Base field \(\Q(\sqrt{221}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 55\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[7,7,-w + 3]$ |
Dimension: | $15$ |
CM: | no |
Base change: | no |
Newspace dimension: | $60$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{15} + 4x^{14} - 26x^{13} - 114x^{12} + 221x^{11} + 1184x^{10} - 551x^{9} - 5490x^{8} - 1181x^{7} + 11353x^{6} + 6350x^{5} - 9474x^{4} - 6955x^{3} + 2503x^{2} + 2130x + 25\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $...$ |
5 | $[5, 5, w + 4]$ | $...$ |
7 | $[7, 7, w + 2]$ | $...$ |
7 | $[7, 7, w + 4]$ | $\phantom{-}1$ |
9 | $[9, 3, 3]$ | $...$ |
11 | $[11, 11, w]$ | $...$ |
11 | $[11, 11, w + 10]$ | $...$ |
13 | $[13, 13, w + 6]$ | $...$ |
17 | $[17, 17, -w - 8]$ | $...$ |
31 | $[31, 31, w + 14]$ | $...$ |
31 | $[31, 31, w + 16]$ | $...$ |
37 | $[37, 37, w + 15]$ | $...$ |
37 | $[37, 37, w + 21]$ | $...$ |
41 | $[41, 41, w + 18]$ | $...$ |
41 | $[41, 41, w + 22]$ | $...$ |
43 | $[43, 43, -w - 3]$ | $...$ |
43 | $[43, 43, w - 4]$ | $...$ |
53 | $[53, 53, -w - 1]$ | $...$ |
53 | $[53, 53, w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7,7,-w + 3]$ | $-1$ |