Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 26x^{4} + 121x^{2} + 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{24}e^{5} + \frac{23}{24}e^{3} + \frac{29}{12}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{1}{24}e^{5} - \frac{23}{24}e^{3} - \frac{29}{12}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{3}{16}e^{4} - \frac{71}{16}e^{2} - 10$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 6]$ | $-e$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{21}{8}e^{2} + 6$ |
| 19 | $[19, 19, w - 2]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{21}{8}e^{2} + 6$ |
| 23 | $[23, 23, w + 9]$ | $-\frac{5}{24}e^{5} - \frac{121}{24}e^{3} - \frac{43}{3}e$ |
| 23 | $[23, 23, w + 13]$ | $\phantom{-}\frac{5}{24}e^{5} + \frac{121}{24}e^{3} + \frac{43}{3}e$ |
| 37 | $[37, 37, w + 11]$ | $-\frac{5}{24}e^{5} - \frac{121}{24}e^{3} - \frac{46}{3}e$ |
| 37 | $[37, 37, w + 25]$ | $\phantom{-}\frac{5}{24}e^{5} + \frac{121}{24}e^{3} + \frac{46}{3}e$ |
| 59 | $[59, 59, 3w + 10]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{29}{8}e^{2} + 14$ |
| 59 | $[59, 59, 3w - 13]$ | $\phantom{-}\frac{1}{8}e^{4} + \frac{29}{8}e^{2} + 14$ |
| 73 | $[73, 73, w + 15]$ | $-\frac{5}{24}e^{5} - \frac{121}{24}e^{3} - \frac{46}{3}e$ |
| 73 | $[73, 73, w + 57]$ | $\phantom{-}\frac{5}{24}e^{5} + \frac{121}{24}e^{3} + \frac{46}{3}e$ |
| 89 | $[89, 89, -w - 10]$ | $\phantom{-}\frac{7}{8}e^{4} + \frac{155}{8}e^{2} + 44$ |
| 89 | $[89, 89, w - 11]$ | $\phantom{-}\frac{7}{8}e^{4} + \frac{155}{8}e^{2} + 44$ |
| 97 | $[97, 97, w + 22]$ | $-\frac{1}{12}e^{5} - \frac{29}{12}e^{3} - \frac{46}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-\frac{1}{24}e^{5} - \frac{23}{24}e^{3} - \frac{29}{12}e$ |
| $3$ | $[3, 3, w + 2]$ | $\frac{1}{24}e^{5} + \frac{23}{24}e^{3} + \frac{29}{12}e$ |