Base field 6.6.1241125.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[55, 55, w^{5} - 8w^{3} - 2w^{2} + 15w + 5]$ |
| Dimension: | $11$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $33$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{11} - 10x^{10} - 9x^{9} + 310x^{8} - 314x^{7} - 2898x^{6} + 3168x^{5} + 10896x^{4} - 9472x^{3} - 17152x^{2} + 8192x + 10240\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $\phantom{-}1$ |
| 9 | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}1$ |
| 25 | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $-\frac{547}{1139968}e^{10} + \frac{7213}{569984}e^{9} - \frac{1497}{18688}e^{8} - \frac{72951}{569984}e^{7} + \frac{1321559}{569984}e^{6} - \frac{1651817}{569984}e^{5} - \frac{2104885}{142496}e^{4} + \frac{375149}{17812}e^{3} + \frac{155485}{4453}e^{2} - \frac{268685}{8906}e - \frac{148526}{4453}$ |
| 29 | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $\phantom{-}\frac{3389}{1139968}e^{10} - \frac{7223}{284992}e^{9} - \frac{1053}{18688}e^{8} + \frac{106573}{142496}e^{7} + \frac{174541}{569984}e^{6} - \frac{3607811}{569984}e^{5} - \frac{1935383}{284992}e^{4} + \frac{363299}{17812}e^{3} + \frac{165181}{4453}e^{2} - \frac{113961}{4453}e - \frac{194864}{4453}$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-\frac{173}{142496}e^{10} - \frac{4829}{569984}e^{9} + \frac{1003}{4672}e^{8} - \frac{121251}{569984}e^{7} - \frac{1564343}{284992}e^{6} + \frac{2646769}{284992}e^{5} + \frac{12230749}{284992}e^{4} - \frac{226808}{4453}e^{3} - \frac{1085205}{8906}e^{2} + \frac{312232}{4453}e + \frac{493362}{4453}$ |
| 49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $-\frac{4391}{569984}e^{10} + \frac{14251}{284992}e^{9} + \frac{2931}{9344}e^{8} - \frac{566901}{284992}e^{7} - \frac{1389705}{284992}e^{6} + \frac{7013903}{284992}e^{5} + \frac{1333013}{35624}e^{4} - \frac{1661641}{17812}e^{3} - \frac{1911939}{17812}e^{2} + \frac{461109}{4453}e + \frac{451470}{4453}$ |
| 59 | $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ | $-\frac{3735}{1139968}e^{10} + \frac{18805}{569984}e^{9} + \frac{523}{18688}e^{8} - \frac{586855}{569984}e^{7} + \frac{670859}{569984}e^{6} + \frac{5365363}{569984}e^{5} - \frac{1883547}{142496}e^{4} - \frac{1051077}{35624}e^{3} + \frac{383563}{8906}e^{2} + \frac{245995}{8906}e - \frac{138228}{4453}$ |
| 59 | $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ | $-\frac{575}{35624}e^{10} + \frac{78733}{569984}e^{9} + \frac{1607}{4672}e^{8} - \frac{2559261}{569984}e^{7} - \frac{411661}{284992}e^{6} + \frac{12540635}{284992}e^{5} + \frac{3932923}{284992}e^{4} - \frac{658391}{4453}e^{3} - \frac{321087}{4453}e^{2} + \frac{675868}{4453}e + \frac{489014}{4453}$ |
| 61 | $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ | $-\frac{501}{284992}e^{10} + \frac{8711}{284992}e^{9} - \frac{521}{4672}e^{8} - \frac{185139}{284992}e^{7} + \frac{74341}{17812}e^{6} + \frac{6742}{4453}e^{5} - \frac{4698885}{142496}e^{4} + \frac{42347}{8906}e^{3} + \frac{704453}{8906}e^{2} - \frac{60711}{4453}e - \frac{205438}{4453}$ |
| 61 | $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ | $\phantom{-}\frac{547}{1139968}e^{10} - \frac{7213}{569984}e^{9} + \frac{1497}{18688}e^{8} + \frac{72951}{569984}e^{7} - \frac{1321559}{569984}e^{6} + \frac{1651817}{569984}e^{5} + \frac{2104885}{142496}e^{4} - \frac{375149}{17812}e^{3} - \frac{155485}{4453}e^{2} + \frac{259779}{8906}e + \frac{166338}{4453}$ |
