Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[5, 5, -3w + 25]$ |
Dimension: | $16$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $88$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{16} + 31x^{14} + 384x^{12} + 2424x^{10} + 8252x^{8} + 14748x^{6} + 12128x^{4} + 3008x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 1]$ | $-\frac{1}{176}e^{15} - \frac{25}{176}e^{13} - \frac{16}{11}e^{11} - \frac{719}{88}e^{9} - \frac{613}{22}e^{7} - \frac{609}{11}e^{5} - \frac{591}{11}e^{3} - \frac{173}{11}e$ |
3 | $[3, 3, w + 2]$ | $-\frac{1}{176}e^{15} - \frac{25}{176}e^{13} - \frac{16}{11}e^{11} - \frac{719}{88}e^{9} - \frac{613}{22}e^{7} - \frac{609}{11}e^{5} - \frac{591}{11}e^{3} - \frac{173}{11}e$ |
5 | $[5, 5, -3w + 25]$ | $-1$ |
7 | $[7, 7, w]$ | $-\frac{3}{88}e^{15} - \frac{43}{44}e^{13} - \frac{977}{88}e^{11} - \frac{2795}{44}e^{9} - \frac{4239}{22}e^{7} - \frac{3291}{11}e^{5} - \frac{4485}{22}e^{3} - \frac{389}{11}e$ |
11 | $[11, 11, w - 9]$ | $-\frac{1}{44}e^{14} - \frac{25}{44}e^{12} - \frac{245}{44}e^{10} - \frac{1207}{44}e^{8} - \frac{1583}{22}e^{6} - \frac{1028}{11}e^{4} - \frac{505}{11}e^{2} - \frac{54}{11}$ |
11 | $[11, 11, -w - 9]$ | $-\frac{1}{44}e^{14} - \frac{25}{44}e^{12} - \frac{245}{44}e^{10} - \frac{1207}{44}e^{8} - \frac{1583}{22}e^{6} - \frac{1028}{11}e^{4} - \frac{505}{11}e^{2} - \frac{54}{11}$ |
17 | $[17, 17, w + 6]$ | $\phantom{-}\frac{1}{44}e^{15} + \frac{61}{88}e^{13} + \frac{183}{22}e^{11} + \frac{4383}{88}e^{9} + \frac{1721}{11}e^{7} + \frac{11009}{44}e^{5} + \frac{3947}{22}e^{3} + \frac{450}{11}e$ |
17 | $[17, 17, w + 11]$ | $\phantom{-}\frac{1}{44}e^{15} + \frac{61}{88}e^{13} + \frac{183}{22}e^{11} + \frac{4383}{88}e^{9} + \frac{1721}{11}e^{7} + \frac{11009}{44}e^{5} + \frac{3947}{22}e^{3} + \frac{450}{11}e$ |
23 | $[23, 23, w + 1]$ | $\phantom{-}\frac{1}{44}e^{15} + \frac{61}{88}e^{13} + \frac{743}{88}e^{11} + \frac{2307}{44}e^{9} + \frac{3871}{22}e^{7} + \frac{6841}{22}e^{5} + \frac{5531}{22}e^{3} + \frac{593}{11}e$ |
23 | $[23, 23, w + 22]$ | $\phantom{-}\frac{1}{44}e^{15} + \frac{61}{88}e^{13} + \frac{743}{88}e^{11} + \frac{2307}{44}e^{9} + \frac{3871}{22}e^{7} + \frac{6841}{22}e^{5} + \frac{5531}{22}e^{3} + \frac{593}{11}e$ |
31 | $[31, 31, 4w - 33]$ | $-\frac{1}{44}e^{14} - \frac{25}{44}e^{12} - \frac{245}{44}e^{10} - \frac{1207}{44}e^{8} - \frac{797}{11}e^{6} - \frac{2155}{22}e^{4} - \frac{560}{11}e^{2} + \frac{12}{11}$ |
31 | $[31, 31, 4w + 33]$ | $-\frac{1}{44}e^{14} - \frac{25}{44}e^{12} - \frac{245}{44}e^{10} - \frac{1207}{44}e^{8} - \frac{797}{11}e^{6} - \frac{2155}{22}e^{4} - \frac{560}{11}e^{2} + \frac{12}{11}$ |
37 | $[37, 37, w + 12]$ | $\phantom{-}\frac{1}{88}e^{15} + \frac{9}{22}e^{13} + \frac{487}{88}e^{11} + \frac{397}{11}e^{9} + \frac{1328}{11}e^{7} + \frac{2274}{11}e^{5} + \frac{3695}{22}e^{3} + \frac{544}{11}e$ |
37 | $[37, 37, w + 25]$ | $\phantom{-}\frac{1}{88}e^{15} + \frac{9}{22}e^{13} + \frac{487}{88}e^{11} + \frac{397}{11}e^{9} + \frac{1328}{11}e^{7} + \frac{2274}{11}e^{5} + \frac{3695}{22}e^{3} + \frac{544}{11}e$ |
53 | $[53, 53, w + 21]$ | $\phantom{-}\frac{1}{22}e^{15} + \frac{111}{88}e^{13} + \frac{1211}{88}e^{11} + \frac{3283}{44}e^{9} + \frac{2298}{11}e^{7} + \frac{3101}{11}e^{5} + \frac{3109}{22}e^{3} + \frac{42}{11}e$ |
53 | $[53, 53, w + 32]$ | $\phantom{-}\frac{1}{22}e^{15} + \frac{111}{88}e^{13} + \frac{1211}{88}e^{11} + \frac{3283}{44}e^{9} + \frac{2298}{11}e^{7} + \frac{3101}{11}e^{5} + \frac{3109}{22}e^{3} + \frac{42}{11}e$ |
61 | $[61, 61, -w - 3]$ | $\phantom{-}\frac{3}{88}e^{14} + \frac{75}{88}e^{12} + \frac{181}{22}e^{10} + \frac{1695}{44}e^{8} + \frac{981}{11}e^{6} + \frac{959}{11}e^{4} + \frac{114}{11}e^{2} - \frac{150}{11}$ |
61 | $[61, 61, w - 3]$ | $\phantom{-}\frac{3}{88}e^{14} + \frac{75}{88}e^{12} + \frac{181}{22}e^{10} + \frac{1695}{44}e^{8} + \frac{981}{11}e^{6} + \frac{959}{11}e^{4} + \frac{114}{11}e^{2} - \frac{150}{11}$ |
73 | $[73, 73, w + 17]$ | $-\frac{7}{176}e^{15} - \frac{219}{176}e^{13} - \frac{1347}{88}e^{11} - \frac{1032}{11}e^{9} - \frac{13213}{44}e^{7} - \frac{21199}{44}e^{5} - \frac{7163}{22}e^{3} - \frac{518}{11}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, -3w + 25]$ | $1$ |