Base field \(\Q(\sqrt{109}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 27\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[21, 21, w + 2]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $29$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 2x^{4} - 7x^{3} + 10x^{2} + 10x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 5]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}e^{2} - e - 3$ |
| 5 | $[5, 5, -3w + 17]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{5}{2}e^{2} + 3e + 2$ |
| 5 | $[5, 5, -3w - 14]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{5}{2}e^{2} - 3e - 2$ |
| 7 | $[7, 7, w - 5]$ | $-1$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}e^{2} - 4$ |
| 29 | $[29, 29, -w - 7]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{9}{2}e^{2} - 7e - 6$ |
| 29 | $[29, 29, -w + 8]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} + 4e - 10$ |
| 31 | $[31, 31, -5w + 28]$ | $-e^{3} + 2e^{2} + 3e - 8$ |
| 31 | $[31, 31, -5w - 23]$ | $\phantom{-}e + 4$ |
| 43 | $[43, 43, 6w + 29]$ | $-e^{3} + 2e^{2} + 5e - 8$ |
| 43 | $[43, 43, -6w + 35]$ | $-e^{4} + 9e^{2} + 2e - 16$ |
| 61 | $[61, 61, 3w - 19]$ | $-\frac{1}{2}e^{4} - e^{3} + \frac{15}{2}e^{2} + 5e - 14$ |
| 61 | $[61, 61, -3w - 16]$ | $-\frac{3}{2}e^{4} + \frac{27}{2}e^{2} + 2e - 18$ |
| 71 | $[71, 71, -7w - 34]$ | $\phantom{-}e^{4} - e^{3} - 9e^{2} + 3e + 16$ |
| 71 | $[71, 71, 7w - 41]$ | $-e^{4} + e^{3} + 6e^{2} - e - 4$ |
| 73 | $[73, 73, 2w - 7]$ | $-\frac{5}{2}e^{4} + 4e^{3} + \frac{29}{2}e^{2} - 12e - 14$ |
| 73 | $[73, 73, -2w - 5]$ | $-\frac{1}{2}e^{4} + 2e^{3} + \frac{1}{2}e^{2} - 7e + 6$ |
| 83 | $[83, 83, -w - 10]$ | $-e^{3} + 8e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 5]$ | $1$ |
| $7$ | $[7, 7, w - 5]$ | $1$ |