1776367538}e^{5} - \frac{560215178}{888183769}e^{4} - \frac{3174177783}{1776367538}e^{3} + \frac{15874565397}{1776367538}e^{2} + \frac{15142989489}{1776367538}e - \frac{28679482617}{1776367538}$
71 $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ $...$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ $-\frac{15388553}{6621006278}e^{7} + \frac{92753525}{6621006278}e^{6} + \frac{576043745}{3310503139}e^{5} - \frac{2974730796}{3310503139}e^{4} - \frac{18543913949}{6621006278}e^{3} + \frac{44438527714}{3310503139}e^{2} + \frac{61030849603}{6621006278}e - \frac{114601927757}{3310503139}$
71 $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ $...$
71 $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ $...$
71 $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
139 $[139, 139, -w^{5} - w^{4} + 8w^{3} + 12w^{2} - 3w - 5]$ $1$