Base field \(\Q(\sqrt{205}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 51\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - 8x^{2} - 12x + 20\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 2]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 8]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - 2e - 4$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} - e - 8$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + e + 8$ |
| 13 | $[13, 13, w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + e - 6$ |
| 13 | $[13, 13, w + 9]$ | $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - e + 6$ |
| 17 | $[17, 17, w]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{11}{2}e^{2} - 4e - 13$ |
| 17 | $[17, 17, w + 16]$ | $-\frac{3}{2}e^{3} - \frac{11}{2}e^{2} + 4e + 13$ |
| 31 | $[31, 31, -w - 4]$ | $-e^{3} - 5e^{2} + e + 13$ |
| 31 | $[31, 31, w - 5]$ | $-e^{3} - 5e^{2} + e + 13$ |
| 41 | $[41, 41, 3w - 22]$ | $-e^{3} - 5e^{2} + 8$ |
| 47 | $[47, 47, w + 19]$ | $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} - 2e + 7$ |
| 47 | $[47, 47, w + 27]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + 2e - 7$ |
| 53 | $[53, 53, w + 14]$ | $\phantom{-}e^{3} + 6e^{2} + e - 16$ |
| 53 | $[53, 53, w + 38]$ | $-e^{3} - 6e^{2} - e + 16$ |
| 59 | $[59, 59, -w - 10]$ | $\phantom{-}e^{3} + 5e^{2} - 2e - 20$ |
| 59 | $[59, 59, w - 11]$ | $\phantom{-}e^{3} + 5e^{2} - 2e - 20$ |
| 61 | $[61, 61, 2w - 13]$ | $\phantom{-}e^{2} - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |
| $3$ | $[3, 3, w + 2]$ | $1$ |