Properties

Label 6.6.1922000.1-44.2-d
Base field 6.6.1922000.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $44$
Level $[44,22,3w^{5} - 3w^{4} - 25w^{3} + 40w + 12]$
Dimension $9$
CM no
Base change no

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Base field 6.6.1922000.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 8x^{4} - x^{3} + 12x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[44,22,3w^{5} - 3w^{4} - 25w^{3} + 40w + 12]$
Dimension: $9$
CM: no
Base change: no
Newspace dimension: $46$

Hecke eigenvalues ($q$-expansion)

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

\(x^{9} - 10x^{8} + 9x^{7} + 145x^{6} - 283x^{5} - 635x^{4} + 1492x^{3} + 634x^{2} - 1983x + 745\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ $-1$
11 $[11, 11, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ $-\frac{56660}{830269}e^{8} + \frac{479652}{830269}e^{7} + \frac{27939}{830269}e^{6} - \frac{6345355}{830269}e^{5} + \frac{4595317}{830269}e^{4} + \frac{25872120}{830269}e^{3} - \frac{1700924}{75479}e^{2} - \frac{29372468}{830269}e + \frac{21602374}{830269}$
11 $[11, 11, -w^{5} + w^{4} + 8w^{3} + w^{2} - 12w - 5]$ $\phantom{-}1$
11 $[11, 11, w - 1]$ $\phantom{-}e$
31 $[31, 31, -4w^{5} + 6w^{4} + 28w^{3} - 8w^{2} - 39w - 11]$ $\phantom{-}\frac{15469}{830269}e^{8} - \frac{88867}{830269}e^{7} - \frac{250891}{830269}e^{6} + \frac{806637}{830269}e^{5} + \frac{3120912}{830269}e^{4} + \frac{845633}{830269}e^{3} - \frac{1635053}{75479}e^{2} - \frac{15613049}{830269}e + \frac{20262512}{830269}$
41 $[41, 41, -4w^{5} + 5w^{4} + 31w^{3} - 4w^{2} - 49w - 16]$ $-\frac{47059}{830269}e^{8} + \frac{251078}{830269}e^{7} + \frac{1185977}{830269}e^{6} - \frac{4832218}{830269}e^{5} - \frac{9733285}{830269}e^{4} + \frac{23280819}{830269}e^{3} + \frac{2689704}{75479}e^{2} - \frac{13916173}{830269}e - \frac{10726212}{830269}$
41 $[41, 41, w^{4} - 3w^{3} - 3w^{2} + 8w + 1]$ $\phantom{-}\frac{138896}{830269}e^{8} - \frac{1155184}{830269}e^{7} - \frac{437524}{830269}e^{6} + \frac{17302840}{830269}e^{5} - \frac{10440409}{830269}e^{4} - \frac{81294212}{830269}e^{3} + \frac{5395928}{75479}e^{2} + \frac{110863020}{830269}e - \frac{82340425}{830269}$
41 $[41, 41, -w^{2} + w + 2]$ $\phantom{-}\frac{5568}{75479}e^{8} - \frac{37379}{75479}e^{7} - \frac{100061}{75479}e^{6} + \frac{766499}{75479}e^{5} + \frac{394410}{75479}e^{4} - \frac{4444891}{75479}e^{3} + \frac{455138}{75479}e^{2} + \frac{6656376}{75479}e - \frac{3337161}{75479}$
59 $[59, 59, w^{2} - w - 4]$ $\phantom{-}\frac{17425}{830269}e^{8} - \frac{42298}{830269}e^{7} - \frac{720534}{830269}e^{6} + \frac{571137}{830269}e^{5} + \frac{9214173}{830269}e^{4} - \frac{222773}{830269}e^{3} - \frac{3517815}{75479}e^{2} - \frac{14345731}{830269}e + \frac{26169112}{830269}$
59 $[59, 59, 4w^{5} - 5w^{4} - 31w^{3} + 4w^{2} + 49w + 14]$ $-\frac{60879}{830269}e^{8} + \frac{416134}{830269}e^{7} + \frac{936941}{830269}e^{6} - \frac{7553961}{830269}e^{5} - \frac{4002729}{830269}e^{4} + \frac{40152700}{830269}e^{3} + \frac{81303}{75479}e^{2} - \frac{56643094}{830269}e + \frac{23769604}{830269}$
59 $[59, 59, -w^{4} + 3w^{3} + 3w^{2} - 8w - 3]$ $\phantom{-}\frac{67983}{830269}e^{8} - \frac{685056}{830269}e^{7} + \frac{642782}{830269}e^{6} + \frac{9739572}{830269}e^{5} - \frac{17356941}{830269}e^{4} - \frac{47944988}{830269}e^{3} + \frac{7336960}{75479}e^{2} + \frac{88700776}{830269}e - \frac{79165685}{830269}$
