Base field \(\Q(\sqrt{79}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 79\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, w + 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $150$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + 22x^{10} + 331x^{8} + 2690x^{6} + 15973x^{4} + 51714x^{2} + 114244\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 9]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 1]$ | $-\frac{550021}{18232265870}e^{11} - \frac{14605349}{9116132935}e^{9} - \frac{439488229}{18232265870}e^{7} - \frac{2261993862}{9116132935}e^{5} - \frac{21208294507}{18232265870}e^{3} - \frac{203147127}{53941615}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{50643}{1402481990}e^{10} + \frac{475277}{701240995}e^{8} + \frac{14301517}{1402481990}e^{6} + \frac{49599026}{701240995}e^{4} + \frac{690145411}{1402481990}e^{2} + \frac{6610671}{4149355}$ |
| 5 | $[5, 5, w + 3]$ | $-\frac{202572}{701240995}e^{10} - \frac{3802216}{701240995}e^{8} - \frac{57206068}{701240995}e^{6} - \frac{396792208}{701240995}e^{4} - \frac{2059340649}{701240995}e^{2} - \frac{19690528}{4149355}$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}\frac{2222}{7705945}e^{11} + \frac{33431}{7705945}e^{9} + \frac{422153}{7705945}e^{7} + \frac{1613273}{7705945}e^{5} + \frac{401778}{592765}e^{3} - \frac{19760978}{7705945}e$ |
| 7 | $[7, 7, w + 4]$ | $-\frac{206594}{1823226587}e^{11} - \frac{7106770}{1823226587}e^{9} - \frac{106924585}{1823226587}e^{7} - \frac{1052745397}{1823226587}e^{5} - \frac{5159838055}{1823226587}e^{3} - \frac{98848710}{10788323}e$ |
| 13 | $[13, 13, w + 1]$ | $-\frac{6}{46865}e^{10} - \frac{418}{46865}e^{8} - \frac{6289}{46865}e^{6} - \frac{65969}{46865}e^{4} - \frac{303487}{46865}e^{2} - \frac{75582}{3605}$ |
| 13 | $[13, 13, w + 12]$ | $-\frac{899793}{701240995}e^{10} - \frac{19007399}{701240995}e^{8} - \frac{254100367}{701240995}e^{6} - \frac{1762488652}{701240995}e^{4} - \frac{7457192101}{701240995}e^{2} - \frac{87462232}{4149355}$ |
| 43 | $[43, 43, -w - 6]$ | $-\frac{8721}{15840370}e^{11} - \frac{92889}{7920185}e^{9} - \frac{2462799}{15840370}e^{7} - \frac{8541222}{7920185}e^{5} - \frac{72407967}{15840370}e^{3} - \frac{32604}{3605}e$ |
| 43 | $[43, 43, w - 6]$ | $\phantom{-}\frac{14042187}{18232265870}e^{11} + \frac{148732253}{9116132935}e^{9} + \frac{3965495253}{18232265870}e^{7} + \frac{13752716034}{9116132935}e^{5} + \frac{120093983699}{18232265870}e^{3} + \frac{52497588}{4149355}e$ |
| 47 | $[47, 47, w + 19]$ | $-\frac{32098}{53941615}e^{11} - \frac{482929}{53941615}e^{9} - \frac{5945637}{53941615}e^{7} - \frac{23304607}{53941615}e^{5} - \frac{5803902}{4149355}e^{3} + \frac{219385332}{53941615}e$ |
| 47 | $[47, 47, w + 28]$ | $-\frac{46776}{260460941}e^{11} - \frac{1609080}{260460941}e^{9} - \frac{24209340}{260460941}e^{7} - \frac{233443091}{260460941}e^{5} - \frac{1168265220}{260460941}e^{3} - \frac{22380840}{1541189}e$ |
| 59 | $[59, 59, w + 16]$ | $-\frac{2222}{7705945}e^{11} - \frac{33431}{7705945}e^{9} - \frac{422153}{7705945}e^{7} - \frac{1613273}{7705945}e^{5} - \frac{401778}{592765}e^{3} + \frac{42878813}{7705945}e$ |
| 59 | $[59, 59, w + 43]$ | $\phantom{-}\frac{1650063}{18232265870}e^{11} + \frac{43816047}{9116132935}e^{9} + \frac{1318464687}{18232265870}e^{7} + \frac{6785981586}{9116132935}e^{5} + \frac{63624883521}{18232265870}e^{3} + \frac{609441381}{53941615}e$ |
| 71 | $[71, 71, w + 24]$ | $\phantom{-}\frac{120776}{701240995}e^{11} + \frac{2571558}{701240995}e^{9} + \frac{38690259}{701240995}e^{7} + \frac{337404594}{701240995}e^{5} + \frac{1867067997}{701240995}e^{3} + \frac{35768034}{4149355}e$ |
| 71 | $[71, 71, w + 47]$ | $\phantom{-}\frac{1606}{7705945}e^{11} + \frac{24163}{7705945}e^{9} + \frac{228824}{7705945}e^{7} + \frac{1166029}{7705945}e^{5} + \frac{290394}{592765}e^{3} + \frac{41871526}{7705945}e$ |
| 73 | $[73, 73, 3w - 28]$ | $\phantom{-}\frac{1166}{829871}e^{10} + \frac{17543}{829871}e^{8} + \frac{226221}{829871}e^{6} + \frac{846569}{829871}e^{4} + \frac{2740842}{829871}e^{2} - \frac{10742888}{829871}$ |
| 73 | $[73, 73, 12w - 107]$ | $-\frac{2442}{4149355}e^{10} - \frac{36741}{4149355}e^{8} - \frac{364178}{4149355}e^{6} - \frac{1773003}{4149355}e^{4} - \frac{5740254}{4149355}e^{2} - \frac{17334552}{4149355}$ |
| 79 | $[79, 79, -w]$ | $-\frac{1275255}{1823226587}e^{11} - \frac{27749551}{1823226587}e^{9} - \frac{360130345}{1823226587}e^{7} - \frac{2497932820}{1823226587}e^{5} - \frac{10272687176}{1823226587}e^{3} - \frac{9535240}{829871}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 2]$ | $-\frac{50643}{1402481990}e^{10} - \frac{475277}{701240995}e^{8} - \frac{14301517}{1402481990}e^{6} - \frac{49599026}{701240995}e^{4} - \frac{690145411}{1402481990}e^{2} - \frac{6610671}{4149355}$ |