Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[16, 4, 4]$ |
Dimension: | $18$ |
CM: | no |
Base change: | no |
Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{18} + 4x^{17} - 71x^{16} - 302x^{15} + 2001x^{14} + 9297x^{13} - 28235x^{12} - 150929x^{11} + 202237x^{10} + 1399415x^{9} - 566123x^{8} - 7519482x^{7} - 1128525x^{6} + 22597312x^{5} + 10966500x^{4} - 34131294x^{3} - 23156396x^{2} + 19425771x + 15090039\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}0$ |
7 | $[7, 7, w - 7]$ | $...$ |
7 | $[7, 7, w + 6]$ | $\phantom{-}e$ |
9 | $[9, 3, 3]$ | $...$ |
19 | $[19, 19, w + 5]$ | $...$ |
19 | $[19, 19, w - 6]$ | $...$ |
23 | $[23, 23, w + 8]$ | $...$ |
23 | $[23, 23, -w + 9]$ | $...$ |
25 | $[25, 5, 5]$ | $...$ |
29 | $[29, 29, -w - 4]$ | $...$ |
29 | $[29, 29, w - 5]$ | $...$ |
37 | $[37, 37, -w - 3]$ | $...$ |
37 | $[37, 37, w - 4]$ | $...$ |
41 | $[41, 41, -w - 9]$ | $...$ |
41 | $[41, 41, w - 10]$ | $...$ |
43 | $[43, 43, -w - 2]$ | $...$ |
43 | $[43, 43, w - 3]$ | $...$ |
47 | $[47, 47, -w - 1]$ | $...$ |
47 | $[47, 47, w - 2]$ | $...$ |
53 | $[53, 53, 2w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, 2]$ | $-1$ |