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: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 22x^{4} + 137x^{2} + 196\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{9}{8}e^{2} - \frac{1}{2}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 4]$ | $-e$ |
| 7 | $[7, 7, w + 2]$ | $-\frac{1}{56}e^{5} - \frac{1}{56}e^{3} + \frac{27}{14}e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{1}{56}e^{5} + \frac{1}{56}e^{3} - \frac{27}{14}e$ |
| 9 | $[9, 3, 3]$ | $-\frac{3}{8}e^{4} - \frac{43}{8}e^{2} - \frac{27}{2}$ |
| 11 | $[11, 11, w]$ | $\phantom{-}\frac{3}{56}e^{5} + \frac{59}{56}e^{3} + \frac{59}{14}e$ |
| 11 | $[11, 11, w + 10]$ | $-\frac{3}{56}e^{5} - \frac{59}{56}e^{3} - \frac{59}{14}e$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{1}{4}e^{4} - \frac{17}{4}e^{2} - 11$ |
| 17 | $[17, 17, -w - 8]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{17}{4}e^{2} + 15$ |
| 31 | $[31, 31, w + 14]$ | $-\frac{3}{28}e^{5} - \frac{31}{28}e^{3} - \frac{3}{7}e$ |
| 31 | $[31, 31, w + 16]$ | $\phantom{-}\frac{3}{28}e^{5} + \frac{31}{28}e^{3} + \frac{3}{7}e$ |
| 37 | $[37, 37, w + 15]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{15}{7}e^{3} + \frac{53}{7}e$ |
| 37 | $[37, 37, w + 21]$ | $-\frac{1}{7}e^{5} - \frac{15}{7}e^{3} - \frac{53}{7}e$ |
| 41 | $[41, 41, w + 18]$ | $\phantom{-}\frac{1}{7}e^{5} + \frac{8}{7}e^{3} - \frac{31}{7}e$ |
| 41 | $[41, 41, w + 22]$ | $-\frac{1}{7}e^{5} - \frac{8}{7}e^{3} + \frac{31}{7}e$ |
| 43 | $[43, 43, -w - 3]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{21}{4}e^{2} + 21$ |
| 43 | $[43, 43, w - 4]$ | $\phantom{-}\frac{1}{4}e^{4} + \frac{21}{4}e^{2} + 21$ |
| 53 | $[53, 53, -w - 1]$ | $-\frac{3}{8}e^{4} - \frac{35}{8}e^{2} - \frac{19}{2}$ |
| 53 | $[53, 53, w - 2]$ | $-\frac{3}{8}e^{4} - \frac{35}{8}e^{2} - \frac{19}{2}$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).