Base field \(\Q(\sqrt{197}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 49\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[36, 6, 6]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $97$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 8x^{3} + 14x^{2} - 8x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $-1$ |
| 7 | $[7, 7, w - 7]$ | $-e - 4$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w + 5]$ | $\phantom{-}e^{3} + \frac{11}{2}e^{2} + 5e - 3$ |
| 19 | $[19, 19, w - 6]$ | $-e^{3} - \frac{13}{2}e^{2} - 9e + 1$ |
| 23 | $[23, 23, w + 8]$ | $\phantom{-}\frac{1}{2}e^{3} + 4e^{2} + 7e - 2$ |
| 23 | $[23, 23, -w + 9]$ | $-\frac{1}{2}e^{3} - 2e^{2} + e + 2$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{3}{2}e^{2} + 6e - 5$ |
| 29 | $[29, 29, -w - 4]$ | $-\frac{1}{2}e^{3} - 3e^{2} + 6$ |
| 29 | $[29, 29, w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} + 3e^{2} - 10$ |
| 37 | $[37, 37, -w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} + 4e^{2} + 5e - 6$ |
| 37 | $[37, 37, w - 4]$ | $-\frac{1}{2}e^{3} - 2e^{2} + 3e + 6$ |
| 41 | $[41, 41, -w - 9]$ | $-\frac{1}{2}e^{3} - \frac{7}{2}e^{2} - 6e + 4$ |
| 41 | $[41, 41, w - 10]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} + 2e + 4$ |
| 43 | $[43, 43, -w - 2]$ | $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + e + 6$ |
| 43 | $[43, 43, w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{7}{2}e^{2} + 3e - 6$ |
| 47 | $[47, 47, -w - 1]$ | $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 6e$ |
| 47 | $[47, 47, w - 2]$ | $-\frac{1}{2}e^{3} - 5e^{2} - 10e + 8$ |
| 53 | $[53, 53, 2w - 13]$ | $-e^{2} - 5e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |
| $9$ | $[9, 3, 3]$ | $-1$ |