Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 5x^{5} - 12x^{4} + 76x^{3} + 5x^{2} - 205x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w - 5]$ | $\phantom{-}1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 3w - 19]$ | $-\frac{30}{109}e^{5} + \frac{57}{109}e^{4} + \frac{504}{109}e^{3} - \frac{674}{109}e^{2} - \frac{1738}{109}e + \frac{457}{109}$ |
| 11 | $[11, 11, -2w - 11]$ | $\phantom{-}\frac{10}{109}e^{5} - \frac{19}{109}e^{4} - \frac{168}{109}e^{3} + \frac{152}{109}e^{2} + \frac{652}{109}e + \frac{429}{109}$ |
| 11 | $[11, 11, -2w + 13]$ | $\phantom{-}\frac{10}{109}e^{5} - \frac{19}{109}e^{4} - \frac{168}{109}e^{3} + \frac{152}{109}e^{2} + \frac{652}{109}e + \frac{429}{109}$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{11}{109}e^{5} - \frac{10}{109}e^{4} - \frac{163}{109}e^{3} + \frac{80}{109}e^{2} + \frac{412}{109}e - \frac{84}{109}$ |
| 13 | $[13, 13, -w + 5]$ | $\phantom{-}\frac{11}{109}e^{5} - \frac{10}{109}e^{4} - \frac{163}{109}e^{3} + \frac{80}{109}e^{2} + \frac{412}{109}e - \frac{84}{109}$ |
| 19 | $[19, 19, 5w - 31]$ | $-\frac{33}{109}e^{5} + \frac{30}{109}e^{4} + \frac{598}{109}e^{3} - \frac{240}{109}e^{2} - \frac{2435}{109}e - \frac{620}{109}$ |
| 23 | $[23, 23, -w - 7]$ | $\phantom{-}\frac{7}{109}e^{5} - \frac{46}{109}e^{4} - \frac{74}{109}e^{3} + \frac{586}{109}e^{2} - \frac{45}{109}e - \frac{648}{109}$ |
| 23 | $[23, 23, w - 8]$ | $\phantom{-}\frac{7}{109}e^{5} - \frac{46}{109}e^{4} - \frac{74}{109}e^{3} + \frac{586}{109}e^{2} - \frac{45}{109}e - \frac{648}{109}$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}\frac{12}{109}e^{5} - \frac{1}{109}e^{4} - \frac{267}{109}e^{3} + \frac{8}{109}e^{2} + \frac{1371}{109}e + \frac{711}{109}$ |
| 31 | $[31, 31, -w - 1]$ | $\phantom{-}\frac{9}{109}e^{5} - \frac{28}{109}e^{4} - \frac{173}{109}e^{3} + \frac{442}{109}e^{2} + \frac{674}{109}e - \frac{1020}{109}$ |
| 31 | $[31, 31, w - 2]$ | $\phantom{-}\frac{9}{109}e^{5} - \frac{28}{109}e^{4} - \frac{173}{109}e^{3} + \frac{442}{109}e^{2} + \frac{674}{109}e - \frac{1020}{109}$ |
| 41 | $[41, 41, 6w + 31]$ | $\phantom{-}\frac{33}{109}e^{5} - \frac{30}{109}e^{4} - \frac{598}{109}e^{3} + \frac{240}{109}e^{2} + \frac{2217}{109}e + \frac{1056}{109}$ |
| 41 | $[41, 41, 6w - 37]$ | $\phantom{-}\frac{33}{109}e^{5} - \frac{30}{109}e^{4} - \frac{598}{109}e^{3} + \frac{240}{109}e^{2} + \frac{2217}{109}e + \frac{1056}{109}$ |
| 43 | $[43, 43, -3w - 17]$ | $\phantom{-}\frac{34}{109}e^{5} - \frac{21}{109}e^{4} - \frac{593}{109}e^{3} + \frac{168}{109}e^{2} + \frac{1977}{109}e + \frac{543}{109}$ |
| 43 | $[43, 43, -3w + 20]$ | $\phantom{-}\frac{34}{109}e^{5} - \frac{21}{109}e^{4} - \frac{593}{109}e^{3} + \frac{168}{109}e^{2} + \frac{1977}{109}e + \frac{543}{109}$ |
| 59 | $[59, 59, 3w - 17]$ | $-\frac{42}{109}e^{5} + \frac{58}{109}e^{4} + \frac{662}{109}e^{3} - \frac{682}{109}e^{2} - \frac{1692}{109}e - \frac{36}{109}$ |
| 59 | $[59, 59, 3w + 14]$ | $-\frac{42}{109}e^{5} + \frac{58}{109}e^{4} + \frac{662}{109}e^{3} - \frac{682}{109}e^{2} - \frac{1692}{109}e - \frac{36}{109}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w + 6]$ | $-1$ |
| $3$ | $[3, 3, -w - 5]$ | $-1$ |