Base field \(\Q(\sqrt{21}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[51, 51, -w - 7]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 3x^{2} - 7x + 17\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{1}{2}e^{2} + e + \frac{3}{2}$ |
| 7 | $[7, 7, -w - 3]$ | $-\frac{1}{2}e^{2} + \frac{9}{2}$ |
| 17 | $[17, 17, -2w + 3]$ | $-1$ |
| 17 | $[17, 17, -2w - 1]$ | $-e^{2} + 7$ |
| 37 | $[37, 37, w + 6]$ | $-\frac{1}{2}e^{2} + \frac{5}{2}$ |
| 37 | $[37, 37, -w + 7]$ | $-e^{2} - 2e + 9$ |
| 41 | $[41, 41, 3w + 1]$ | $-\frac{1}{2}e^{2} - e + \frac{15}{2}$ |
| 41 | $[41, 41, -3w + 4]$ | $\phantom{-}e^{2} - 3$ |
| 43 | $[43, 43, 3w + 8]$ | $\phantom{-}e^{2} - 2e - 3$ |
| 43 | $[43, 43, 3w - 11]$ | $\phantom{-}e^{2} - 2e - 3$ |
| 47 | $[47, 47, 3w - 2]$ | $\phantom{-}\frac{3}{2}e^{2} - 3e - \frac{13}{2}$ |
| 47 | $[47, 47, 3w - 1]$ | $\phantom{-}e^{2} - 2e + 1$ |
| 59 | $[59, 59, -5w - 6]$ | $\phantom{-}e^{2} - 2e - 11$ |
| 59 | $[59, 59, -4w - 3]$ | $-2e^{2} + 2e + 12$ |
| 67 | $[67, 67, -w - 8]$ | $-2e^{2} + 2e + 12$ |
| 67 | $[67, 67, w - 9]$ | $\phantom{-}\frac{1}{2}e^{2} - e - \frac{7}{2}$ |
| 79 | $[79, 79, 2w - 11]$ | $-\frac{1}{2}e^{2} - e + \frac{3}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $1$ |
| $17$ | $[17, 17, -2w + 3]$ | $1$ |