Base field \(\Q(\sqrt{11}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 11\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[19, 19, 2w - 5]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 5x^{2} - x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 4]$ | $\phantom{-}e^{3} + e^{2} - 3e$ |
5 | $[5, 5, -w - 4]$ | $-e^{3} - 2e^{2} + 2e + 3$ |
7 | $[7, 7, w + 2]$ | $\phantom{-}e^{2} + e - 4$ |
7 | $[7, 7, w - 2]$ | $-e^{3} - 2e^{2} + 3e + 2$ |
9 | $[9, 3, 3]$ | $\phantom{-}e^{3} + 2e^{2} - 3e - 5$ |
11 | $[11, 11, -w]$ | $-2e - 3$ |
19 | $[19, 19, 2w - 5]$ | $\phantom{-}1$ |
19 | $[19, 19, -2w - 5]$ | $\phantom{-}e^{3} + e^{2} - 4e - 4$ |
37 | $[37, 37, 2w - 9]$ | $-4e^{3} - 5e^{2} + 14e + 2$ |
37 | $[37, 37, -2w - 9]$ | $-e^{3} + 7e + 2$ |
43 | $[43, 43, 2w - 1]$ | $\phantom{-}3e^{3} + 3e^{2} - 13e - 4$ |
43 | $[43, 43, -2w - 1]$ | $\phantom{-}e^{3} + 3e^{2} - e - 7$ |
53 | $[53, 53, -w - 8]$ | $-e^{3} - 2e^{2} + 5e$ |
53 | $[53, 53, w - 8]$ | $\phantom{-}e^{3} - 6e + 3$ |
79 | $[79, 79, 5w - 14]$ | $-e^{3} + 10e - 7$ |
79 | $[79, 79, 8w - 25]$ | $\phantom{-}2e^{3} + 2e^{2} - 10e - 4$ |
83 | $[83, 83, -3w - 4]$ | $-3e^{3} - e^{2} + 14e + 6$ |
83 | $[83, 83, 3w - 4]$ | $-3e^{3} - 2e^{2} + 7e - 6$ |
89 | $[89, 89, -w - 10]$ | $\phantom{-}3e^{3} + 9e^{2} - 5e - 15$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, 2w - 5]$ | $-1$ |