Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
Weight: | $[2, 2]$ |
Level: | $[4, 4, w]$ |
Dimension: | $20$ |
CM: | no |
Base change: | no |
Newspace dimension: | $100$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{20} - 29x^{18} + 6x^{17} + 350x^{16} - 141x^{15} - 2267x^{14} + 1328x^{13} + 8457x^{12} - 6385x^{11} - 18041x^{10} + 16485x^{9} + 20301x^{8} - 21899x^{7} - 9670x^{6} + 12866x^{5} + 943x^{4} - 2479x^{3} + 85x^{2} + 114x - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}0$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $...$ |
5 | $[5, 5, w + 4]$ | $...$ |
7 | $[7, 7, w + 1]$ | $...$ |
7 | $[7, 7, w + 5]$ | $...$ |
9 | $[9, 3, 3]$ | $...$ |
11 | $[11, 11, w + 3]$ | $...$ |
11 | $[11, 11, w + 7]$ | $...$ |
29 | $[29, 29, w + 6]$ | $...$ |
29 | $[29, 29, w + 22]$ | $...$ |
41 | $[41, 41, w + 13]$ | $...$ |
41 | $[41, 41, w + 27]$ | $...$ |
43 | $[43, 43, w + 16]$ | $...$ |
43 | $[43, 43, w + 26]$ | $...$ |
47 | $[47, 47, w + 2]$ | $...$ |
47 | $[47, 47, w + 44]$ | $...$ |
73 | $[73, 73, w + 33]$ | $...$ |
73 | $[73, 73, w + 39]$ | $...$ |
83 | $[83, 83, -4w - 37]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $-1$ |