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: | $[9,9,5w + 31]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} - 22x^{8} + 172x^{6} - 581x^{4} + 772x^{2} - 208\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w + 7]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $-\frac{3}{184}e^{9} + \frac{35}{92}e^{7} - \frac{137}{46}e^{5} + \frac{1615}{184}e^{3} - \frac{160}{23}e$ |
| 5 | $[5, 5, 4w + 25]$ | $\phantom{-}\frac{25}{184}e^{9} - \frac{215}{92}e^{7} + \frac{559}{46}e^{5} - \frac{3829}{184}e^{3} + \frac{313}{46}e$ |
| 5 | $[5, 5, -4w + 29]$ | $\phantom{-}\frac{15}{92}e^{8} - \frac{129}{46}e^{6} + \frac{340}{23}e^{4} - \frac{2463}{92}e^{2} + \frac{266}{23}$ |
| 11 | $[11, 11, w - 8]$ | $\phantom{-}\frac{10}{23}e^{8} - \frac{172}{23}e^{6} + \frac{899}{23}e^{4} - \frac{1573}{23}e^{2} + \frac{556}{23}$ |
| 11 | $[11, 11, -w - 7]$ | $-\frac{5}{46}e^{9} + \frac{43}{23}e^{7} - \frac{219}{23}e^{5} + \frac{637}{46}e^{3} + \frac{91}{23}e$ |
| 13 | $[13, 13, 3w + 19]$ | $\phantom{-}\frac{5}{92}e^{8} - \frac{43}{46}e^{6} + \frac{121}{23}e^{4} - \frac{1097}{92}e^{2} + \frac{173}{23}$ |
| 13 | $[13, 13, 3w - 22]$ | $\phantom{-}\frac{35}{92}e^{8} - \frac{301}{46}e^{6} + \frac{778}{23}e^{4} - \frac{5195}{92}e^{2} + \frac{383}{23}$ |
| 29 | $[29, 29, 6w + 37]$ | $-\frac{17}{92}e^{9} + \frac{80}{23}e^{7} - \frac{485}{23}e^{5} + \frac{4245}{92}e^{3} - \frac{1089}{46}e$ |
| 29 | $[29, 29, 6w - 43]$ | $\phantom{-}\frac{13}{92}e^{8} - \frac{121}{46}e^{6} + \frac{356}{23}e^{4} - \frac{2889}{92}e^{2} + \frac{275}{23}$ |
| 37 | $[37, 37, 2w - 13]$ | $-\frac{5}{184}e^{9} + \frac{43}{92}e^{7} - \frac{121}{46}e^{5} + \frac{1097}{184}e^{3} - \frac{219}{46}e$ |
| 37 | $[37, 37, 2w + 11]$ | $-\frac{65}{184}e^{9} + \frac{559}{92}e^{7} - \frac{1435}{46}e^{5} + \frac{8741}{184}e^{3} + \frac{189}{46}e$ |
| 43 | $[43, 43, -w - 1]$ | $\phantom{-}\frac{13}{23}e^{8} - \frac{219}{23}e^{6} + \frac{1102}{23}e^{4} - \frac{1785}{23}e^{2} + \frac{410}{23}$ |
| 43 | $[43, 43, w - 2]$ | $-\frac{17}{23}e^{8} + \frac{297}{23}e^{6} - \frac{1595}{23}e^{4} + \frac{2865}{23}e^{2} - \frac{844}{23}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{51}{92}e^{8} - \frac{457}{46}e^{6} + \frac{1271}{23}e^{4} - \frac{9515}{92}e^{2} + \frac{748}{23}$ |
| 59 | $[59, 59, 5w - 37]$ | $\phantom{-}\frac{3}{46}e^{9} - \frac{35}{23}e^{7} + \frac{274}{23}e^{5} - \frac{1569}{46}e^{3} + \frac{594}{23}e$ |
| 59 | $[59, 59, 5w + 32]$ | $-\frac{13}{46}e^{8} + \frac{98}{23}e^{6} - \frac{390}{23}e^{4} + \frac{681}{46}e^{2} + \frac{94}{23}$ |
| 67 | $[67, 67, 21w + 131]$ | $-\frac{33}{92}e^{9} + \frac{293}{46}e^{7} - \frac{817}{23}e^{5} + \frac{6633}{92}e^{3} - \frac{967}{23}e$ |
| 67 | $[67, 67, 21w - 152]$ | $\phantom{-}\frac{3}{23}e^{9} - \frac{47}{23}e^{7} + \frac{203}{23}e^{5} - \frac{258}{23}e^{3} + \frac{176}{23}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w - 7]$ | $1$ |