Base field \(\Q(\zeta_{36})^+\)
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} + 9x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[24, 6, w^{5} - w^{4} - 4w^{3} + 4w^{2} + 2w - 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 11x^{5} - 40x^{4} + 797x^{3} - 2208x^{2} - 1332x + 5832\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 8 | $[8, 2, w^{3} - 3w - 1]$ | $\phantom{-}1$ |
| 37 | $[37, 37, w^{4} - 5w^{2} - w + 5]$ | $\phantom{-}\frac{25}{2754}e^{5} - \frac{155}{2754}e^{4} - \frac{872}{1377}e^{3} + \frac{11003}{2754}e^{2} - \frac{214}{459}e - \frac{60}{17}$ |
| 37 | $[37, 37, w^{5} - 5w^{3} - w^{2} + 4w + 1]$ | $-\frac{35}{2754}e^{5} + \frac{217}{2754}e^{4} + \frac{1129}{1377}e^{3} - \frac{15955}{2754}e^{2} + \frac{1799}{459}e + \frac{220}{17}$ |
| 37 | $[37, 37, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w + 1]$ | $\phantom{-}e$ |
| 37 | $[37, 37, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 5w + 1]$ | $\phantom{-}\frac{139}{2754}e^{5} - \frac{385}{1377}e^{4} - \frac{9715}{2754}e^{3} + \frac{57725}{2754}e^{2} + \frac{1225}{918}e - \frac{915}{17}$ |
| 37 | $[37, 37, w^{5} - 5w^{3} + w^{2} + 4w - 1]$ | $-\frac{133}{5508}e^{5} + \frac{641}{5508}e^{4} + \frac{4841}{2754}e^{3} - \frac{47777}{5508}e^{2} - \frac{5465}{918}e + \frac{367}{17}$ |
| 37 | $[37, 37, -w^{4} + 5w^{2} - w - 5]$ | $-\frac{125}{5508}e^{5} + \frac{775}{5508}e^{4} + \frac{2180}{1377}e^{3} - \frac{57769}{5508}e^{2} + \frac{76}{459}e + \frac{575}{17}$ |
| 71 | $[71, 71, w^{5} - 5w^{3} - w^{2} + 5w + 4]$ | $-\frac{125}{5508}e^{5} + \frac{775}{5508}e^{4} + \frac{2180}{1377}e^{3} - \frac{57769}{5508}e^{2} + \frac{535}{459}e + \frac{507}{17}$ |
| 71 | $[71, 71, w^{5} - 4w^{3} - w^{2} + w + 2]$ | $-\frac{83}{5508}e^{5} + \frac{331}{5508}e^{4} + \frac{3097}{2754}e^{3} - \frac{25771}{5508}e^{2} - \frac{5893}{918}e + \frac{239}{17}$ |
| 71 | $[71, 71, w^{5} + w^{4} - 5w^{3} - 5w^{2} + 4w + 2]$ | $\phantom{-}\frac{52}{1377}e^{5} - \frac{553}{2754}e^{4} - \frac{7457}{2754}e^{3} + \frac{20885}{1377}e^{2} + \frac{4823}{918}e - \frac{763}{17}$ |
| 71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 4w - 2]$ | $-\frac{133}{5508}e^{5} + \frac{641}{5508}e^{4} + \frac{4841}{2754}e^{3} - \frac{47777}{5508}e^{2} - \frac{4547}{918}e + \frac{299}{17}$ |
| 71 | $[71, 71, -w^{5} + 4w^{3} - w^{2} - w + 2]$ | $-\frac{65}{1836}e^{5} + \frac{403}{1836}e^{4} + \frac{1103}{459}e^{3} - \frac{29893}{1836}e^{2} + \frac{625}{153}e + \frac{727}{17}$ |
| 71 | $[71, 71, -w^{5} + 5w^{3} - w^{2} - 5w + 4]$ | $\phantom{-}\frac{82}{1377}e^{5} - \frac{925}{2754}e^{4} - \frac{11459}{2754}e^{3} + \frac{34364}{1377}e^{2} + \frac{797}{918}e - \frac{1043}{17}$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - w^{2} + 3w + 2]$ | $-\frac{65}{1836}e^{5} + \frac{403}{1836}e^{4} + \frac{1103}{459}e^{3} - \frac{29893}{1836}e^{2} + \frac{625}{153}e + \frac{761}{17}$ |
| 73 | $[73, 73, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 2]$ | $-\frac{133}{5508}e^{5} + \frac{641}{5508}e^{4} + \frac{4841}{2754}e^{3} - \frac{47777}{5508}e^{2} - \frac{4547}{918}e + \frac{333}{17}$ |
| 73 | $[73, 73, -w^{5} + 4w^{3} - w^{2} - 2w + 2]$ | $-\frac{125}{5508}e^{5} + \frac{775}{5508}e^{4} + \frac{2180}{1377}e^{3} - \frac{57769}{5508}e^{2} + \frac{535}{459}e + \frac{541}{17}$ |
| 73 | $[73, 73, w^{5} - 4w^{3} - w^{2} + 2w + 2]$ | $\phantom{-}\frac{82}{1377}e^{5} - \frac{925}{2754}e^{4} - \frac{11459}{2754}e^{3} + \frac{34364}{1377}e^{2} + \frac{797}{918}e - \frac{1009}{17}$ |
| 73 | $[73, 73, -2w^{5} - w^{4} + 10w^{3} + 4w^{2} - 9w - 2]$ | $\phantom{-}\frac{52}{1377}e^{5} - \frac{553}{2754}e^{4} - \frac{7457}{2754}e^{3} + \frac{20885}{1377}e^{2} + \frac{4823}{918}e - \frac{729}{17}$ |
| 73 | $[73, 73, w^{5} - 5w^{3} + w^{2} + 3w - 2]$ | $-\frac{83}{5508}e^{5} + \frac{331}{5508}e^{4} + \frac{3097}{2754}e^{3} - \frac{25771}{5508}e^{2} - \frac{5893}{918}e + \frac{273}{17}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |
| $8$ | $[8, 2, w^{3} - 3w - 1]$ | $-1$ |