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: | $[5, 5, w]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 10x^{4} + 17x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-\frac{1}{13}e^{4} - e^{2} - \frac{30}{13}$ |
5 | $[5, 5, w]$ | $\phantom{-}\frac{4}{13}e^{5} + 3e^{3} + \frac{55}{13}e$ |
5 | $[5, 5, w + 4]$ | $\phantom{-}e$ |
7 | $[7, 7, w + 2]$ | $-\frac{6}{13}e^{5} - 4e^{3} - \frac{37}{13}e$ |
7 | $[7, 7, w + 4]$ | $-\frac{10}{13}e^{5} - 7e^{3} - \frac{118}{13}e$ |
9 | $[9, 3, 3]$ | $-\frac{4}{13}e^{4} - 2e^{2} + \frac{10}{13}$ |
11 | $[11, 11, w]$ | $-\frac{2}{13}e^{5} - 2e^{3} - \frac{73}{13}e$ |
11 | $[11, 11, w + 10]$ | $-\frac{16}{13}e^{5} - 13e^{3} - \frac{337}{13}e$ |
13 | $[13, 13, w + 6]$ | $-\frac{1}{13}e^{4} + \frac{48}{13}$ |
17 | $[17, 17, -w - 8]$ | $-\frac{1}{13}e^{4} - e^{2} - \frac{30}{13}$ |
31 | $[31, 31, w + 14]$ | $\phantom{-}e$ |
31 | $[31, 31, w + 16]$ | $-\frac{15}{13}e^{5} - 11e^{3} - \frac{216}{13}e$ |
37 | $[37, 37, w + 15]$ | $\phantom{-}\frac{37}{13}e^{5} + 28e^{3} + \frac{603}{13}e$ |
37 | $[37, 37, w + 21]$ | $-\frac{3}{13}e^{5} - e^{3} + \frac{92}{13}e$ |
41 | $[41, 41, w + 18]$ | $-\frac{1}{13}e^{5} - 2e^{3} - \frac{95}{13}e$ |
41 | $[41, 41, w + 22]$ | $\phantom{-}\frac{7}{13}e^{5} + 6e^{3} + \frac{158}{13}e$ |
43 | $[43, 43, -w - 3]$ | $-\frac{5}{13}e^{4} - 4e^{2} + \frac{58}{13}$ |
43 | $[43, 43, w - 4]$ | $\phantom{-}\frac{8}{13}e^{4} + 6e^{2} + \frac{58}{13}$ |
53 | $[53, 53, -w - 1]$ | $-\frac{2}{13}e^{4} - e^{2} - \frac{34}{13}$ |
53 | $[53, 53, w - 2]$ | $\phantom{-}\frac{11}{13}e^{4} + 9e^{2} + \frac{135}{13}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w]$ | $-\frac{4}{13}e^{5} - 3e^{3} - \frac{55}{13}e$ |