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: | $[37, 37, w^{4} - 5w^{2} - w + 5]$ |
Dimension: | $22$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{22} - 50x^{20} + 1066x^{18} - 12665x^{16} + 92003x^{14} - 422173x^{12} + 1222435x^{10} - 2172392x^{8} + 2241113x^{6} - 1228148x^{4} + 322256x^{2} - 30976\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
8 | $[8, 2, w^{3} - 3w - 1]$ | $...$ |
37 | $[37, 37, w^{4} - 5w^{2} - w + 5]$ | $-1$ |
37 | $[37, 37, w^{5} - 5w^{3} - w^{2} + 4w + 1]$ | $...$ |
37 | $[37, 37, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w + 1]$ | $...$ |
37 | $[37, 37, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 5w + 1]$ | $...$ |
37 | $[37, 37, w^{5} - 5w^{3} + w^{2} + 4w - 1]$ | $...$ |
37 | $[37, 37, -w^{4} + 5w^{2} - w - 5]$ | $...$ |
71 | $[71, 71, w^{5} - 5w^{3} - w^{2} + 5w + 4]$ | $...$ |
71 | $[71, 71, w^{5} - 4w^{3} - w^{2} + w + 2]$ | $...$ |
71 | $[71, 71, w^{5} + w^{4} - 5w^{3} - 5w^{2} + 4w + 2]$ | $...$ |
71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 4w - 2]$ | $...$ |
71 | $[71, 71, -w^{5} + 4w^{3} - w^{2} - w + 2]$ | $...$ |
71 | $[71, 71, -w^{5} + 5w^{3} - w^{2} - 5w + 4]$ | $...$ |
73 | $[73, 73, w^{5} - 5w^{3} - w^{2} + 3w + 2]$ | $...$ |
73 | $[73, 73, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 2]$ | $...$ |
73 | $[73, 73, -w^{5} + 4w^{3} - w^{2} - 2w + 2]$ | $...$ |
73 | $[73, 73, w^{5} - 4w^{3} - w^{2} + 2w + 2]$ | $...$ |
73 | $[73, 73, -2w^{5} - w^{4} + 10w^{3} + 4w^{2} - 9w - 2]$ | $...$ |
73 | $[73, 73, w^{5} - 5w^{3} + w^{2} + 3w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$37$ | $[37, 37, w^{4} - 5w^{2} - w + 5]$ | $1$ |