Properties

Label 2.2.168.1-11.2-b
Base field \(\Q(\sqrt{42}) \)
Weight $[2, 2]$
Level norm $11$
Level $[11,11,-w + 3]$
Dimension $16$
CM no
Base change no

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Base field \(\Q(\sqrt{42}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 42\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[11,11,-w + 3]$
Dimension: $16$
CM: no
Base change: no
Newspace dimension: $80$

Hecke eigenvalues ($q$-expansion)

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

\(x^{16} - 28x^{14} + 308x^{12} - 1725x^{10} + 5310x^{8} - 8957x^{6} + 7646x^{4} - 2584x^{2} + 28\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}\frac{32414}{1502359}e^{14} - \frac{817611}{1502359}e^{12} + \frac{7787850}{1502359}e^{10} - \frac{36050196}{1502359}e^{8} + \frac{87128153}{1502359}e^{6} - \frac{106843533}{1502359}e^{4} + \frac{52694765}{1502359}e^{2} - \frac{1199130}{1502359}$
3 $[3, 3, w]$ $\phantom{-}e$
7 $[7, 7, w - 7]$ $\phantom{-}\frac{53160}{1502359}e^{14} - \frac{1404870}{1502359}e^{12} + \frac{14223050}{1502359}e^{10} - \frac{70655314}{1502359}e^{8} + \frac{181613542}{1502359}e^{6} - \frac{226984559}{1502359}e^{4} + \frac{106901743}{1502359}e^{2} - \frac{2854660}{1502359}$
11 $[11, 11, w + 3]$ $\phantom{-}\frac{1427}{1502359}e^{14} - \frac{141995}{1502359}e^{12} + \frac{2823271}{1502359}e^{10} - \frac{22437862}{1502359}e^{8} + \frac{81574412}{1502359}e^{6} - \frac{131285487}{1502359}e^{4} + \frac{69521140}{1502359}e^{2} + \frac{86720}{1502359}$
11 $[11, 11, w + 8]$ $\phantom{-}1$
13 $[13, 13, w + 4]$ $\phantom{-}\frac{93537}{3004718}e^{15} - \frac{1051557}{1502359}e^{13} + \frac{8183537}{1502359}e^{11} - \frac{51288883}{3004718}e^{9} + \frac{23199643}{1502359}e^{7} + \frac{50158299}{3004718}e^{5} - \frac{39003361}{1502359}e^{3} + \frac{12394301}{1502359}e$
13 $[13, 13, w + 9]$ $-\frac{133469}{3004718}e^{15} + \frac{1723334}{1502359}e^{13} - \frac{17099371}{1502359}e^{11} + \frac{170252011}{3004718}e^{9} - \frac{234442553}{1502359}e^{7} + \frac{731138793}{3004718}e^{5} - \frac{300526302}{1502359}e^{3} + \frac{95408655}{1502359}e$
17 $[17, 17, -w - 5]$ $\phantom{-}\frac{135050}{1502359}e^{15} - \frac{3702951}{1502359}e^{13} + \frac{39236493}{1502359}e^{11} - \frac{205567841}{1502359}e^{9} + \frac{562473992}{1502359}e^{7} - \frac{771418888}{1502359}e^{5} + \frac{452544601}{1502359}e^{3} - \frac{71688496}{1502359}e$
17 $[17, 17, -w + 5]$ $\phantom{-}\frac{11816}{1502359}e^{15} - \frac{437743}{1502359}e^{13} + \frac{6290458}{1502359}e^{11} - \frac{44746489}{1502359}e^{9} + \frac{167243871}{1502359}e^{7} - \frac{321327614}{1502359}e^{5} + \frac{283112330}{1502359}e^{3} - \frac{85245924}{1502359}e$
19 $[19, 19, w + 2]$ $-\frac{74482}{1502359}e^{15} + \frac{2068395}{1502359}e^{13} - \frac{22131587}{1502359}e^{11} + \frac{115712313}{1502359}e^{9} - \frac{305836994}{1502359}e^{7} + \frac{368790789}{1502359}e^{5} - \frac{120059893}{1502359}e^{3} - \frac{49676065}{1502359}e$
