Properties

Label 6.6.1922000.1-44.1-c
Base field 6.6.1922000.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $44$
Level $[44, 22, 3w^{5} - 5w^{4} - 20w^{3} + 8w^{2} + 28w + 7]$
Dimension $8$
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: $[44, 22, 3w^{5} - 5w^{4} - 20w^{3} + 8w^{2} + 28w + 7]$
Dimension: $8$
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:

\(x^{8} + 11x^{7} + 37x^{6} + 13x^{5} - 141x^{4} - 175x^{3} + 106x^{2} + 189x + 6\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ $\phantom{-}1$
11 $[11, 11, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ $-1$
11 $[11, 11, -w^{5} + w^{4} + 8w^{3} + w^{2} - 12w - 5]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $-\frac{2217}{1163}e^{7} - \frac{20672}{1163}e^{6} - \frac{47396}{1163}e^{5} + \frac{50634}{1163}e^{4} + \frac{228279}{1163}e^{3} + \frac{6173}{1163}e^{2} - \frac{246850}{1163}e - \frac{7067}{1163}$
31 $[31, 31, -4w^{5} + 6w^{4} + 28w^{3} - 8w^{2} - 39w - 11]$ $\phantom{-}\frac{1475}{1163}e^{7} + \frac{13735}{1163}e^{6} + \frac{31625}{1163}e^{5} - \frac{31906}{1163}e^{4} - \frac{147159}{1163}e^{3} - \frac{6188}{1163}e^{2} + \frac{151074}{1163}e + \frac{3533}{1163}$
41 $[41, 41, -4w^{5} + 5w^{4} + 31w^{3} - 4w^{2} - 49w - 16]$ $\phantom{-}\frac{1899}{1163}e^{7} + \frac{17699}{1163}e^{6} + \frac{40637}{1163}e^{5} - \frac{42940}{1163}e^{4} - \frac{195507}{1163}e^{3} - \frac{6844}{1163}e^{2} + \frac{211452}{1163}e + \frac{1565}{1163}$
41 $[41, 41, w^{4} - 3w^{3} - 3w^{2} + 8w + 1]$ $\phantom{-}\frac{227}{1163}e^{7} + \frac{1826}{1163}e^{6} + \frac{2817}{1163}e^{5} - \frac{6626}{1163}e^{4} - \frac{13256}{1163}e^{3} + \frac{4608}{1163}e^{2} + \frac{7326}{1163}e - \frac{132}{1163}$
41 $[41, 41, -w^{2} + w + 2]$ $-\frac{39}{1163}e^{7} + \frac{173}{1163}e^{6} + \frac{3461}{1163}e^{5} + \frac{7768}{1163}e^{4} - \frac{9081}{1163}e^{3} - \frac{26557}{1163}e^{2} + \frac{2922}{1163}e + \frac{9880}{1163}$
59 $[59, 59, w^{2} - w - 4]$ $-\frac{2979}{1163}e^{7} - \frac{27401}{1163}e^{6} - \frac{60915}{1163}e^{5} + \frac{71616}{1163}e^{4} + \frac{297943}{1163}e^{3} - \frac{4300}{1163}e^{2} - \frac{327261}{1163}e - \frac{11737}{1163}$
59 $[59, 59, 4w^{5} - 5w^{4} - 31w^{3} + 4w^{2} + 49w + 14]$ $\phantom{-}\frac{1354}{1163}e^{7} + \frac{12900}{1163}e^{6} + \frac{31061}{1163}e^{5} - \frac{27457}{1163}e^{4} - \frac{142501}{1163}e^{3} - \frac{8634}{1163}e^{2} + \frac{150120}{1163}e - \frac{6131}{1163}$
59 $[59, 59, -w^{4} + 3w^{3} + 3w^{2} - 8w - 3]$ $-\frac{703}{1163}e^{7} - \frac{7110}{1163}e^{6} - \frac{19232}{1163}e^{5} + \frac{10960}{1163}e^{4} + \frac{90201}{1163}e^{3} + \frac{27705}{1163}e^{2} - \frac{97535}{1163}e - \frac{18066}{1163}$
