Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, -4w + 37]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $108$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 18x^{8} + 114x^{6} - 293x^{4} + 251x^{2} - 27\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $-e$ |
| 5 | $[5, 5, -4w + 37]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w + 2]$ | $-\frac{1}{6}e^{9} + \frac{3}{2}e^{7} - \frac{3}{2}e^{5} - \frac{32}{3}e^{3} + \frac{79}{6}e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{1}{6}e^{9} - \frac{3}{2}e^{7} + \frac{3}{2}e^{5} + \frac{32}{3}e^{3} - \frac{79}{6}e$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{2}e^{8} + \frac{13}{2}e^{6} - \frac{53}{2}e^{4} + 35e^{2} - \frac{19}{2}$ |
| 17 | $[17, 17, w + 6]$ | $\phantom{-}\frac{1}{3}e^{9} - 4e^{7} + 14e^{5} - \frac{38}{3}e^{3} - \frac{1}{3}e$ |
| 17 | $[17, 17, w + 10]$ | $-\frac{1}{3}e^{9} + 4e^{7} - 14e^{5} + \frac{38}{3}e^{3} + \frac{1}{3}e$ |
| 19 | $[19, 19, -2w + 19]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{13}{2}e^{6} + \frac{51}{2}e^{4} - 29e^{2} + \frac{5}{2}$ |
| 19 | $[19, 19, -2w - 17]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{13}{2}e^{6} + \frac{51}{2}e^{4} - 29e^{2} + \frac{5}{2}$ |
| 23 | $[23, 23, w + 5]$ | $-e^{5} + 8e^{3} - 13e$ |
| 23 | $[23, 23, w + 17]$ | $\phantom{-}e^{5} - 8e^{3} + 13e$ |
| 37 | $[37, 37, w + 1]$ | $-\frac{1}{3}e^{9} + 4e^{7} - 15e^{5} + \frac{62}{3}e^{3} - \frac{32}{3}e$ |
| 37 | $[37, 37, w + 35]$ | $\phantom{-}\frac{1}{3}e^{9} - 4e^{7} + 15e^{5} - \frac{62}{3}e^{3} + \frac{32}{3}e$ |
| 41 | $[41, 41, -22w + 203]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{11}{2}e^{6} + \frac{35}{2}e^{4} - 18e^{2} + \frac{9}{2}$ |
| 41 | $[41, 41, -6w + 55]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{11}{2}e^{6} + \frac{35}{2}e^{4} - 18e^{2} + \frac{9}{2}$ |
| 43 | $[43, 43, w + 20]$ | $-\frac{1}{6}e^{9} + \frac{7}{2}e^{7} - \frac{47}{2}e^{5} + \frac{169}{3}e^{3} - \frac{215}{6}e$ |
| 43 | $[43, 43, w + 22]$ | $\phantom{-}\frac{1}{6}e^{9} - \frac{7}{2}e^{7} + \frac{47}{2}e^{5} - \frac{169}{3}e^{3} + \frac{215}{6}e$ |
| 53 | $[53, 53, w + 13]$ | $-\frac{2}{3}e^{9} + 9e^{7} - 40e^{5} + \frac{202}{3}e^{3} - \frac{109}{3}e$ |
| 53 | $[53, 53, w + 39]$ | $\phantom{-}\frac{2}{3}e^{9} - 9e^{7} + 40e^{5} - \frac{202}{3}e^{3} + \frac{109}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -4w + 37]$ | $-1$ |