Base field \(\Q(\sqrt{11}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[22, 22, -3w + 11]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 15x^{2} + 60x - 48\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 3]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 4]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w - 4]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{11}{4}e$ |
| 7 | $[7, 7, w + 2]$ | $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{19}{4}e - 11$ |
| 7 | $[7, 7, w - 2]$ | $\phantom{-}\frac{3}{4}e^{3} - \frac{1}{4}e^{2} - \frac{49}{4}e + 16$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{4}e^{3} - \frac{1}{4}e^{2} + \frac{15}{4}e - 2$ |
| 11 | $[11, 11, -w]$ | $\phantom{-}1$ |
| 19 | $[19, 19, 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{15}{2}e + 10$ |
| 19 | $[19, 19, -2w - 5]$ | $-\frac{3}{4}e^{3} + \frac{1}{4}e^{2} + \frac{45}{4}e - 17$ |
| 37 | $[37, 37, 2w - 9]$ | $\phantom{-}2e^{3} - e^{2} - 32e + 44$ |
| 37 | $[37, 37, -2w - 9]$ | $-\frac{5}{4}e^{3} + \frac{7}{4}e^{2} + \frac{83}{4}e - 37$ |
| 43 | $[43, 43, 2w - 1]$ | $-\frac{5}{4}e^{3} - \frac{1}{4}e^{2} + \frac{75}{4}e - 17$ |
| 43 | $[43, 43, -2w - 1]$ | $-e^{2} + 10$ |
| 53 | $[53, 53, -w - 8]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{23}{4}e + 9$ |
| 53 | $[53, 53, w - 8]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{19}{2}e - 18$ |
| 79 | $[79, 79, 5w - 14]$ | $\phantom{-}2e^{3} - 2e^{2} - 32e + 52$ |
| 79 | $[79, 79, 8w - 25]$ | $-\frac{5}{2}e^{3} + \frac{3}{2}e^{2} + \frac{79}{2}e - 56$ |
| 83 | $[83, 83, -3w - 4]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{1}{2}e^{2} - \frac{47}{2}e + 24$ |
| 83 | $[83, 83, 3w - 4]$ | $-\frac{3}{4}e^{3} + \frac{5}{4}e^{2} + \frac{49}{4}e - 30$ |
| 89 | $[89, 89, -w - 10]$ | $\phantom{-}\frac{3}{2}e^{3} - \frac{1}{2}e^{2} - \frac{45}{2}e + 24$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 3]$ | $-1$ |
| $11$ | $[11, 11, -w]$ | $-1$ |