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: | yes |
| Newspace dimension: | $108$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} + 14x^{8} + 62x^{6} + 97x^{4} + 39x^{2} + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -4w + 37]$ | $-1$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}\frac{2}{3}e^{9} + 9e^{7} + \frac{112}{3}e^{5} + 51e^{3} + 12e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{2}{3}e^{9} + 9e^{7} + \frac{112}{3}e^{5} + 51e^{3} + 12e$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{3}e^{8} - 4e^{6} - \frac{41}{3}e^{4} - 14e^{2} - 4$ |
| 17 | $[17, 17, w + 6]$ | $-e^{9} - 14e^{7} - 62e^{5} - 96e^{3} - 33e$ |
| 17 | $[17, 17, w + 10]$ | $-e^{9} - 14e^{7} - 62e^{5} - 96e^{3} - 33e$ |
| 19 | $[19, 19, -2w + 19]$ | $-\frac{2}{3}e^{8} - 9e^{6} - \frac{109}{3}e^{4} - 44e^{2} - 6$ |
| 19 | $[19, 19, -2w - 17]$ | $-\frac{2}{3}e^{8} - 9e^{6} - \frac{109}{3}e^{4} - 44e^{2} - 6$ |
| 23 | $[23, 23, w + 5]$ | $-\frac{1}{3}e^{9} - 5e^{7} - \frac{74}{3}e^{5} - 46e^{3} - 26e$ |
| 23 | $[23, 23, w + 17]$ | $-\frac{1}{3}e^{9} - 5e^{7} - \frac{74}{3}e^{5} - 46e^{3} - 26e$ |
| 37 | $[37, 37, w + 1]$ | $-e^{9} - 14e^{7} - 61e^{5} - 88e^{3} - 22e$ |
| 37 | $[37, 37, w + 35]$ | $-e^{9} - 14e^{7} - 61e^{5} - 88e^{3} - 22e$ |
| 41 | $[41, 41, -22w + 203]$ | $\phantom{-}e^{8} + 13e^{6} + 50e^{4} + 59e^{2} + 9$ |
| 41 | $[41, 41, -6w + 55]$ | $\phantom{-}e^{8} + 13e^{6} + 50e^{4} + 59e^{2} + 9$ |
| 43 | $[43, 43, w + 20]$ | $\phantom{-}\frac{7}{3}e^{9} + 32e^{7} + \frac{407}{3}e^{5} + 190e^{3} + 46e$ |
| 43 | $[43, 43, w + 22]$ | $\phantom{-}\frac{7}{3}e^{9} + 32e^{7} + \frac{407}{3}e^{5} + 190e^{3} + 46e$ |
| 53 | $[53, 53, w + 13]$ | $-\frac{2}{3}e^{9} - 9e^{7} - \frac{112}{3}e^{5} - 50e^{3} - 3e$ |
| 53 | $[53, 53, w + 39]$ | $-\frac{2}{3}e^{9} - 9e^{7} - \frac{112}{3}e^{5} - 50e^{3} - 3e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -4w + 37]$ | $1$ |