Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, -5w + 36]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - x^{6} - 13x^{5} + 10x^{4} + 41x^{3} - 25x^{2} - 26x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{4}{37}e^{6} + \frac{7}{37}e^{5} + \frac{56}{37}e^{4} - \frac{82}{37}e^{3} - \frac{195}{37}e^{2} + \frac{200}{37}e + \frac{65}{37}$ |
| 5 | $[5, 5, 4w + 25]$ | $\phantom{-}\frac{21}{74}e^{6} - \frac{9}{74}e^{5} - \frac{257}{74}e^{4} + \frac{21}{37}e^{3} + \frac{663}{74}e^{2} - \frac{51}{74}e - \frac{92}{37}$ |
| 5 | $[5, 5, -4w + 29]$ | $-\frac{21}{74}e^{6} + \frac{9}{74}e^{5} + \frac{257}{74}e^{4} - \frac{21}{37}e^{3} - \frac{663}{74}e^{2} + \frac{51}{74}e + \frac{92}{37}$ |
| 11 | $[11, 11, w - 8]$ | $\phantom{-}\frac{1}{37}e^{6} - \frac{11}{37}e^{5} - \frac{14}{37}e^{4} + \frac{113}{37}e^{3} + \frac{95}{37}e^{2} - \frac{198}{37}e - \frac{118}{37}$ |
| 11 | $[11, 11, -w - 7]$ | $-\frac{1}{37}e^{6} + \frac{11}{37}e^{5} + \frac{14}{37}e^{4} - \frac{113}{37}e^{3} - \frac{95}{37}e^{2} + \frac{198}{37}e + \frac{118}{37}$ |
| 13 | $[13, 13, 3w + 19]$ | $-\frac{7}{74}e^{6} + \frac{3}{74}e^{5} + \frac{61}{74}e^{4} - \frac{7}{37}e^{3} + \frac{1}{74}e^{2} + \frac{17}{74}e - \frac{105}{37}$ |
| 13 | $[13, 13, 3w - 22]$ | $-\frac{7}{74}e^{6} + \frac{3}{74}e^{5} + \frac{61}{74}e^{4} - \frac{7}{37}e^{3} + \frac{1}{74}e^{2} + \frac{17}{74}e - \frac{105}{37}$ |
| 29 | $[29, 29, 6w + 37]$ | $-\frac{39}{74}e^{6} - \frac{15}{74}e^{5} + \frac{509}{74}e^{4} + \frac{109}{37}e^{3} - \frac{1485}{74}e^{2} - \frac{233}{74}e + \frac{377}{37}$ |
| 29 | $[29, 29, 6w - 43]$ | $\phantom{-}\frac{39}{74}e^{6} + \frac{15}{74}e^{5} - \frac{509}{74}e^{4} - \frac{109}{37}e^{3} + \frac{1485}{74}e^{2} + \frac{233}{74}e - \frac{377}{37}$ |
| 37 | $[37, 37, 2w - 13]$ | $\phantom{-}\frac{1}{74}e^{6} - \frac{11}{74}e^{5} + \frac{23}{74}e^{4} + \frac{75}{37}e^{3} - \frac{349}{74}e^{2} - \frac{531}{74}e + \frac{200}{37}$ |
| 37 | $[37, 37, 2w + 11]$ | $\phantom{-}\frac{1}{74}e^{6} - \frac{11}{74}e^{5} + \frac{23}{74}e^{4} + \frac{75}{37}e^{3} - \frac{349}{74}e^{2} - \frac{531}{74}e + \frac{200}{37}$ |
| 43 | $[43, 43, -w - 1]$ | $\phantom{-}\frac{19}{37}e^{6} - \frac{24}{37}e^{5} - \frac{229}{37}e^{4} + \frac{223}{37}e^{3} + \frac{621}{37}e^{2} - \frac{469}{37}e - \frac{244}{37}$ |
| 43 | $[43, 43, w - 2]$ | $\phantom{-}\frac{19}{37}e^{6} - \frac{24}{37}e^{5} - \frac{229}{37}e^{4} + \frac{223}{37}e^{3} + \frac{621}{37}e^{2} - \frac{469}{37}e - \frac{244}{37}$ |
| 49 | $[49, 7, -7]$ | $-\frac{11}{74}e^{6} + \frac{47}{74}e^{5} + \frac{117}{74}e^{4} - \frac{270}{37}e^{3} - \frac{305}{74}e^{2} + \frac{1105}{74}e + \frac{316}{37}$ |
| 59 | $[59, 59, 5w - 37]$ | $-\frac{13}{37}e^{6} - \frac{5}{37}e^{5} + \frac{182}{37}e^{4} + \frac{85}{37}e^{3} - \frac{606}{37}e^{2} - \frac{275}{37}e + \frac{350}{37}$ |
| 59 | $[59, 59, 5w + 32]$ | $\phantom{-}\frac{13}{37}e^{6} + \frac{5}{37}e^{5} - \frac{182}{37}e^{4} - \frac{85}{37}e^{3} + \frac{606}{37}e^{2} + \frac{275}{37}e - \frac{350}{37}$ |
| 67 | $[67, 67, 21w + 131]$ | $\phantom{-}\frac{18}{37}e^{6} - \frac{13}{37}e^{5} - \frac{215}{37}e^{4} + \frac{110}{37}e^{3} + \frac{526}{37}e^{2} - \frac{197}{37}e - \frac{200}{37}$ |
| 67 | $[67, 67, 21w - 152]$ | $\phantom{-}\frac{18}{37}e^{6} - \frac{13}{37}e^{5} - \frac{215}{37}e^{4} + \frac{110}{37}e^{3} + \frac{526}{37}e^{2} - \frac{197}{37}e - \frac{200}{37}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w - 6]$ | $-1$ |