71 $[71, 71, 5w^{5} - 7w^{4} - 37w^{3} + 9w^{2} + 55w + 16]$ $-\frac{491}{830269}e^{8} + \frac{60895}{830269}e^{7} - \frac{391901}{830269}e^{6} - \frac{852652}{830269}e^{5} + \frac{6458610}{830269}e^{4} + \frac{5045212}{830269}e^{3} - \frac{2605276}{75479}e^{2} - \frac{17100935}{830269}e + \frac{20049972}{830269}$
71 $[71, 71, -w^{5} + 11w^{3} + 4w^{2} - 19w - 7]$ $-\frac{82963}{830269}e^{8} + \frac{577998}{830269}e^{7} + \frac{943669}{830269}e^{6} - \frac{8114277}{830269}e^{5} - \frac{6035217}{830269}e^{4} + \frac{33132815}{830269}e^{3} + \frac{2167832}{75479}e^{2} - \frac{25860699}{830269}e - \frac{5211428}{830269}$
71 $[71, 71, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ $\phantom{-}\frac{79210}{830269}e^{8} - \frac{729748}{830269}e^{7} + \frac{114071}{830269}e^{6} + \frac{11724212}{830269}e^{5} - \frac{13134782}{830269}e^{4} - \frac{60689837}{830269}e^{3} + \frac{6472334}{75479}e^{2} + \frac{97106541}{830269}e - \frac{86489636}{830269}$
79 $[79, 79, 3w^{5} - 6w^{4} - 17w^{3} + 11w^{2} + 21w + 7]$ $\phantom{-}\frac{61244}{830269}e^{8} - \frac{681229}{830269}e^{7} + \frac{786647}{830269}e^{6} + \frac{11590049}{830269}e^{5} - \frac{23286762}{830269}e^{4} - \frac{66736457}{830269}e^{3} + \frac{11059543}{75479}e^{2} + \frac{135963129}{830269}e - \frac{127328836}{830269}$
79 $[79, 79, -5w^{5} + 8w^{4} + 35w^{3} - 14w^{2} - 52w - 11]$ $-\frac{8273}{830269}e^{8} + \frac{219442}{830269}e^{7} - \frac{894519}{830269}e^{6} - \frac{4016117}{830269}e^{5} + \frac{17258339}{830269}e^{4} + \frac{25631310}{830269}e^{3} - \frac{7656209}{75479}e^{2} - \frac{64496901}{830269}e + \frac{71585325}{830269}$
79 $[79, 79, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 2]$ $-\frac{22798}{830269}e^{8} + \frac{111756}{830269}e^{7} + \frac{634046}{830269}e^{6} - \frac{2170545}{830269}e^{5} - \frac{5497025}{830269}e^{4} + \frac{9583283}{830269}e^{3} + \frac{1544367}{75479}e^{2} - \frac{1887521}{830269}e - \frac{6529579}{830269}$
101 $[101, 101, -2w^{5} + 3w^{4} + 14w^{3} - 3w^{2} - 21w - 9]$ $-\frac{75645}{830269}e^{8} + \frac{642713}{830269}e^{7} + \frac{353890}{830269}e^{6} - \frac{11348633}{830269}e^{5} + \frac{7549643}{830269}e^{4} + \frac{63305647}{830269}e^{3} - \frac{4979116}{75479}e^{2} - \frac{107107294}{830269}e + \frac{75374259}{830269}$
101 $[101, 101, -2w^{5} + 2w^{4} + 17w^{3} - 29w - 9]$ $\phantom{-}\frac{27249}{830269}e^{8} - \frac{159869}{830269}e^{7} - \frac{581715}{830269}e^{6} + \frac{2841851}{830269}e^{5} + \frac{4808718}{830269}e^{4} - \frac{13541761}{830269}e^{3} - \frac{1567696}{75479}e^{2} + \frac{10037393}{830269}e + \frac{12195770}{830269}$
101 $[101, 101, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 9w + 1]$ $\phantom{-}\frac{24151}{830269}e^{8} - \frac{93551}{830269}e^{7} - \frac{957633}{830269}e^{6} + \frac{3174097}{830269}e^{5} + \frac{6728222}{830269}e^{4} - \frac{20323749}{830269}e^{3} - \frac{684442}{75479}e^{2} + \frac{25031147}{830269}e - \frac{19880552}{830269}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,3w^{5} - 4w^{4} - 23w^{3} + 5w^{2} + 36w + 9]$ $1$
$11$ $[11,11,-w^{5} + w^{4} + 8w^{3} + w^{2} - 12w - 5]$ $-1$