Base field \(\Q(\sqrt{86}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 86\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10,10,-3w - 28]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $56$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 3x^{6} - 12x^{5} + 31x^{4} + 11x^{3} - 35x^{2} - x + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w + 102]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 9]$ | $-1$ |
| 5 | $[5, 5, w + 9]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 4w - 37]$ | $-\frac{46}{659}e^{6} + \frac{131}{659}e^{5} + \frac{443}{659}e^{4} - \frac{1201}{659}e^{3} + \frac{1102}{659}e^{2} + \frac{517}{659}e - \frac{1838}{659}$ |
| 7 | $[7, 7, 4w + 37]$ | $\phantom{-}\frac{230}{659}e^{6} - \frac{655}{659}e^{5} - \frac{2874}{659}e^{4} + \frac{6664}{659}e^{3} + \frac{3716}{659}e^{2} - \frac{6539}{659}e - \frac{1354}{659}$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}\frac{152}{659}e^{6} - \frac{175}{659}e^{5} - \frac{2438}{659}e^{4} + \frac{1046}{659}e^{3} + \frac{6788}{659}e^{2} - \frac{419}{659}e - \frac{3038}{659}$ |
| 11 | $[11, 11, 7w + 65]$ | $-\frac{307}{659}e^{6} + \frac{774}{659}e^{5} + \frac{4031}{659}e^{4} - \frac{7428}{659}e^{3} - \frac{6513}{659}e^{2} + \frac{5585}{659}e + \frac{2919}{659}$ |
| 11 | $[11, 11, -7w + 65]$ | $\phantom{-}\frac{272}{659}e^{6} - \frac{660}{659}e^{5} - \frac{3565}{659}e^{4} + \frac{6242}{659}e^{3} + \frac{5661}{659}e^{2} - \frac{5779}{659}e - \frac{1968}{659}$ |
| 17 | $[17, 17, -2w - 19]$ | $\phantom{-}\frac{357}{659}e^{6} - \frac{1031}{659}e^{5} - \frac{4226}{659}e^{4} + \frac{10252}{659}e^{3} + \frac{3023}{659}e^{2} - \frac{8697}{659}e - \frac{606}{659}$ |
| 17 | $[17, 17, 2w - 19]$ | $-\frac{285}{659}e^{6} + \frac{740}{659}e^{5} + \frac{3418}{659}e^{4} - \frac{6739}{659}e^{3} - \frac{2513}{659}e^{2} + \frac{3504}{659}e - \frac{729}{659}$ |
| 29 | $[29, 29, -15w + 139]$ | $\phantom{-}\frac{13}{659}e^{6} - \frac{80}{659}e^{5} + \frac{147}{659}e^{4} + \frac{497}{659}e^{3} - \frac{3807}{659}e^{2} + \frac{2275}{659}e + \frac{5333}{659}$ |
| 29 | $[29, 29, -15w - 139]$ | $\phantom{-}\frac{253}{659}e^{6} - \frac{1050}{659}e^{5} - \frac{2107}{659}e^{4} + \frac{10889}{659}e^{3} - \frac{6061}{659}e^{2} - \frac{8445}{659}e + \frac{4178}{659}$ |
| 37 | $[37, 37, -w - 7]$ | $-\frac{822}{659}e^{6} + \frac{2169}{659}e^{5} + \frac{10323}{659}e^{4} - \frac{20831}{659}e^{3} - \frac{12742}{659}e^{2} + \frac{14969}{659}e + \frac{3544}{659}$ |
| 37 | $[37, 37, w - 7]$ | $-\frac{365}{659}e^{6} + \frac{1283}{659}e^{5} + \frac{3730}{659}e^{4} - \frac{13498}{659}e^{3} + \frac{2412}{659}e^{2} + \frac{13887}{659}e - \frac{2321}{659}$ |
| 41 | $[41, 41, -40w + 371]$ | $-\frac{81}{659}e^{6} + \frac{245}{659}e^{5} + \frac{909}{659}e^{4} - \frac{2387}{659}e^{3} - \frac{409}{659}e^{2} + \frac{323}{659}e + \frac{1090}{659}$ |
| 41 | $[41, 41, 62w - 575]$ | $\phantom{-}\frac{149}{659}e^{6} - \frac{410}{659}e^{5} - \frac{1306}{659}e^{4} + \frac{2959}{659}e^{3} - \frac{4601}{659}e^{2} + \frac{3669}{659}e + \frac{5008}{659}$ |
| 43 | $[43, 43, -51w + 473]$ | $\phantom{-}\frac{281}{659}e^{6} - \frac{614}{659}e^{5} - \frac{3666}{659}e^{4} + \frac{5116}{659}e^{3} + \frac{4901}{659}e^{2} - \frac{909}{659}e - \frac{1723}{659}$ |
| 59 | $[59, 59, -5w + 47]$ | $-\frac{456}{659}e^{6} + \frac{1184}{659}e^{5} + \frac{5996}{659}e^{4} - \frac{11705}{659}e^{3} - \frac{10479}{659}e^{2} + \frac{13119}{659}e + \frac{5819}{659}$ |
| 59 | $[59, 59, 5w + 47]$ | $\phantom{-}\frac{88}{659}e^{6} - \frac{795}{659}e^{5} + \frac{184}{659}e^{4} + \frac{9346}{659}e^{3} - \frac{10360}{659}e^{2} - \frac{8324}{659}e + \frac{3860}{659}$ |
| 61 | $[61, 61, -w - 5]$ | $-\frac{600}{659}e^{6} + \frac{1107}{659}e^{5} + \frac{8930}{659}e^{4} - \frac{9505}{659}e^{3} - \frac{22702}{659}e^{2} + \frac{5712}{659}e + \frac{9807}{659}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,11w + 102]$ | $-1$ |
| $5$ | $[5,5,-w + 9]$ | $1$ |