Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[11,11,2w - 13]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - x^{3} - 6x^{2} + 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 6]$ | $\phantom{-}e^{2} - 3$ |
3 | $[3, 3, -w - 5]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $-e + 1$ |
7 | $[7, 7, 3w - 19]$ | $\phantom{-}2e^{3} - e^{2} - 12e + 7$ |
11 | $[11, 11, -2w - 11]$ | $-e^{3} + 5e + 2$ |
11 | $[11, 11, -2w + 13]$ | $-1$ |
13 | $[13, 13, w + 4]$ | $\phantom{-}3e^{3} - e^{2} - 18e + 6$ |
13 | $[13, 13, -w + 5]$ | $\phantom{-}3e^{3} - e^{2} - 18e + 6$ |
19 | $[19, 19, 5w - 31]$ | $\phantom{-}e - 4$ |
23 | $[23, 23, -w - 7]$ | $-2e^{2} + 5$ |
23 | $[23, 23, w - 8]$ | $-3e^{3} + 2e^{2} + 19e - 6$ |
25 | $[25, 5, -5]$ | $\phantom{-}2e^{3} - e^{2} - 15e + 4$ |
31 | $[31, 31, -w - 1]$ | $-3e^{3} + 2e^{2} + 20e - 9$ |
31 | $[31, 31, w - 2]$ | $\phantom{-}e^{3} - 8e + 3$ |
41 | $[41, 41, 6w + 31]$ | $-3e^{3} + 2e^{2} + 18e - 8$ |
41 | $[41, 41, 6w - 37]$ | $-2e^{2} - e + 3$ |
43 | $[43, 43, -3w - 17]$ | $\phantom{-}3e^{3} - 17e + 3$ |
43 | $[43, 43, -3w + 20]$ | $\phantom{-}e^{3} - 2e^{2} - 4e + 5$ |
59 | $[59, 59, 3w - 17]$ | $\phantom{-}4e^{3} - 2e^{2} - 27e + 14$ |
59 | $[59, 59, 3w + 14]$ | $\phantom{-}2e^{3} - 2e^{2} - 8e + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11,11,2w - 13]$ | $1$ |