Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15,15,w - 6]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $41$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} + 2x^{8} - 14x^{7} - 29x^{6} + 53x^{5} + 117x^{4} - 56x^{3} - 150x^{2} + 6x + 46\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{92}{67}e^{8} + \frac{53}{67}e^{7} - \frac{1354}{67}e^{6} - \frac{724}{67}e^{5} + \frac{5770}{67}e^{4} + \frac{2331}{67}e^{3} - \frac{7965}{67}e^{2} - \frac{1731}{67}e + \frac{2633}{67}$ |
| 5 | $[5, 5, 4w + 25]$ | $-\frac{65}{67}e^{8} - \frac{44}{67}e^{7} + \frac{961}{67}e^{6} + \frac{596}{67}e^{5} - \frac{4148}{67}e^{4} - \frac{1920}{67}e^{3} + \frac{5969}{67}e^{2} + \frac{1432}{67}e - \frac{2196}{67}$ |
| 5 | $[5, 5, -4w + 29]$ | $-1$ |
| 11 | $[11, 11, w - 8]$ | $\phantom{-}\frac{65}{67}e^{8} + \frac{44}{67}e^{7} - \frac{961}{67}e^{6} - \frac{596}{67}e^{5} + \frac{4148}{67}e^{4} + \frac{1920}{67}e^{3} - \frac{5902}{67}e^{2} - \frac{1432}{67}e + \frac{1928}{67}$ |
| 11 | $[11, 11, -w - 7]$ | $\phantom{-}\frac{113}{67}e^{8} + \frac{60}{67}e^{7} - \frac{1682}{67}e^{6} - \frac{831}{67}e^{5} + \frac{7374}{67}e^{4} + \frac{2740}{67}e^{3} - \frac{10917}{67}e^{2} - \frac{2239}{67}e + \frac{4164}{67}$ |
| 13 | $[13, 13, 3w + 19]$ | $-\frac{75}{67}e^{8} - \frac{25}{67}e^{7} + \frac{1114}{67}e^{6} + \frac{363}{67}e^{5} - \frac{4848}{67}e^{4} - \frac{1231}{67}e^{3} + \frac{6877}{67}e^{2} + \frac{1039}{67}e - \frac{2204}{67}$ |
| 13 | $[13, 13, 3w - 22]$ | $-\frac{131}{67}e^{8} - \frac{66}{67}e^{7} + \frac{1944}{67}e^{6} + \frac{894}{67}e^{5} - \frac{8433}{67}e^{4} - \frac{2746}{67}e^{3} + \frac{12002}{67}e^{2} + \frac{1746}{67}e - \frac{4098}{67}$ |
| 29 | $[29, 29, 6w + 37]$ | $-\frac{60}{67}e^{8} - \frac{20}{67}e^{7} + \frac{918}{67}e^{6} + \frac{277}{67}e^{5} - \frac{4200}{67}e^{4} - \frac{891}{67}e^{3} + \frac{6386}{67}e^{2} + \frac{724}{67}e - \frac{2192}{67}$ |
| 29 | $[29, 29, 6w - 43]$ | $-\frac{145}{67}e^{8} - \frac{93}{67}e^{7} + \frac{2118}{67}e^{6} + \frac{1278}{67}e^{5} - \frac{8944}{67}e^{4} - \frac{4247}{67}e^{3} + \frac{12429}{67}e^{2} + \frac{3514}{67}e - \frac{4404}{67}$ |
| 37 | $[37, 37, 2w - 13]$ | $-\frac{71}{67}e^{8} - \frac{46}{67}e^{7} + \frac{1026}{67}e^{6} + \frac{617}{67}e^{5} - \frac{4233}{67}e^{4} - \frac{1922}{67}e^{3} + \frac{5616}{67}e^{2} + \frac{1223}{67}e - \frac{2040}{67}$ |
| 37 | $[37, 37, 2w + 11]$ | $-\frac{29}{67}e^{8} - \frac{32}{67}e^{7} + \frac{437}{67}e^{6} + \frac{470}{67}e^{5} - \frac{1963}{67}e^{4} - \frac{1841}{67}e^{3} + \frac{2995}{67}e^{2} + \frac{1882}{67}e - \frac{1122}{67}$ |
| 43 | $[43, 43, -w - 1]$ | $\phantom{-}\frac{114}{67}e^{8} + \frac{38}{67}e^{7} - \frac{1704}{67}e^{6} - \frac{533}{67}e^{5} + \frac{7511}{67}e^{4} + \frac{1646}{67}e^{3} - \frac{11115}{67}e^{2} - \frac{987}{67}e + \frac{4138}{67}$ |
| 43 | $[43, 43, w - 2]$ | $-\frac{184}{67}e^{8} - \frac{106}{67}e^{7} + \frac{2708}{67}e^{6} + \frac{1448}{67}e^{5} - \frac{11540}{67}e^{4} - \frac{4662}{67}e^{3} + \frac{15997}{67}e^{2} + \frac{3462}{67}e - \frac{5534}{67}$ |
| 49 | $[49, 7, -7]$ | $-2e^{8} - e^{7} + 29e^{6} + 14e^{5} - 120e^{4} - 46e^{3} + 155e^{2} + 33e - 42$ |
| 59 | $[59, 59, 5w - 37]$ | $\phantom{-}\frac{105}{67}e^{8} + \frac{35}{67}e^{7} - \frac{1506}{67}e^{6} - \frac{468}{67}e^{5} + \frac{6144}{67}e^{4} + \frac{1241}{67}e^{3} - \frac{7926}{67}e^{2} - \frac{530}{67}e + \frac{2362}{67}$ |
| 59 | $[59, 59, 5w + 32]$ | $\phantom{-}\frac{64}{67}e^{8} + \frac{66}{67}e^{7} - \frac{939}{67}e^{6} - \frac{894}{67}e^{5} + \frac{3944}{67}e^{4} + \frac{2947}{67}e^{3} - \frac{5235}{67}e^{2} - \frac{2148}{67}e + \frac{1418}{67}$ |
| 67 | $[67, 67, 21w + 131]$ | $\phantom{-}\frac{204}{67}e^{8} + \frac{135}{67}e^{7} - \frac{3014}{67}e^{6} - \frac{1853}{67}e^{5} + \frac{13007}{67}e^{4} + \frac{6165}{67}e^{3} - \frac{18617}{67}e^{2} - \frac{5088}{67}e + \frac{6354}{67}$ |
| 67 | $[67, 67, 21w - 152]$ | $-\frac{246}{67}e^{8} - \frac{149}{67}e^{7} + \frac{3603}{67}e^{6} + \frac{2067}{67}e^{5} - \frac{15277}{67}e^{4} - \frac{6916}{67}e^{3} + \frac{21238}{67}e^{2} + \frac{5836}{67}e - \frac{7406}{67}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w + 6]$ | $-1$ |
| $5$ | $[5,5,-4w + 29]$ | $1$ |