Base field 3.3.1509.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 9, w + 1]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 19x^{8} + 126x^{6} - 347x^{4} + 391x^{2} - 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w^{2} + w + 15]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w - 1]$ | $-\frac{1}{12}e^{9} + \frac{19}{12}e^{7} - \frac{19}{2}e^{5} + \frac{227}{12}e^{3} - \frac{115}{12}e$ |
| 4 | $[4, 2, -w^{2} + 3w - 1]$ | $-\frac{1}{6}e^{9} + \frac{8}{3}e^{7} - 14e^{5} + \frac{161}{6}e^{3} - \frac{47}{3}e$ |
| 11 | $[11, 11, w + 3]$ | $-e^{4} + 9e^{2} - 12$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-\frac{1}{6}e^{9} + \frac{19}{6}e^{7} - 20e^{5} + \frac{275}{6}e^{3} - \frac{169}{6}e$ |
| 23 | $[23, 23, -2w^{2} + 2w + 17]$ | $-e^{4} + 7e^{2} - 6$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{12}e^{9} - \frac{19}{12}e^{7} + \frac{21}{2}e^{5} - \frac{323}{12}e^{3} + \frac{199}{12}e$ |
| 37 | $[37, 37, 2w^{2} - 13]$ | $\phantom{-}\frac{1}{12}e^{9} - \frac{7}{12}e^{7} - \frac{3}{2}e^{5} + \frac{157}{12}e^{3} - \frac{221}{12}e$ |
| 43 | $[43, 43, 5w^{2} - 2w - 35]$ | $\phantom{-}\frac{1}{12}e^{9} - \frac{19}{12}e^{7} + \frac{21}{2}e^{5} - \frac{347}{12}e^{3} + \frac{367}{12}e$ |
| 43 | $[43, 43, 3w - 1]$ | $-e^{8} + 15e^{6} - 74e^{4} + 137e^{2} - 73$ |
| 43 | $[43, 43, 2w - 3]$ | $-\frac{1}{6}e^{9} + \frac{19}{6}e^{7} - 21e^{5} + \frac{335}{6}e^{3} - \frac{271}{6}e$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{1}{2}e^{9} + \frac{17}{2}e^{7} - 49e^{5} + \frac{215}{2}e^{3} - \frac{133}{2}e$ |
| 59 | $[59, 59, -3w^{2} + 2w + 21]$ | $\phantom{-}2e^{6} - 22e^{4} + 62e^{2} - 42$ |
| 71 | $[71, 71, 2w + 3]$ | $\phantom{-}2e^{6} - 22e^{4} + 60e^{2} - 36$ |
| 71 | $[71, 71, 3w^{2} - 19]$ | $\phantom{-}e^{7} - 10e^{5} + 22e^{3} - 9e$ |
| 71 | $[71, 71, 4w^{2} - 13w + 5]$ | $\phantom{-}\frac{1}{2}e^{9} - \frac{17}{2}e^{7} + 46e^{5} - \frac{163}{2}e^{3} + \frac{63}{2}e$ |
| 83 | $[83, 83, 2w^{2} - 15]$ | $-\frac{1}{2}e^{9} + \frac{17}{2}e^{7} - 48e^{5} + \frac{199}{2}e^{3} - \frac{127}{2}e$ |
| 89 | $[89, 89, -w^{2} - 1]$ | $-e^{8} + 16e^{6} - 84e^{4} + 161e^{2} - 90$ |
| 89 | $[89, 89, 2w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{9} - \frac{15}{2}e^{7} + 35e^{5} - \frac{103}{2}e^{3} + \frac{27}{2}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -2w^{2} + w + 15]$ | $-1$ |