Properties

Base field 6.6.434581.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 64
Level $[64, 2, -2]$
Label 6.6.434581.1-64.1-b
Dimension 8
CM no
Base change yes

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Base field 6.6.434581.1

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

Form

Weight [2, 2, 2, 2, 2, 2]
Level $[64, 2, -2]$
Label 6.6.434581.1-64.1-b
Dimension 8
Is CM no
Is base change yes
Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut x^{7} \) \(\mathstrut -\mathstrut 73x^{6} \) \(\mathstrut +\mathstrut 105x^{5} \) \(\mathstrut +\mathstrut 1154x^{4} \) \(\mathstrut -\mathstrut 3116x^{3} \) \(\mathstrut +\mathstrut 1968x^{2} \) \(\mathstrut -\mathstrut 240x \) \(\mathstrut -\mathstrut 32\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 2]$ $\phantom{-}e$
27 $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ $-\frac{73819}{4112952}e^{7} + \frac{5393}{685492}e^{6} + \frac{2720603}{2056476}e^{5} - \frac{1176551}{1028238}e^{4} - \frac{89670745}{4112952}e^{3} + \frac{22427675}{514119}e^{2} - \frac{3892525}{514119}e - \frac{869167}{514119}$
27 $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ $-\frac{73819}{4112952}e^{7} + \frac{5393}{685492}e^{6} + \frac{2720603}{2056476}e^{5} - \frac{1176551}{1028238}e^{4} - \frac{89670745}{4112952}e^{3} + \frac{22427675}{514119}e^{2} - \frac{3892525}{514119}e - \frac{869167}{514119}$
29 $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ $\phantom{-}\frac{13871}{4112952}e^{7} - \frac{2043}{1370984}e^{6} - \frac{1065077}{4112952}e^{5} + \frac{829225}{4112952}e^{4} + \frac{4941689}{1028238}e^{3} - \frac{3916054}{514119}e^{2} - \frac{4259488}{514119}e + \frac{3861734}{514119}$
29 $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ $\phantom{-}\frac{13871}{4112952}e^{7} - \frac{2043}{1370984}e^{6} - \frac{1065077}{4112952}e^{5} + \frac{829225}{4112952}e^{4} + \frac{4941689}{1028238}e^{3} - \frac{3916054}{514119}e^{2} - \frac{4259488}{514119}e + \frac{3861734}{514119}$
43 $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ $-\frac{172735}{8225904}e^{7} + \frac{15607}{2741968}e^{6} + \frac{12721777}{8225904}e^{5} - \frac{9002813}{8225904}e^{4} - \frac{26324519}{1028238}e^{3} + \frac{24431785}{514119}e^{2} + \frac{126335}{1028238}e - \frac{2536517}{514119}$
43 $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ $-\frac{172735}{8225904}e^{7} + \frac{15607}{2741968}e^{6} + \frac{12721777}{8225904}e^{5} - \frac{9002813}{8225904}e^{4} - \frac{26324519}{1028238}e^{3} + \frac{24431785}{514119}e^{2} + \frac{126335}{1028238}e - \frac{2536517}{514119}$
49 $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ $-\frac{93843}{2741968}e^{7} + \frac{122043}{2741968}e^{6} + \frac{6886707}{2741968}e^{5} - \frac{11787555}{2741968}e^{4} - \frac{55008367}{1370984}e^{3} + \frac{80089373}{685492}e^{2} - \frac{12497180}{171373}e + \frac{1194445}{171373}$
64 $[64, 2, -2]$ $-1$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ $-\frac{39851}{1028238}e^{7} + \frac{11355}{342746}e^{6} + \frac{2912495}{1028238}e^{5} - \frac{3761281}{1028238}e^{4} - \frac{23293771}{514119}e^{3} + \frac{58688077}{514119}e^{2} - \frac{28321397}{514119}e + \frac{161038}{514119}$
71 $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ $\phantom{-}\frac{143999}{2056476}e^{7} - \frac{31587}{685492}e^{6} - \frac{10527827}{2056476}e^{5} + \frac{11467351}{2056476}e^{4} + \frac{84489829}{1028238}e^{3} - \frac{194077801}{1028238}e^{2} + \frac{41612164}{514119}e - \frac{2053760}{514119}$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ $-\frac{39851}{1028238}e^{7} + \frac{11355}{342746}e^{6} + \frac{2912495}{1028238}e^{5} - \frac{3761281}{1028238}e^{4} - \frac{23293771}{514119}e^{3} + \frac{58688077}{514119}e^{2} - \frac{28321397}{514119}e + \frac{161038}{514119}$
71 $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ $\phantom{-}\frac{143999}{2056476}e^{7} - \frac{31587}{685492}e^{6} - \frac{10527827}{2056476}e^{5} + \frac{11467351}{2056476}e^{4} + \frac{84489829}{1028238}e^{3} - \frac{194077801}{1028238}e^{2} + \frac{41612164}{514119}e - \frac{2053760}{514119}$
83 $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ $-\frac{95755}{2741968}e^{7} + \frac{18663}{2741968}e^{6} + \frac{6939079}{2741968}e^{5} - \frac{4539551}{2741968}e^{4} - \frac{54915933}{1370984}e^{3} + \frac{53341699}{685492}e^{2} - \frac{4520565}{171373}e + \frac{584977}{171373}$
83 $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ $\phantom{-}\frac{176551}{4112952}e^{7} - \frac{11625}{342746}e^{6} - \frac{6422831}{2056476}e^{5} + \frac{4030919}{1028238}e^{4} + \frac{201461353}{4112952}e^{3} - \frac{260267639}{2056476}e^{2} + \frac{41383033}{514119}e - \frac{3185288}{514119}$
83 $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ $-\frac{95755}{2741968}e^{7} + \frac{18663}{2741968}e^{6} + \frac{6939079}{2741968}e^{5} - \frac{4539551}{2741968}e^{4} - \frac{54915933}{1370984}e^{3} + \frac{53341699}{685492}e^{2} - \frac{4520565}{171373}e + \frac{584977}{171373}$
83 $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ $\phantom{-}\frac{176551}{4112952}e^{7} - \frac{11625}{342746}e^{6} - \frac{6422831}{2056476}e^{5} + \frac{4030919}{1028238}e^{4} + \frac{201461353}{4112952}e^{3} - \frac{260267639}{2056476}e^{2} + \frac{41383033}{514119}e - \frac{3185288}{514119}$
97 $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ $-\frac{77831}{1370984}e^{7} + \frac{36067}{685492}e^{6} + \frac{2847971}{685492}e^{5} - \frac{966129}{171373}e^{4} - \frac{91260433}{1370984}e^{3} + \frac{58657355}{342746}e^{2} - \frac{29024577}{342746}e - \frac{7320}{171373}$
97 $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ $-\frac{146479}{2741968}e^{7} + \frac{152837}{2741968}e^{6} + \frac{10763545}{2741968}e^{5} - \frac{15720085}{2741968}e^{4} - \frac{10853584}{171373}e^{3} + \frac{57313289}{342746}e^{2} - \frac{29316571}{342746}e + \frac{294399}{171373}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
64 $[64, 2, -2]$ $1$