19 $[19, 19, w + 17]$ $-\frac{258872}{1502359}e^{15} + \frac{6858219}{1502359}e^{13} - \frac{69711568}{1502359}e^{11} + \frac{349046086}{1502359}e^{9} - \frac{914665222}{1502359}e^{7} + \frac{1206192946}{1502359}e^{5} - \frac{672342742}{1502359}e^{3} + \frac{90234447}{1502359}e$
25 $[25, 5, 5]$ $\phantom{-}\frac{18429}{1502359}e^{14} - \frac{233525}{1502359}e^{12} - \frac{1069399}{1502359}e^{10} + \frac{26669016}{1502359}e^{8} - \frac{130665713}{1502359}e^{6} + \frac{239446960}{1502359}e^{4} - \frac{133777791}{1502359}e^{2} - \frac{1476282}{1502359}$
29 $[29, 29, w + 10]$ $\phantom{-}\frac{153958}{1502359}e^{14} - \frac{3765155}{1502359}e^{12} + \frac{34089720}{1502359}e^{10} - \frac{145104598}{1502359}e^{8} + \frac{305908622}{1502359}e^{6} - \frac{302214180}{1502359}e^{4} + \frac{105923029}{1502359}e^{2} + \frac{4220554}{1502359}$
29 $[29, 29, w + 19]$ $-\frac{419631}{1502359}e^{14} + \frac{11007433}{1502359}e^{12} - \frac{110266181}{1502359}e^{10} + \frac{540148479}{1502359}e^{8} - \frac{1366479153}{1502359}e^{6} + \frac{1683807003}{1502359}e^{4} - \frac{776442209}{1502359}e^{2} + \frac{2492870}{1502359}$
41 $[41, 41, -w - 1]$ $-\frac{39783}{1502359}e^{15} + \frac{901287}{1502359}e^{13} - \frac{7338312}{1502359}e^{11} + \frac{28400119}{1502359}e^{9} - \frac{70411268}{1502359}e^{7} + \frac{163804857}{1502359}e^{5} - \frac{270384069}{1502359}e^{3} + \frac{158519008}{1502359}e$
41 $[41, 41, w - 1]$ $\phantom{-}\frac{75146}{1502359}e^{15} - \frac{1780723}{1502359}e^{13} + \frac{15212319}{1502359}e^{11} - \frac{57546592}{1502359}e^{9} + \frac{91331895}{1502359}e^{7} - \frac{25103749}{1502359}e^{5} - \frac{60385984}{1502359}e^{3} + \frac{31952364}{1502359}e$
47 $[47, 47, -2w + 11]$ $-\frac{197492}{1502359}e^{15} + \frac{5303944}{1502359}e^{13} - \frac{54588122}{1502359}e^{11} + \frac{274054868}{1502359}e^{9} - \frac{697932216}{1502359}e^{7} + \frac{814129139}{1502359}e^{5} - \frac{252205317}{1502359}e^{3} - \frac{100001882}{1502359}e$
47 $[47, 47, 4w - 25]$ $\phantom{-}\frac{352431}{1502359}e^{15} - \frac{9621528}{1502359}e^{13} + \frac{101633209}{1502359}e^{11} - \frac{532665289}{1502359}e^{9} + \frac{1465641881}{1502359}e^{7} - \frac{2021699269}{1502359}e^{5} + \frac{1154045332}{1502359}e^{3} - \frac{140512976}{1502359}e$
53 $[53, 53, w + 25]$ $\phantom{-}\frac{7388}{1502359}e^{14} - \frac{39243}{1502359}e^{12} - \frac{1561615}{1502359}e^{10} + \frac{18606910}{1502359}e^{8} - \frac{74607027}{1502359}e^{6} + \frac{122784467}{1502359}e^{4} - \frac{74006047}{1502359}e^{2} + \frac{1769198}{1502359}$
53 $[53, 53, w + 28]$ $-\frac{330813}{1502359}e^{14} + \frac{8543221}{1502359}e^{12} - \frac{83849056}{1502359}e^{10} + \frac{401005468}{1502359}e^{8} - \frac{992216215}{1502359}e^{6} + \frac{1212145184}{1502359}e^{4} - \frac{582154609}{1502359}e^{2} + \frac{20136694}{1502359}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11,11,-w + 3]$ $-1$