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: | $[8, 8, -w + 8]$ |
Dimension: | $14$ |
CM: | no |
Base change: | no |
Newspace dimension: | $25$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{14} - 2x^{13} - 21x^{12} + 40x^{11} + 169x^{10} - 307x^{9} - 645x^{8} + 1130x^{7} + 1149x^{6} - 2017x^{5} - 738x^{4} + 1537x^{3} - 39x^{2} - 377x + 88\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -9w - 58]$ | $\phantom{-}0$ |
2 | $[2, 2, -9w + 67]$ | $\phantom{-}e$ |
3 | $[3, 3, -2w + 15]$ | $...$ |
3 | $[3, 3, 2w + 13]$ | $...$ |
7 | $[7, 7, 186w - 1385]$ | $...$ |
7 | $[7, 7, -186w - 1199]$ | $...$ |
23 | $[23, 23, -38w - 245]$ | $...$ |
23 | $[23, 23, 38w - 283]$ | $...$ |
25 | $[25, 5, 5]$ | $...$ |
31 | $[31, 31, 16w - 119]$ | $...$ |
31 | $[31, 31, 16w + 103]$ | $...$ |
43 | $[43, 43, 4w + 25]$ | $...$ |
43 | $[43, 43, -4w + 29]$ | $...$ |
59 | $[59, 59, 12w - 89]$ | $...$ |
59 | $[59, 59, -12w - 77]$ | $...$ |
67 | $[67, 67, 92w + 593]$ | $...$ |
67 | $[67, 67, 92w - 685]$ | $...$ |
83 | $[83, 83, 204w - 1519]$ | $...$ |
83 | $[83, 83, 204w + 1315]$ | $...$ |
97 | $[97, 97, -24w + 179]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -9w - 58]$ | $1$ |