Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w + 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $132$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 18x^{8} + 103x^{6} + 234x^{4} + 217x^{2} + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{1}{4}e^{8} - 4e^{6} - 18e^{4} - \frac{101}{4}e^{2} - 11$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{9}{56}e^{9} - \frac{75}{28}e^{7} - \frac{727}{56}e^{5} - \frac{573}{28}e^{3} - \frac{509}{56}e$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}\frac{3}{14}e^{9} + \frac{25}{7}e^{7} + \frac{120}{7}e^{5} + \frac{347}{14}e^{3} + \frac{37}{7}e$ |
| 11 | $[11, 11, w + 7]$ | $\phantom{-}\frac{3}{14}e^{9} + \frac{25}{7}e^{7} + \frac{120}{7}e^{5} + \frac{347}{14}e^{3} + \frac{37}{7}e$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{5}{7}e^{8} - \frac{81}{7}e^{6} - \frac{365}{7}e^{4} - \frac{464}{7}e^{2} - \frac{114}{7}$ |
| 23 | $[23, 23, w + 4]$ | $-\frac{1}{14}e^{9} - \frac{19}{14}e^{7} - \frac{115}{14}e^{5} - \frac{129}{7}e^{3} - \frac{101}{7}e$ |
| 23 | $[23, 23, w + 18]$ | $-\frac{1}{14}e^{9} - \frac{19}{14}e^{7} - \frac{115}{14}e^{5} - \frac{129}{7}e^{3} - \frac{101}{7}e$ |
| 25 | $[25, 5, 5]$ | $-\frac{8}{7}e^{8} - \frac{131}{7}e^{6} - \frac{612}{7}e^{4} - \frac{895}{7}e^{2} - \frac{314}{7}$ |
| 29 | $[29, 29, w + 1]$ | $\phantom{-}\frac{9}{14}e^{9} + \frac{75}{7}e^{7} + \frac{367}{7}e^{5} + \frac{1223}{14}e^{3} + \frac{328}{7}e$ |
| 29 | $[29, 29, w + 27]$ | $\phantom{-}\frac{9}{14}e^{9} + \frac{75}{7}e^{7} + \frac{367}{7}e^{5} + \frac{1223}{14}e^{3} + \frac{328}{7}e$ |
| 31 | $[31, 31, w + 13]$ | $\phantom{-}\frac{1}{7}e^{9} + \frac{19}{7}e^{7} + \frac{115}{7}e^{5} + \frac{251}{7}e^{3} + \frac{139}{7}e$ |
| 31 | $[31, 31, w + 17]$ | $\phantom{-}\frac{1}{7}e^{9} + \frac{19}{7}e^{7} + \frac{115}{7}e^{5} + \frac{251}{7}e^{3} + \frac{139}{7}e$ |
| 43 | $[43, 43, -w - 11]$ | $-\frac{3}{7}e^{8} - \frac{93}{14}e^{6} - \frac{389}{14}e^{4} - \frac{463}{14}e^{2} - \frac{60}{7}$ |
| 43 | $[43, 43, w - 12]$ | $-\frac{3}{7}e^{8} - \frac{93}{14}e^{6} - \frac{389}{14}e^{4} - \frac{463}{14}e^{2} - \frac{60}{7}$ |
| 47 | $[47, 47, -w - 6]$ | $-\frac{5}{14}e^{8} - \frac{81}{14}e^{6} - \frac{379}{14}e^{4} - \frac{295}{7}e^{2} - \frac{120}{7}$ |
| 47 | $[47, 47, w - 7]$ | $-\frac{5}{14}e^{8} - \frac{81}{14}e^{6} - \frac{379}{14}e^{4} - \frac{295}{7}e^{2} - \frac{120}{7}$ |
| 59 | $[59, 59, -w - 5]$ | $\phantom{-}\frac{2}{7}e^{8} + \frac{31}{7}e^{6} + \frac{125}{7}e^{4} + \frac{103}{7}e^{2} + \frac{12}{7}$ |
| 59 | $[59, 59, w - 6]$ | $\phantom{-}\frac{2}{7}e^{8} + \frac{31}{7}e^{6} + \frac{125}{7}e^{4} + \frac{103}{7}e^{2} + \frac{12}{7}$ |
| 61 | $[61, 61, w + 16]$ | $\phantom{-}\frac{13}{14}e^{9} + \frac{219}{14}e^{7} + \frac{1089}{14}e^{5} + \frac{914}{7}e^{3} + \frac{445}{7}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 3]$ | $\frac{9}{56}e^{9} + \frac{75}{28}e^{7} + \frac{727}{56}e^{5} + \frac{573}{28}e^{3} + \frac{509}{56}e$ |