Base field \(\Q(\sqrt{493}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 123\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $118$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 17x^{6} + 83x^{4} + 112x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $-\frac{13}{112}e^{7} - \frac{31}{16}e^{5} - \frac{995}{112}e^{3} - \frac{253}{28}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}\frac{5}{56}e^{7} + \frac{11}{8}e^{5} + \frac{303}{56}e^{3} + \frac{22}{7}e$ |
| 11 | $[11, 11, w + 9]$ | $\phantom{-}\frac{3}{112}e^{7} + \frac{9}{16}e^{5} + \frac{389}{112}e^{3} + \frac{137}{28}e$ |
| 13 | $[13, 13, w - 11]$ | $-\frac{1}{8}e^{6} - \frac{13}{8}e^{4} - \frac{39}{8}e^{2} - \frac{5}{2}$ |
| 13 | $[13, 13, w + 10]$ | $\phantom{-}\frac{9}{56}e^{6} + \frac{19}{8}e^{4} + \frac{495}{56}e^{2} + \frac{75}{14}$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{13}{112}e^{7} - \frac{31}{16}e^{5} - \frac{995}{112}e^{3} - \frac{225}{28}e$ |
| 25 | $[25, 5, -5]$ | $-\frac{1}{14}e^{6} - \frac{3}{2}e^{4} - \frac{111}{14}e^{2} - \frac{47}{7}$ |
| 29 | $[29, 29, w + 14]$ | $-\frac{1}{8}e^{7} - \frac{17}{8}e^{5} - \frac{75}{8}e^{3} - 4e$ |
| 31 | $[31, 31, w + 5]$ | $\phantom{-}\frac{17}{112}e^{7} + \frac{35}{16}e^{5} + \frac{823}{112}e^{3} + \frac{67}{28}e$ |
| 31 | $[31, 31, w + 25]$ | $-\frac{17}{112}e^{7} - \frac{35}{16}e^{5} - \frac{823}{112}e^{3} - \frac{67}{28}e$ |
| 37 | $[37, 37, w + 3]$ | $\phantom{-}\frac{11}{56}e^{7} + \frac{25}{8}e^{5} + \frac{717}{56}e^{3} + \frac{143}{14}e$ |
| 37 | $[37, 37, w + 33]$ | $-\frac{17}{56}e^{7} - \frac{39}{8}e^{5} - \frac{1187}{56}e^{3} - \frac{156}{7}e$ |
| 41 | $[41, 41, w]$ | $-\frac{13}{112}e^{7} - \frac{31}{16}e^{5} - \frac{1107}{112}e^{3} - \frac{449}{28}e$ |
| 41 | $[41, 41, w + 40]$ | $-\frac{23}{112}e^{7} - \frac{53}{16}e^{5} - \frac{1713}{112}e^{3} - \frac{565}{28}e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{1}{56}e^{6} + \frac{3}{8}e^{4} + \frac{111}{56}e^{2} - \frac{43}{14}$ |
| 53 | $[53, 53, -4w - 43]$ | $-\frac{1}{28}e^{6} - \frac{3}{4}e^{4} - \frac{167}{28}e^{2} - \frac{62}{7}$ |
| 53 | $[53, 53, 4w - 47]$ | $\phantom{-}2e^{2} + 11$ |
| 59 | $[59, 59, -w - 13]$ | $-\frac{3}{56}e^{6} - \frac{9}{8}e^{4} - \frac{277}{56}e^{2} - \frac{81}{14}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |