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: | $3$ |
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:
\(x^{3} + 3x^{2} - x - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
8 | $[8, 2, w^{3} - 3w - 1]$ | $-e$ |
37 | $[37, 37, w^{4} - 5w^{2} - w + 5]$ | $\phantom{-}1$ |
37 | $[37, 37, w^{5} - 5w^{3} - w^{2} + 4w + 1]$ | $-2e - 4$ |
37 | $[37, 37, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w + 1]$ | $-2e^{2} - 6e + 2$ |
37 | $[37, 37, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 5w + 1]$ | $-5e^{2} - 4e + 15$ |
37 | $[37, 37, w^{5} - 5w^{3} + w^{2} + 4w - 1]$ | $\phantom{-}e^{2} + 4e - 3$ |
37 | $[37, 37, -w^{4} + 5w^{2} - w - 5]$ | $\phantom{-}3e^{2} - 13$ |
71 | $[71, 71, w^{5} - 5w^{3} - w^{2} + 5w + 4]$ | $-e^{2} + 2e + 11$ |
71 | $[71, 71, w^{5} - 4w^{3} - w^{2} + w + 2]$ | $\phantom{-}4e^{2} + 2e - 16$ |
71 | $[71, 71, w^{5} + w^{4} - 5w^{3} - 5w^{2} + 4w + 2]$ | $\phantom{-}5e^{2} - 21$ |
71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 4w - 2]$ | $\phantom{-}14$ |
71 | $[71, 71, -w^{5} + 4w^{3} - w^{2} - w + 2]$ | $\phantom{-}e^{2} + 4e - 5$ |
71 | $[71, 71, -w^{5} + 5w^{3} - w^{2} - 5w + 4]$ | $\phantom{-}3e^{2} + 8e - 3$ |
73 | $[73, 73, w^{5} - 5w^{3} - w^{2} + 3w + 2]$ | $\phantom{-}5e^{2} + 6e - 18$ |
73 | $[73, 73, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 2]$ | $\phantom{-}2e^{2} + 4e - 9$ |
73 | $[73, 73, -w^{5} + 4w^{3} - w^{2} - 2w + 2]$ | $-2e^{2} + 2e + 5$ |
73 | $[73, 73, w^{5} - 4w^{3} - w^{2} + 2w + 2]$ | $-3e^{2} + 8$ |
73 | $[73, 73, -2w^{5} - w^{4} + 10w^{3} + 4w^{2} - 9w - 2]$ | $\phantom{-}3e^{2} + 10e - 4$ |
73 | $[73, 73, w^{5} - 5w^{3} + w^{2} + 3w - 2]$ | $-5e^{2} - 6e + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$37$ | $[37, 37, w^{4} - 5w^{2} - w + 5]$ | $-1$ |