Properties

Label 6.6.1868969.1-26.1-e
Base field 6.6.1868969.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $26$
Level $[26, 26, w^{3} - 3w]$
Dimension $9$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 6.6.1868969.1

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

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[26, 26, w^{3} - 3w]$
Dimension: $9$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

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

\(x^{9} - 8x^{8} - 46x^{7} + 412x^{6} + 324x^{5} - 5168x^{4} + 5472x^{3} + 5376x^{2} - 4608x - 2048\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}1$
17 $[17, 17, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 5w + 1]$ $\phantom{-}e$
23 $[23, 23, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ $\phantom{-}\frac{5191}{2356288}e^{8} - \frac{5017}{294536}e^{7} - \frac{124363}{1178144}e^{6} + \frac{513885}{589072}e^{5} + \frac{573493}{589072}e^{4} - \frac{799275}{73634}e^{3} + \frac{1164221}{147268}e^{2} + \frac{417422}{36817}e - \frac{92336}{36817}$
31 $[31, 31, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 7w - 5]$ $-\frac{2499}{2356288}e^{8} + \frac{6719}{589072}e^{7} + \frac{3003}{107104}e^{6} - \frac{342159}{589072}e^{5} + \frac{400509}{589072}e^{4} + \frac{507747}{73634}e^{3} - \frac{59018}{3347}e^{2} + \frac{175900}{36817}e + \frac{44698}{3347}$
32 $[32, 2, w^{5} - 6w^{3} - w^{2} + 8w + 1]$ $\phantom{-}\frac{6251}{2356288}e^{8} - \frac{21679}{1178144}e^{7} - \frac{162563}{1178144}e^{6} + \frac{272781}{294536}e^{5} + \frac{964515}{589072}e^{4} - \frac{3195391}{294536}e^{3} + \frac{830121}{147268}e^{2} + \frac{165370}{36817}e + \frac{35273}{36817}$
43 $[43, 43, w^{4} - 5w^{2} + 3]$ $-\frac{1721}{1178144}e^{8} + \frac{6111}{589072}e^{7} + \frac{42381}{589072}e^{6} - \frac{37683}{73634}e^{5} - \frac{208317}{294536}e^{4} + \frac{871067}{147268}e^{3} - \frac{422633}{73634}e^{2} - \frac{192692}{36817}e + \frac{260886}{36817}$
47 $[47, 47, -w^{4} + w^{3} + 5w^{2} - 2w - 5]$ $-\frac{23467}{4712576}e^{8} + \frac{1206}{36817}e^{7} + \frac{624985}{2356288}e^{6} - \frac{1895165}{1178144}e^{5} - \frac{3875799}{1178144}e^{4} + \frac{5196891}{294536}e^{3} - \frac{407421}{36817}e^{2} - \frac{246435}{73634}e + \frac{220866}{36817}$
49 $[49, 7, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 1]$ $-\frac{3471}{4712576}e^{8} + \frac{3953}{589072}e^{7} + \frac{62757}{2356288}e^{6} - \frac{416637}{1178144}e^{5} + \frac{219757}{1178144}e^{4} + \frac{1349101}{294536}e^{3} - \frac{359906}{36817}e^{2} - \frac{204691}{73634}e + \frac{244742}{36817}$
53 $[53, 53, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 5w - 7]$ $-\frac{505}{214208}e^{8} + \frac{9597}{589072}e^{7} + \frac{141775}{1178144}e^{6} - \frac{42641}{53552}e^{5} - \frac{808229}{589072}e^{4} + \frac{1292145}{147268}e^{3} - \frac{867365}{147268}e^{2} - \frac{5589}{3347}e + \frac{10966}{36817}$
