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: | $[1, 1, 1]$ |
Dimension: | $16$ |
CM: | no |
Base change: | no |
Newspace dimension: | $120$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{16} - x^{15} + 9x^{14} + x^{13} + 46x^{12} - 73x^{11} + 396x^{10} - 614x^{9} + 1661x^{8} - 1674x^{7} + 3375x^{6} - 326x^{5} - 723x^{4} + 228x^{3} + 3930x^{2} + 779x + 361\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $...$ |
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
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).