Base field \(\Q(\sqrt{97}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 24\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, 26w + 115]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 6x^{2} - 12x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 7w - 38]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + \frac{5}{2}$ |
| 2 | $[2, 2, -7w - 31]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 2w + 9]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{5}{2}$ |
| 3 | $[3, 3, 2w - 11]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -12w + 65]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{3}{2}$ |
| 11 | $[11, 11, -12w - 53]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{7}{2}e - \frac{1}{2}$ |
| 25 | $[25, 5, 5]$ | $-2e^{3} - e^{2} + 12e + 5$ |
| 31 | $[31, 31, 8w - 43]$ | $\phantom{-}3e^{3} + e^{2} - 19e - 9$ |
| 31 | $[31, 31, 8w + 35]$ | $-e^{3} - 2e^{2} + 7e + 8$ |
| 43 | $[43, 43, 54w + 239]$ | $-e^{2} + 5$ |
| 43 | $[43, 43, -54w + 293]$ | $\phantom{-}\frac{5}{2}e^{3} + \frac{3}{2}e^{2} - \frac{29}{2}e - \frac{27}{2}$ |
| 47 | $[47, 47, 2w - 13]$ | $\phantom{-}e^{3} - 3e - 2$ |
| 47 | $[47, 47, -2w - 11]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} - \frac{3}{2}e - \frac{19}{2}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}e^{3} + e^{2} - 5e - 7$ |
| 53 | $[53, 53, 4w + 19]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{1}{2}e^{2} - \frac{19}{2}e - \frac{13}{2}$ |
| 53 | $[53, 53, 4w - 23]$ | $\phantom{-}e^{3} + 2e^{2} - 5e - 12$ |
| 61 | $[61, 61, 2w - 7]$ | $\phantom{-}\frac{3}{2}e^{3} + \frac{3}{2}e^{2} - \frac{15}{2}e - \frac{19}{2}$ |
| 61 | $[61, 61, -2w - 5]$ | $-\frac{1}{2}e^{3} - \frac{7}{2}e^{2} + \frac{5}{2}e + \frac{23}{2}$ |
| 73 | $[73, 73, 22w + 97]$ | $\phantom{-}e^{3} - 5e + 2$ |
| 73 | $[73, 73, -22w + 119]$ | $\phantom{-}4e^{3} + 2e^{2} - 22e - 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, 2w - 11]$ | $-1$ |