Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
Weight: | $[2, 2]$ |
Level: | $[5,5,-w + 1]$ |
Dimension: | $20$ |
CM: | no |
Base change: | no |
Newspace dimension: | $168$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{20} - x^{19} - 28x^{18} + 24x^{17} + 327x^{16} - 237x^{15} - 2064x^{14} + 1261x^{13} + 7642x^{12} - 3999x^{11} - 16920x^{10} + 7874x^{9} + 21988x^{8} - 9483x^{7} - 15757x^{6} + 6404x^{5} + 5386x^{4} - 1955x^{3} - 569x^{2} + 116x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $...$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, -2w + 19]$ | $...$ |
5 | $[5, 5, w]$ | $...$ |
5 | $[5, 5, w + 4]$ | $-1$ |
13 | $[13, 13, w + 1]$ | $...$ |
13 | $[13, 13, w + 11]$ | $...$ |
17 | $[17, 17, w + 3]$ | $...$ |
17 | $[17, 17, w + 13]$ | $...$ |
19 | $[19, 19, w + 6]$ | $...$ |
19 | $[19, 19, w + 12]$ | $...$ |
37 | $[37, 37, w + 2]$ | $...$ |
37 | $[37, 37, w + 34]$ | $...$ |
49 | $[49, 7, -7]$ | $...$ |
59 | $[59, 59, -4w - 33]$ | $...$ |
59 | $[59, 59, 4w - 37]$ | $...$ |
61 | $[61, 61, w + 28]$ | $...$ |
61 | $[61, 61, w + 32]$ | $...$ |
71 | $[71, 71, w + 22]$ | $...$ |
71 | $[71, 71, w + 48]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,-w + 1]$ | $1$ |