Base field \(\Q(\sqrt{193}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 48\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[6,6,w - 7]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -9w - 58]$ | $\phantom{-}e$ |
2 | $[2, 2, -9w + 67]$ | $\phantom{-}1$ |
3 | $[3, 3, -2w + 15]$ | $\phantom{-}e + 1$ |
3 | $[3, 3, 2w + 13]$ | $\phantom{-}1$ |
7 | $[7, 7, 186w - 1385]$ | $\phantom{-}2e + 2$ |
7 | $[7, 7, -186w - 1199]$ | $-e - 3$ |
23 | $[23, 23, -38w - 245]$ | $-2e + 2$ |
23 | $[23, 23, 38w - 283]$ | $\phantom{-}2e - 3$ |
25 | $[25, 5, 5]$ | $\phantom{-}5$ |
31 | $[31, 31, 16w - 119]$ | $-2e + 3$ |
31 | $[31, 31, 16w + 103]$ | $\phantom{-}3e + 2$ |
43 | $[43, 43, 4w + 25]$ | $-5e + 3$ |
43 | $[43, 43, -4w + 29]$ | $\phantom{-}4e + 4$ |
59 | $[59, 59, 12w - 89]$ | $-5e - 2$ |
59 | $[59, 59, -12w - 77]$ | $-4e - 5$ |
67 | $[67, 67, 92w + 593]$ | $\phantom{-}5$ |
67 | $[67, 67, 92w - 685]$ | $-3e$ |
83 | $[83, 83, 204w - 1519]$ | $-4e - 2$ |
83 | $[83, 83, 204w + 1315]$ | $\phantom{-}e - 10$ |
97 | $[97, 97, -24w + 179]$ | $\phantom{-}6e + 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,9w - 67]$ | $-1$ |
$3$ | $[3,3,2w + 13]$ | $-1$ |