Base field \(\Q(\sqrt{221}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 55\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[5, 5, w]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 9x^{2} + x + 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $-1$ |
5 | $[5, 5, w + 4]$ | $\phantom{-}e^{3} + 3e^{2} - 4e - 6$ |
7 | $[7, 7, w + 2]$ | $-e^{3} - 2e^{2} + 6e + 4$ |
7 | $[7, 7, w + 4]$ | $\phantom{-}e^{3} + 3e^{2} - 5e - 7$ |
9 | $[9, 3, 3]$ | $-e^{3} - 2e^{2} + 5e + 2$ |
11 | $[11, 11, w]$ | $-2e^{3} - 5e^{2} + 10e + 12$ |
11 | $[11, 11, w + 10]$ | $-e + 1$ |
13 | $[13, 13, w + 6]$ | $\phantom{-}3e^{3} + 8e^{2} - 13e - 16$ |
17 | $[17, 17, -w - 8]$ | $-4e^{3} - 10e^{2} + 19e + 21$ |
31 | $[31, 31, w + 14]$ | $-4e^{3} - 10e^{2} + 19e + 23$ |
31 | $[31, 31, w + 16]$ | $\phantom{-}2e^{3} + 5e^{2} - 9e - 10$ |
37 | $[37, 37, w + 15]$ | $-4e^{3} - 11e^{2} + 18e + 24$ |
37 | $[37, 37, w + 21]$ | $\phantom{-}4e^{3} + 13e^{2} - 14e - 31$ |
41 | $[41, 41, w + 18]$ | $\phantom{-}4e^{3} + 9e^{2} - 20e - 14$ |
41 | $[41, 41, w + 22]$ | $-9e^{3} - 24e^{2} + 40e + 52$ |
43 | $[43, 43, -w - 3]$ | $\phantom{-}3e^{3} + 10e^{2} - 10e - 24$ |
43 | $[43, 43, w - 4]$ | $-e^{2} - 4e + 9$ |
53 | $[53, 53, -w - 1]$ | $\phantom{-}7e^{3} + 18e^{2} - 31e - 36$ |
53 | $[53, 53, w - 2]$ | $-4e^{3} - 10e^{2} + 18e + 19$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w]$ | $1$ |