Base field \(\Q(\sqrt{46}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 46\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 36x^{10} + 484x^{8} - 2976x^{6} + 8216x^{4} - 8736x^{2} + 3072\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 23w - 156]$ | $\phantom{-}\frac{1}{80}e^{10} - \frac{3}{8}e^{8} + \frac{81}{20}e^{6} - \frac{189}{10}e^{4} + \frac{353}{10}e^{2} - \frac{87}{5}$ |
| 3 | $[3, 3, -w - 7]$ | $-1$ |
| 3 | $[3, 3, w - 7]$ | $-1$ |
| 5 | $[5, 5, -9w + 61]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -9w - 61]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 4w - 27]$ | $\phantom{-}\frac{1}{320}e^{11} - \frac{3}{16}e^{9} + \frac{261}{80}e^{7} - \frac{221}{10}e^{5} + \frac{2203}{40}e^{3} - \frac{301}{10}e$ |
| 7 | $[7, 7, 4w + 27]$ | $\phantom{-}\frac{1}{320}e^{11} - \frac{3}{16}e^{9} + \frac{261}{80}e^{7} - \frac{221}{10}e^{5} + \frac{2203}{40}e^{3} - \frac{301}{10}e$ |
| 23 | $[23, 23, 78w - 529]$ | $\phantom{-}\frac{11}{160}e^{11} - \frac{19}{8}e^{9} + \frac{1211}{40}e^{7} - \frac{856}{5}e^{5} + \frac{7913}{20}e^{3} - \frac{1171}{5}e$ |
| 37 | $[37, 37, -w - 3]$ | $-\frac{1}{320}e^{11} + \frac{3}{16}e^{9} - \frac{261}{80}e^{7} + \frac{221}{10}e^{5} - \frac{2243}{40}e^{3} + \frac{391}{10}e$ |
| 37 | $[37, 37, w - 3]$ | $-\frac{1}{320}e^{11} + \frac{3}{16}e^{9} - \frac{261}{80}e^{7} + \frac{221}{10}e^{5} - \frac{2243}{40}e^{3} + \frac{391}{10}e$ |
| 41 | $[41, 41, -2w + 15]$ | $-\frac{3}{40}e^{10} + \frac{9}{4}e^{8} - \frac{124}{5}e^{6} + \frac{612}{5}e^{4} - \frac{1269}{5}e^{2} + \frac{702}{5}$ |
| 41 | $[41, 41, 2w + 15]$ | $-\frac{3}{40}e^{10} + \frac{9}{4}e^{8} - \frac{124}{5}e^{6} + \frac{612}{5}e^{4} - \frac{1269}{5}e^{2} + \frac{702}{5}$ |
| 53 | $[53, 53, -3w - 19]$ | $-\frac{1}{80}e^{11} + \frac{1}{4}e^{9} - \frac{21}{20}e^{7} - \frac{23}{5}e^{5} + \frac{307}{10}e^{3} - \frac{133}{5}e$ |
| 53 | $[53, 53, 3w - 19]$ | $-\frac{1}{80}e^{11} + \frac{1}{4}e^{9} - \frac{21}{20}e^{7} - \frac{23}{5}e^{5} + \frac{307}{10}e^{3} - \frac{133}{5}e$ |
| 59 | $[59, 59, 11w - 75]$ | $\phantom{-}\frac{3}{40}e^{10} - \frac{9}{4}e^{8} + \frac{124}{5}e^{6} - \frac{612}{5}e^{4} + \frac{1274}{5}e^{2} - \frac{732}{5}$ |
| 59 | $[59, 59, -11w - 75]$ | $\phantom{-}\frac{3}{40}e^{10} - \frac{9}{4}e^{8} + \frac{124}{5}e^{6} - \frac{612}{5}e^{4} + \frac{1274}{5}e^{2} - \frac{732}{5}$ |
| 61 | $[61, 61, -5w + 33]$ | $-\frac{31}{320}e^{11} + \frac{53}{16}e^{9} - \frac{3331}{80}e^{7} + \frac{2311}{10}e^{5} - \frac{20893}{40}e^{3} + \frac{3061}{10}e$ |
| 61 | $[61, 61, 5w + 33]$ | $-\frac{31}{320}e^{11} + \frac{53}{16}e^{9} - \frac{3331}{80}e^{7} + \frac{2311}{10}e^{5} - \frac{20893}{40}e^{3} + \frac{3061}{10}e$ |
| 73 | $[73, 73, -24w - 163]$ | $-\frac{3}{40}e^{10} + \frac{5}{2}e^{8} - \frac{154}{5}e^{6} + \frac{847}{5}e^{4} - \frac{1929}{5}e^{2} + \frac{1142}{5}$ |
| 73 | $[73, 73, -24w + 163]$ | $-\frac{3}{40}e^{10} + \frac{5}{2}e^{8} - \frac{154}{5}e^{6} + \frac{847}{5}e^{4} - \frac{1929}{5}e^{2} + \frac{1142}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w - 7]$ | $1$ |
| $3$ | $[3, 3, w - 7]$ | $1$ |