Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[15, 15, w]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} + 25x^{6} + 98x^{4} + 20x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-\frac{68}{39}e^{7} - \frac{1694}{39}e^{5} - 167e^{3} - \frac{749}{39}e$ |
3 | $[3, 3, w]$ | $-\frac{2}{13}e^{7} - \frac{151}{39}e^{5} - \frac{47}{3}e^{3} - \frac{185}{39}e$ |
5 | $[5, 5, -w + 5]$ | $-1$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 4]$ | $-\frac{62}{13}e^{7} - \frac{1543}{13}e^{5} - 454e^{3} - \frac{577}{13}e$ |
13 | $[13, 13, w + 2]$ | $-\frac{75}{13}e^{7} - \frac{1868}{13}e^{5} - 552e^{3} - \frac{837}{13}e$ |
13 | $[13, 13, w + 11]$ | $\phantom{-}\frac{7}{13}e^{7} + \frac{174}{13}e^{5} + 51e^{3} + \frac{88}{13}e$ |
17 | $[17, 17, w + 8]$ | $\phantom{-}\frac{149}{39}e^{7} + \frac{3713}{39}e^{5} + 367e^{3} + \frac{1979}{39}e$ |
17 | $[17, 17, w + 9]$ | $-\frac{31}{39}e^{7} - \frac{778}{39}e^{5} - 80e^{3} - \frac{1036}{39}e$ |
19 | $[19, 19, w + 7]$ | $\phantom{-}\frac{27}{13}e^{6} + \frac{673}{13}e^{4} + 199e^{2} + \frac{254}{13}$ |
19 | $[19, 19, -w + 7]$ | $-\frac{34}{13}e^{6} - \frac{847}{13}e^{4} - 250e^{2} - \frac{316}{13}$ |
29 | $[29, 29, -w - 1]$ | $-\frac{131}{39}e^{6} - \frac{3260}{39}e^{4} - 320e^{2} - \frac{1307}{39}$ |
29 | $[29, 29, w - 1]$ | $-\frac{58}{39}e^{6} - \frac{1438}{39}e^{4} - 139e^{2} - \frac{484}{39}$ |
37 | $[37, 37, w + 17]$ | $-\frac{82}{13}e^{7} - \frac{2042}{13}e^{5} - 603e^{3} - \frac{912}{13}e$ |
37 | $[37, 37, w + 20]$ | $\phantom{-}\frac{20}{13}e^{7} + \frac{499}{13}e^{5} + 149e^{3} + \frac{348}{13}e$ |
71 | $[71, 71, 2w - 7]$ | $\phantom{-}\frac{53}{39}e^{6} + \frac{441}{13}e^{4} + \frac{392}{3}e^{2} + \frac{163}{39}$ |
71 | $[71, 71, -2w - 7]$ | $-\frac{179}{39}e^{6} - \frac{1485}{13}e^{4} - \frac{1310}{3}e^{2} - \frac{1864}{39}$ |
83 | $[83, 83, w + 14]$ | $-\frac{54}{13}e^{7} - \frac{4025}{39}e^{5} - \frac{1174}{3}e^{3} - \frac{952}{39}e$ |
83 | $[83, 83, w + 69]$ | $-\frac{54}{13}e^{7} - \frac{4025}{39}e^{5} - \frac{1174}{3}e^{3} - \frac{952}{39}e$ |
101 | $[101, 101, -7w + 37]$ | $\phantom{-}\frac{142}{39}e^{6} + \frac{3539}{39}e^{4} + \frac{1049}{3}e^{2} + \frac{405}{13}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $\frac{2}{13}e^{7} + \frac{151}{39}e^{5} + \frac{47}{3}e^{3} + \frac{185}{39}e$ |
$5$ | $[5, 5, -w + 5]$ | $1$ |