Base field \(\Q(\sqrt{119}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 119\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $10$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $64$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 50x^{8} + 875x^{6} - 6250x^{4} + 15625x^{2} - 11492\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 11]$ | $\phantom{-}\frac{1}{312}e^{8} - \frac{5}{39}e^{6} + \frac{125}{78}e^{4} - \frac{2161}{312}e^{2} + \frac{55}{6}$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}0$ |
| 9 | $[9, 3, 3]$ | $-\frac{1}{39}e^{6} + \frac{38}{39}e^{4} - \frac{385}{39}e^{2} + \frac{50}{3}$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, w + 8]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w]$ | $-\frac{1}{13}e^{5} + \frac{25}{13}e^{3} - \frac{125}{13}e$ |
| 19 | $[19, 19, w - 10]$ | $\phantom{-}0$ |
| 19 | $[19, 19, -w - 10]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 2]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 21]$ | $\phantom{-}0$ |
| 41 | $[41, 41, w + 18]$ | $\phantom{-}\frac{1}{26}e^{7} - \frac{35}{26}e^{5} + \frac{323}{26}e^{3} - \frac{235}{13}e$ |
| 41 | $[41, 41, w + 23]$ | $\phantom{-}\frac{1}{26}e^{7} - \frac{35}{26}e^{5} + \frac{323}{26}e^{3} - \frac{235}{13}e$ |
| 47 | $[47, 47, -3w + 32]$ | $\phantom{-}0$ |
| 47 | $[47, 47, 8w - 87]$ | $\phantom{-}0$ |
| 53 | $[53, 53, -2w + 23]$ | $\phantom{-}\frac{7}{78}e^{6} - \frac{227}{78}e^{4} + \frac{1915}{78}e^{2} - \frac{100}{3}$ |
| 53 | $[53, 53, -13w + 142]$ | $\phantom{-}\frac{7}{78}e^{6} - \frac{227}{78}e^{4} + \frac{1915}{78}e^{2} - \frac{100}{3}$ |
| 59 | $[59, 59, -5w + 54]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 6w - 65]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).