71 $[71, 71, 5w^{5} - 7w^{4} - 37w^{3} + 9w^{2} + 55w + 16]$ $-\frac{4854}{1163}e^{7} - \frac{45117}{1163}e^{6} - \frac{103324}{1163}e^{5} + \frac{106734}{1163}e^{4} + \frac{484635}{1163}e^{3} + \frac{18350}{1163}e^{2} - \frac{508305}{1163}e - \frac{19382}{1163}$
71 $[71, 71, -w^{5} + 11w^{3} + 4w^{2} - 19w - 7]$ $\phantom{-}\frac{6610}{1163}e^{7} + \frac{61512}{1163}e^{6} + \frac{140757}{1163}e^{5} - \frac{149491}{1163}e^{4} - \frac{673897}{1163}e^{3} - \frac{22164}{1163}e^{2} + \frac{720004}{1163}e + \frac{21896}{1163}$
71 $[71, 71, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ $\phantom{-}\frac{1325}{1163}e^{7} + \frac{11806}{1163}e^{6} + \frac{24092}{1163}e^{5} - \frac{37098}{1163}e^{4} - \frac{127246}{1163}e^{3} + \frac{16558}{1163}e^{2} + \frac{149430}{1163}e + \frac{828}{1163}$
79 $[79, 79, 3w^{5} - 6w^{4} - 17w^{3} + 11w^{2} + 21w + 7]$ $\phantom{-}\frac{2176}{1163}e^{7} + \frac{20168}{1163}e^{6} + \frac{45965}{1163}e^{5} - \frac{48223}{1163}e^{4} - \frac{217339}{1163}e^{3} - \frac{6329}{1163}e^{2} + \frac{239097}{1163}e + \frac{4273}{1163}$
79 $[79, 79, -5w^{5} + 8w^{4} + 35w^{3} - 14w^{2} - 52w - 11]$ $-\frac{1853}{1163}e^{7} - \frac{17247}{1163}e^{6} - \frac{39769}{1163}e^{5} + \frac{39384}{1163}e^{4} + \frac{185105}{1163}e^{3} + \frac{16011}{1163}e^{2} - \frac{186897}{1163}e - \frac{13606}{1163}$
79 $[79, 79, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 2w + 2]$ $-\frac{1730}{1163}e^{7} - \frac{15735}{1163}e^{6} - \frac{34313}{1163}e^{5} + \frac{41455}{1163}e^{4} + \frac{167404}{1163}e^{3} + \frac{1360}{1163}e^{2} - \frac{179920}{1163}e - \frac{16854}{1163}$
101 $[101, 101, -2w^{5} + 3w^{4} + 14w^{3} - 3w^{2} - 21w - 9]$ $\phantom{-}\frac{669}{1163}e^{7} + \frac{6068}{1163}e^{6} + \frac{12826}{1163}e^{5} - \frac{18293}{1163}e^{4} - \frac{66180}{1163}e^{3} + \frac{9410}{1163}e^{2} + \frac{82369}{1163}e - \frac{6660}{1163}$
101 $[101, 101, -2w^{5} + 2w^{4} + 17w^{3} - 29w - 9]$ $\phantom{-}\frac{1745}{1163}e^{7} + \frac{16742}{1163}e^{6} + \frac{40765}{1163}e^{5} - \frac{36749}{1163}e^{4} - \frac{197191}{1163}e^{3} - \frac{20847}{1163}e^{2} + \frac{217533}{1163}e + \frac{10728}{1163}$
101 $[101, 101, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 9w + 1]$ $-\frac{876}{1163}e^{7} - \frac{8102}{1163}e^{6} - \frac{17895}{1163}e^{5} + \frac{23828}{1163}e^{4} + \frac{96707}{1163}e^{3} - \frac{1234}{1163}e^{2} - \frac{116690}{1163}e - \frac{10680}{1163}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -2w^{5} + 2w^{4} + 17w^{3} - w^{2} - 27w - 8]$ $-1$
$11$ $[11, 11, -w^{5} + 2w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ $1$