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: | $[2, 2, -11w + 102]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 15x^{2} - 17x + 29\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -11w + 102]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 9]$ | $-\frac{1}{7}e^{3} + \frac{3}{7}e^{2} + \frac{3}{7}e - \frac{23}{7}$ |
| 5 | $[5, 5, w + 9]$ | $\phantom{-}e$ |
| 7 | $[7, 7, 4w - 37]$ | $\phantom{-}\frac{4}{7}e^{3} - \frac{5}{7}e^{2} - \frac{40}{7}e + \frac{15}{7}$ |
| 7 | $[7, 7, 4w + 37]$ | $-\frac{3}{7}e^{3} + \frac{2}{7}e^{2} + \frac{30}{7}e - \frac{13}{7}$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{7}e^{3} + \frac{3}{7}e^{2} + \frac{10}{7}e - \frac{37}{7}$ |
| 11 | $[11, 11, 7w + 65]$ | $\phantom{-}\frac{1}{7}e^{3} - \frac{3}{7}e^{2} - \frac{17}{7}e + \frac{16}{7}$ |
| 11 | $[11, 11, -7w + 65]$ | $\phantom{-}\frac{2}{7}e^{3} - \frac{6}{7}e^{2} - \frac{13}{7}e + \frac{39}{7}$ |
| 17 | $[17, 17, -2w - 19]$ | $\phantom{-}\frac{3}{7}e^{3} - \frac{2}{7}e^{2} - \frac{37}{7}e + \frac{20}{7}$ |
| 17 | $[17, 17, 2w - 19]$ | $-\frac{3}{7}e^{3} + \frac{2}{7}e^{2} + \frac{37}{7}e + \frac{15}{7}$ |
| 29 | $[29, 29, -15w + 139]$ | $-\frac{2}{7}e^{3} - \frac{1}{7}e^{2} + \frac{27}{7}e - \frac{11}{7}$ |
| 29 | $[29, 29, -15w - 139]$ | $\phantom{-}\frac{4}{7}e^{3} - \frac{5}{7}e^{2} - \frac{47}{7}e - \frac{6}{7}$ |
| 37 | $[37, 37, -w - 7]$ | $-\frac{6}{7}e^{3} + \frac{11}{7}e^{2} + \frac{53}{7}e - \frac{82}{7}$ |
| 37 | $[37, 37, w - 7]$ | $\phantom{-}\frac{2}{7}e^{3} + \frac{1}{7}e^{2} - \frac{13}{7}e - \frac{31}{7}$ |
| 41 | $[41, 41, -40w + 371]$ | $\phantom{-}\frac{6}{7}e^{3} + \frac{3}{7}e^{2} - \frac{60}{7}e - \frac{37}{7}$ |
| 41 | $[41, 41, 62w - 575]$ | $-\frac{15}{7}e^{3} + \frac{24}{7}e^{2} + \frac{150}{7}e - \frac{121}{7}$ |
| 43 | $[43, 43, -51w + 473]$ | $\phantom{-}\frac{1}{7}e^{3} - \frac{3}{7}e^{2} - \frac{10}{7}e - \frac{19}{7}$ |
| 59 | $[59, 59, -5w + 47]$ | $\phantom{-}\frac{8}{7}e^{3} - \frac{17}{7}e^{2} - \frac{73}{7}e + \frac{114}{7}$ |
| 59 | $[59, 59, 5w + 47]$ | $-e^{2} - e + 9$ |
| 61 | $[61, 61, -w - 5]$ | $\phantom{-}\frac{2}{7}e^{3} + \frac{1}{7}e^{2} - \frac{20}{7}e - \frac{38}{7}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -11w + 102]$ | $-1$ |