Base field \(\Q(\sqrt{201}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 50\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[32, 16, -2w + 14]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $48$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - x^{2} - 4x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -17w - 112]$ | $-1$ |
2 | $[2, 2, -17w + 129]$ | $\phantom{-}0$ |
3 | $[3, 3, -124w + 941]$ | $\phantom{-}e$ |
5 | $[5, 5, -2w + 15]$ | $\phantom{-}e^{2} - e - 3$ |
5 | $[5, 5, -2w - 13]$ | $-e^{2} + e + 3$ |
11 | $[11, 11, 12w + 79]$ | $\phantom{-}e^{2} + 2e - 6$ |
11 | $[11, 11, -12w + 91]$ | $\phantom{-}e^{2} + 2e - 6$ |
19 | $[19, 19, -90w - 593]$ | $-2e^{2} + 2e + 6$ |
19 | $[19, 19, 90w - 683]$ | $\phantom{-}2e^{2} - 2e - 6$ |
37 | $[37, 37, -4w - 27]$ | $-4e^{2} - 2e + 12$ |
37 | $[37, 37, -4w + 31]$ | $-4e^{2} - 2e + 12$ |
41 | $[41, 41, 158w + 1041]$ | $-6$ |
41 | $[41, 41, 158w - 1199]$ | $\phantom{-}6$ |
49 | $[49, 7, -7]$ | $-4e^{2} + 4e + 10$ |
53 | $[53, 53, 46w - 349]$ | $-3e - 6$ |
53 | $[53, 53, 46w + 303]$ | $\phantom{-}3e + 6$ |
67 | $[67, 67, 586w - 4447]$ | $\phantom{-}0$ |
73 | $[73, 73, -32w - 211]$ | $\phantom{-}e^{2} - 4e - 6$ |
73 | $[73, 73, 32w - 243]$ | $\phantom{-}e^{2} - 4e - 6$ |
101 | $[101, 101, 2w - 11]$ | $-4e^{2} - 5e + 18$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -17w - 112]$ | $1$ |
$2$ | $[2, 2, -17w + 129]$ | $-1$ |