Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[2, 2, w]$ |
Dimension: | $4$ |
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:
\(x^{4} + 3x^{3} - x^{2} - 7x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}1$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, -2w + 19]$ | $-e^{3} - 2e^{2} + 3e + 4$ |
5 | $[5, 5, w]$ | $\phantom{-}e^{3} + e^{2} - 2e$ |
5 | $[5, 5, w + 4]$ | $\phantom{-}e^{3} + 2e^{2} - 3e - 6$ |
13 | $[13, 13, w + 1]$ | $-4e^{3} - 6e^{2} + 11e + 11$ |
13 | $[13, 13, w + 11]$ | $\phantom{-}e^{3} - 5e - 1$ |
17 | $[17, 17, w + 3]$ | $\phantom{-}2e^{3} + 5e^{2} - 6e - 12$ |
17 | $[17, 17, w + 13]$ | $\phantom{-}2e^{3} + 4e^{2} - 4e - 9$ |
19 | $[19, 19, w + 6]$ | $\phantom{-}e^{3} - 7e - 1$ |
19 | $[19, 19, w + 12]$ | $\phantom{-}2e - 1$ |
37 | $[37, 37, w + 2]$ | $\phantom{-}2e^{3} + 6e^{2} - 4e - 10$ |
37 | $[37, 37, w + 34]$ | $-5e^{3} - 9e^{2} + 10e + 14$ |
49 | $[49, 7, -7]$ | $\phantom{-}e^{3} + 2e^{2} - 3e - 13$ |
59 | $[59, 59, -4w - 33]$ | $-7e^{3} - 11e^{2} + 22e + 21$ |
59 | $[59, 59, 4w - 37]$ | $\phantom{-}2e^{3} + 2e^{2} - 4e - 3$ |
61 | $[61, 61, w + 28]$ | $\phantom{-}3e^{2} + 2e - 4$ |
61 | $[61, 61, w + 32]$ | $\phantom{-}4e^{2} + 2e - 13$ |
71 | $[71, 71, w + 22]$ | $\phantom{-}e^{3} - e^{2} - 8e$ |
71 | $[71, 71, w + 48]$ | $-e^{3} + e^{2} + 3e + 3$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $-1$ |