Base field \(\Q(\sqrt{15}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 15\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[153,51,-3w + 21]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $152$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 24x^{14} + 232x^{12} + 1163x^{10} + 3240x^{8} + 4962x^{6} + 3821x^{4} + 1181x^{2} + 100\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w]$ | $-\frac{673}{66720}e^{15} - \frac{22207}{66720}e^{13} - \frac{280241}{66720}e^{11} - \frac{871577}{33360}e^{9} - \frac{566383}{6672}e^{7} - \frac{2318959}{16680}e^{5} - \frac{2198331}{22240}e^{3} - \frac{327197}{16680}e$ |
| 7 | $[7, 7, w + 1]$ | $-\frac{1497}{22240}e^{15} - \frac{31783}{22240}e^{13} - \frac{258729}{22240}e^{11} - \frac{507153}{11120}e^{9} - \frac{197559}{2224}e^{7} - \frac{447751}{5560}e^{5} - \frac{710377}{22240}e^{3} - \frac{46653}{5560}e$ |
| 7 | $[7, 7, w + 6]$ | $-\frac{529}{6672}e^{15} - \frac{11983}{6672}e^{13} - \frac{106577}{6672}e^{11} - \frac{236225}{3336}e^{9} - \frac{545987}{3336}e^{7} - \frac{310831}{1668}e^{5} - \frac{193595}{2224}e^{3} - \frac{19013}{1668}e$ |
| 11 | $[11, 11, -w - 2]$ | $-\frac{763}{13344}e^{14} - \frac{15253}{13344}e^{12} - \frac{114395}{13344}e^{10} - \frac{199067}{6672}e^{8} - \frac{316217}{6672}e^{6} - \frac{80413}{3336}e^{4} + \frac{41223}{4448}e^{2} + \frac{7693}{3336}$ |
| 11 | $[11, 11, w - 2]$ | $-\frac{683}{13344}e^{14} - \frac{14021}{13344}e^{12} - \frac{109099}{13344}e^{10} - \frac{199339}{6672}e^{8} - \frac{335065}{6672}e^{6} - \frac{88277}{3336}e^{4} + \frac{49143}{4448}e^{2} + \frac{16925}{3336}$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}\frac{7969}{66720}e^{15} + \frac{166591}{66720}e^{13} + \frac{1326353}{66720}e^{11} + \frac{2502761}{33360}e^{9} + \frac{890863}{6672}e^{7} + \frac{1407607}{16680}e^{5} - \frac{499877}{22240}e^{3} - \frac{400099}{16680}e$ |
| 17 | $[17, 17, w + 10]$ | $\phantom{-}\frac{16}{2085}e^{15} + \frac{743}{4170}e^{13} + \frac{7039}{4170}e^{11} + \frac{35561}{4170}e^{9} + \frac{10385}{417}e^{7} + \frac{85282}{2085}e^{5} + \frac{22017}{695}e^{3} + \frac{26197}{4170}e$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}\frac{599}{8340}e^{15} + \frac{13061}{8340}e^{13} + \frac{109543}{8340}e^{11} + \frac{220141}{4170}e^{9} + \frac{84215}{834}e^{7} + \frac{141737}{2085}e^{5} - \frac{67467}{2780}e^{3} - \frac{50054}{2085}e$ |
| 43 | $[43, 43, w + 31]$ | $\phantom{-}\frac{841}{4170}e^{15} + \frac{18289}{4170}e^{13} + \frac{155087}{4170}e^{11} + \frac{326654}{2085}e^{9} + \frac{145003}{417}e^{7} + \frac{833291}{2085}e^{5} + \frac{305937}{1390}e^{3} + \frac{98443}{2085}e$ |
