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: | $[9, 9, -w + 7]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 11x^{2} - 12x + 65\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{2}{33}e^{3} - \frac{1}{11}e^{2} + \frac{7}{33}e + \frac{4}{33}$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $-\frac{2}{33}e^{3} - \frac{1}{11}e^{2} + \frac{40}{33}e + \frac{4}{33}$ |
| 5 | $[5, 5, -w + 8]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{33}e^{3} + \frac{6}{11}e^{2} + \frac{13}{33}e - \frac{101}{33}$ |
| 7 | $[7, 7, w + 5]$ | $-\frac{1}{33}e^{3} - \frac{6}{11}e^{2} - \frac{13}{33}e + \frac{101}{33}$ |
| 13 | $[13, 13, w + 3]$ | $-\frac{5}{33}e^{3} - \frac{8}{11}e^{2} + \frac{1}{33}e + \frac{109}{33}$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{5}{33}e^{3} + \frac{8}{11}e^{2} - \frac{1}{33}e - \frac{109}{33}$ |
| 17 | $[17, 17, w]$ | $\phantom{-}\frac{2}{11}e^{3} + \frac{3}{11}e^{2} - \frac{7}{11}e - \frac{4}{11}$ |
| 17 | $[17, 17, w + 16]$ | $\phantom{-}\frac{2}{11}e^{3} + \frac{3}{11}e^{2} - \frac{7}{11}e - \frac{4}{11}$ |
| 31 | $[31, 31, -w - 4]$ | $-\frac{2}{33}e^{3} - \frac{1}{11}e^{2} + \frac{40}{33}e + \frac{136}{33}$ |
| 31 | $[31, 31, w - 5]$ | $-\frac{2}{33}e^{3} - \frac{1}{11}e^{2} + \frac{40}{33}e + \frac{136}{33}$ |
| 41 | $[41, 41, 3w - 22]$ | $\phantom{-}0$ |
| 47 | $[47, 47, w + 19]$ | $-\frac{1}{11}e^{3} + \frac{15}{11}e^{2} + \frac{20}{11}e - \frac{97}{11}$ |
| 47 | $[47, 47, w + 27]$ | $-\frac{1}{11}e^{3} + \frac{15}{11}e^{2} + \frac{20}{11}e - \frac{97}{11}$ |
| 53 | $[53, 53, w + 14]$ | $\phantom{-}\frac{4}{11}e^{3} + \frac{6}{11}e^{2} - \frac{14}{11}e - \frac{8}{11}$ |
| 53 | $[53, 53, w + 38]$ | $\phantom{-}\frac{4}{11}e^{3} + \frac{6}{11}e^{2} - \frac{14}{11}e - \frac{8}{11}$ |
| 59 | $[59, 59, -w - 10]$ | $\phantom{-}\frac{2}{11}e^{3} + \frac{3}{11}e^{2} - \frac{40}{11}e - \frac{37}{11}$ |
| 59 | $[59, 59, w - 11]$ | $-\frac{2}{11}e^{3} - \frac{3}{11}e^{2} + \frac{40}{11}e + \frac{37}{11}$ |
| 61 | $[61, 61, 2w - 13]$ | $-\frac{4}{33}e^{3} - \frac{2}{11}e^{2} + \frac{80}{33}e + \frac{107}{33}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 2]$ | $1$ |