| 64 | $[64, 2, 2]$ | $\phantom{-}\frac{8325}{1139968}e^{10} - \frac{36657}{569984}e^{9} - \frac{2777}{18688}e^{8} + \frac{1236695}{569984}e^{7} + \frac{12723}{569984}e^{6} - \frac{12669061}{569984}e^{5} + \frac{399885}{71248}e^{4} + \frac{2646639}{35624}e^{3} - \frac{355557}{17812}e^{2} - \frac{284908}{4453}e + \frac{31637}{4453}$ |
| 71 | $[71, 71, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}\frac{3067}{1139968}e^{10} - \frac{5847}{142496}e^{9} + \frac{2189}{18688}e^{8} + \frac{260659}{284992}e^{7} - \frac{2695153}{569984}e^{6} - \frac{1874513}{569984}e^{5} + \frac{10239625}{284992}e^{4} + \frac{32341}{8906}e^{3} - \frac{378661}{4453}e^{2} - \frac{20777}{4453}e + \frac{235994}{4453}$ |
| 71 | $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ | $-\frac{6981}{569984}e^{10} + \frac{8863}{71248}e^{9} + \frac{557}{9344}e^{8} - \frac{495369}{142496}e^{7} + \frac{1241919}{284992}e^{6} + \frac{7472351}{284992}e^{5} - \frac{3877135}{142496}e^{4} - \frac{331147}{4453}e^{3} + \frac{141445}{4453}e^{2} + \frac{317967}{4453}e + \frac{81680}{4453}$ |
| 79 | $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ | $\phantom{-}\frac{8747}{1139968}e^{10} - \frac{15221}{284992}e^{9} - \frac{5243}{18688}e^{8} + \frac{283177}{142496}e^{7} + \frac{2419859}{569984}e^{6} - \frac{13255093}{569984}e^{5} - \frac{10735297}{284992}e^{4} + \frac{3190215}{35624}e^{3} + \frac{1123219}{8906}e^{2} - \frac{990827}{8906}e - \frac{573658}{4453}$ |
| 81 | $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ | $-\frac{15347}{1139968}e^{10} + \frac{8491}{71248}e^{9} + \frac{4251}{18688}e^{8} - \frac{1018745}{284992}e^{7} - \frac{69615}{569984}e^{6} + \frac{17689537}{569984}e^{5} + \frac{3578883}{284992}e^{4} - \frac{1772581}{17812}e^{3} - \frac{751925}{8906}e^{2} + \frac{497092}{4453}e + \frac{473076}{4453}$ |
| 89 | $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ | $\phantom{-}\frac{14903}{1139968}e^{10} - \frac{16137}{142496}e^{9} - \frac{4975}{18688}e^{8} + \frac{1055827}{284992}e^{7} + \frac{262731}{569984}e^{6} - \frac{20745349}{569984}e^{5} + \frac{119077}{284992}e^{4} + \frac{2110255}{17812}e^{3} + \frac{112637}{17812}e^{2} - \frac{456307}{4453}e - \frac{147260}{4453}$ |
| 89 | $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ | $-\frac{1257}{284992}e^{10} + \frac{23473}{569984}e^{9} + \frac{77}{1168}e^{8} - \frac{766713}{569984}e^{7} + \frac{224397}{284992}e^{6} + \frac{3736237}{284992}e^{5} - \frac{3261237}{284992}e^{4} - \frac{739673}{17812}e^{3} + \frac{319195}{8906}e^{2} + \frac{144135}{4453}e - \frac{73500}{4453}$ |
| 89 | $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ | $-\frac{525}{1139968}e^{10} - \frac{1191}{284992}e^{9} + \frac{1693}{18688}e^{8} - \frac{5391}{71248}e^{7} - \frac{1278693}{569984}e^{6} + \frac{1990027}{569984}e^{5} + \frac{4427107}{284992}e^{4} - \frac{234313}{17812}e^{3} - \frac{285515}{8906}e^{2} + \frac{22019}{4453}e + \frac{99782}{4453}$ |
| 89 | $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ | $\phantom{-}\frac{149}{7808}e^{10} - \frac{341}{1952}e^{9} - \frac{37}{128}e^{8} + \frac{655}{122}e^{7} - \frac{6547}{3904}e^{6} - \frac{187731}{3904}e^{5} + \frac{21325}{1952}e^{4} + \frac{18317}{122}e^{3} + \frac{197}{61}e^{2} - \frac{8758}{61}e - \frac{2746}{61}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $-1$ |
| $11$ | $[11, 11, w - 1]$ | $-1$ |