| 53 | $[53, 53, w + 11]$ | $\phantom{-}\frac{4663}{22240}e^{15} + \frac{94217}{22240}e^{13} + \frac{709511}{22240}e^{11} + \frac{1208847}{11120}e^{9} + \frac{339065}{2224}e^{7} + \frac{85409}{5560}e^{5} - \frac{2439257}{22240}e^{3} - \frac{155333}{5560}e$ |
| 53 | $[53, 53, w + 42]$ | $\phantom{-}\frac{2659}{33360}e^{15} + \frac{56461}{33360}e^{13} + \frac{456083}{33360}e^{11} + \frac{864491}{16680}e^{9} + \frac{297229}{3336}e^{7} + \frac{370417}{8340}e^{5} - \frac{291647}{11120}e^{3} - \frac{107149}{8340}e$ |
| 59 | $[59, 59, 2w - 1]$ | $-\frac{121}{6672}e^{14} - \frac{3031}{6672}e^{12} - \frac{31529}{6672}e^{10} - \frac{86825}{3336}e^{8} - \frac{262475}{3336}e^{6} - \frac{201151}{1668}e^{4} - \frac{168771}{2224}e^{2} - \frac{27641}{1668}$ |
| 59 | $[59, 59, -2w - 1]$ | $\phantom{-}\frac{5911}{13344}e^{14} + \frac{127225}{13344}e^{12} + \frac{1060343}{13344}e^{10} + \frac{2163815}{6672}e^{8} + \frac{4508669}{6672}e^{6} + \frac{2260345}{3336}e^{4} + \frac{1224589}{4448}e^{2} + \frac{128687}{3336}$ |
| 61 | $[61, 61, 2w - 11]$ | $-\frac{2053}{13344}e^{14} - \frac{46795}{13344}e^{12} - \frac{421637}{13344}e^{10} - \frac{960293}{6672}e^{8} - \frac{2348327}{6672}e^{6} - \frac{1496923}{3336}e^{4} - \frac{1142887}{4448}e^{2} - \frac{131165}{3336}$ |
| 61 | $[61, 61, -2w - 11]$ | $\phantom{-}\frac{187}{1668}e^{14} + \frac{4381}{1668}e^{12} + \frac{40235}{1668}e^{10} + \frac{91271}{834}e^{8} + \frac{210563}{834}e^{6} + \frac{112681}{417}e^{4} + \frac{57989}{556}e^{2} + \frac{7235}{417}$ |
| 67 | $[67, 67, w + 22]$ | $-\frac{5669}{66720}e^{15} - \frac{114491}{66720}e^{13} - \frac{857173}{66720}e^{11} - \frac{1426381}{33360}e^{9} - \frac{360395}{6672}e^{7} + \frac{230293}{16680}e^{5} + \frac{1594937}{22240}e^{3} + \frac{648839}{16680}e$ |
| 67 | $[67, 67, w + 45]$ | $\phantom{-}\frac{8213}{22240}e^{15} + \frac{179467}{22240}e^{13} + \frac{1525541}{22240}e^{11} + \frac{3195597}{11120}e^{9} + \frac{1378587}{2224}e^{7} + \frac{3612459}{5560}e^{5} + \frac{6210053}{22240}e^{3} + \frac{248777}{5560}e$ |
| 71 | $[71, 71, 3w - 8]$ | $\phantom{-}\frac{649}{6672}e^{14} + \frac{13831}{6672}e^{12} + \frac{114521}{6672}e^{10} + \frac{235817}{3336}e^{8} + \frac{521051}{3336}e^{6} + \frac{314047}{1668}e^{4} + \frac{256627}{2224}e^{2} + \frac{44537}{1668}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w]$ | $1$ |
| $17$ | $[17,17,-w + 7]$ | $-\frac{16}{2085}e^{15} - \frac{743}{4170}e^{13} - \frac{7039}{4170}e^{11} - \frac{35561}{4170}e^{9} - \frac{10385}{417}e^{7} - \frac{85282}{2085}e^{5} - \frac{22017}{695}e^{3} - \frac{26197}{4170}e$ |