Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[10, 10, w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 7x^{3} + 10x^{2} - 3x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{2}e^{3} + 3e^{2} + 3e - \frac{3}{2}$ |
| 5 | $[5, 5, -w + 5]$ | $-1$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} + 3e^{2} + 2e - \frac{9}{2}$ |
| 13 | $[13, 13, w + 2]$ | $-e^{3} - 7e^{2} - 9e + 3$ |
| 13 | $[13, 13, w + 11]$ | $\phantom{-}e^{2} + 3e - 3$ |
| 17 | $[17, 17, w + 8]$ | $-e^{3} - 6e^{2} - 5e + 3$ |
| 17 | $[17, 17, w + 9]$ | $-\frac{1}{2}e^{3} - 3e^{2} - 4e - \frac{3}{2}$ |
| 19 | $[19, 19, w + 7]$ | $\phantom{-}e^{2} + 6e + 4$ |
| 19 | $[19, 19, -w + 7]$ | $\phantom{-}\frac{1}{2}e^{3} + 2e^{2} - 3e - \frac{7}{2}$ |
| 29 | $[29, 29, -w - 1]$ | $-e^{3} - 8e^{2} - 15e + 3$ |
| 29 | $[29, 29, w - 1]$ | $-\frac{1}{2}e^{3} - e^{2} + 6e + \frac{9}{2}$ |
| 37 | $[37, 37, w + 17]$ | $\phantom{-}\frac{1}{2}e^{3} + 4e^{2} + 7e - \frac{15}{2}$ |
| 37 | $[37, 37, w + 20]$ | $-e^{2} - 4e - 6$ |
| 71 | $[71, 71, 2w - 7]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 6e - \frac{9}{2}$ |
| 71 | $[71, 71, -2w - 7]$ | $\phantom{-}e^{3} + 8e^{2} + 15e - 3$ |
| 83 | $[83, 83, w + 14]$ | $\phantom{-}\frac{1}{2}e^{3} + 3e^{2} + 4e + \frac{3}{2}$ |
| 83 | $[83, 83, w + 69]$ | $\phantom{-}e^{3} + 6e^{2} + 5e - 3$ |
| 101 | $[101, 101, -7w + 37]$ | $\phantom{-}\frac{3}{2}e^{3} + 9e^{2} + 3e - \frac{27}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $5$ | $[5, 5, -w + 5]$ | $1$ |