59 $[59, 59, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ $\phantom{-}\frac{535}{4712576}e^{8} + \frac{7511}{1178144}e^{7} - \frac{117101}{2356288}e^{6} - \frac{434673}{1178144}e^{5} + \frac{2636087}{1178144}e^{4} + \frac{204958}{36817}e^{3} - \frac{1762625}{73634}e^{2} + \frac{175657}{73634}e + \frac{566326}{36817}$
71 $[71, 71, w^{5} - w^{4} - 5w^{3} + 4w^{2} + 4w - 5]$ $\phantom{-}\frac{13735}{4712576}e^{8} - \frac{25633}{1178144}e^{7} - \frac{344237}{2356288}e^{6} + \frac{1318551}{1178144}e^{5} + \frac{1791015}{1178144}e^{4} - \frac{1017319}{73634}e^{3} + \frac{707687}{73634}e^{2} + \frac{1003407}{73634}e - \frac{58508}{36817}$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-\frac{1443}{589072}e^{8} + \frac{761}{53552}e^{7} + \frac{10443}{73634}e^{6} - \frac{202045}{294536}e^{5} - \frac{316147}{147268}e^{4} + \frac{1081739}{147268}e^{3} - \frac{72931}{73634}e^{2} - \frac{246481}{36817}e + \frac{328696}{36817}$
83 $[83, 83, w^{5} - 6w^{3} - w^{2} + 7w - 1]$ $-\frac{10577}{2356288}e^{8} + \frac{3793}{147268}e^{7} + \frac{315431}{1178144}e^{6} - \frac{743403}{589072}e^{5} - \frac{2630185}{589072}e^{4} + \frac{2085873}{147268}e^{3} + \frac{632305}{73634}e^{2} - \frac{708590}{36817}e - \frac{99664}{36817}$
83 $[83, 83, 2w^{5} - w^{4} - 11w^{3} + 2w^{2} + 12w + 1]$ $-\frac{4541}{4712576}e^{8} - \frac{1779}{294536}e^{7} + \frac{296959}{2356288}e^{6} + \frac{452709}{1178144}e^{5} - \frac{5052417}{1178144}e^{4} - \frac{1930227}{294536}e^{3} + \frac{1402719}{36817}e^{2} - \frac{482371}{73634}e - \frac{740642}{36817}$
89 $[89, 89, -w^{5} + w^{4} + 4w^{3} - 2w^{2} - w - 1]$ $-\frac{9197}{4712576}e^{8} + \frac{10235}{589072}e^{7} + \frac{14877}{214208}e^{6} - \frac{1011287}{1178144}e^{5} + \frac{551303}{1178144}e^{4} + \frac{2767279}{294536}e^{3} - \frac{84990}{3347}e^{2} + \frac{932629}{73634}e + \frac{59550}{3347}$
89 $[89, 89, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w + 3]$ $\phantom{-}2$
89 $[89, 89, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 6w + 3]$ $\phantom{-}\frac{1165}{1178144}e^{8} - \frac{565}{147268}e^{7} - \frac{41163}{589072}e^{6} + \frac{51313}{294536}e^{5} + \frac{423977}{294536}e^{4} - \frac{4788}{3347}e^{3} - \frac{174851}{36817}e^{2} + \frac{53789}{36817}e - \frac{288712}{36817}$
89 $[89, 89, 2w^{4} - w^{3} - 9w^{2} + w + 5]$ $-\frac{1363}{2356288}e^{8} + \frac{345}{294536}e^{7} + \frac{63581}{1178144}e^{6} - \frac{37849}{589072}e^{5} - \frac{948963}{589072}e^{4} + \frac{12097}{13388}e^{3} + \frac{1127869}{73634}e^{2} - \frac{269417}{36817}e - \frac{762880}{36817}$
101 $[101, 101, w^{5} - 5w^{3} - w^{2} + 5w - 1]$ $-\frac{13809}{4712576}e^{8} + \frac{10317}{589072}e^{7} + \frac{394267}{2356288}e^{6} - \frac{1005595}{1178144}e^{5} - \frac{2980909}{1178144}e^{4} + \frac{2744559}{294536}e^{3} + \frac{30109}{36817}e^{2} - \frac{343389}{73634}e + \frac{176816}{36817}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w]$ $-1$
$13$ $[13, 13, -w^{2} + 3]$ $-1$