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: | $[4, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 2x^{3} - 18x^{2} - 34x + 29\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w - 7]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{18}{5}e - \frac{8}{5}$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $-3$ |
| 19 | $[19, 19, w + 5]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{15}{2}e - \frac{5}{2}$ |
| 19 | $[19, 19, w - 6]$ | $-\frac{1}{10}e^{3} - \frac{1}{2}e^{2} + \frac{3}{10}e + \frac{53}{10}$ |
| 23 | $[23, 23, w + 8]$ | $-\frac{2}{5}e^{3} + \frac{1}{2}e^{2} + \frac{26}{5}e - \frac{73}{10}$ |
| 23 | $[23, 23, -w + 9]$ | $-\frac{1}{5}e^{3} - \frac{1}{2}e^{2} + \frac{13}{5}e + \frac{21}{10}$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{13}{10}e - \frac{24}{5}$ |
| 29 | $[29, 29, -w - 4]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{15}{2}e - 2$ |
| 29 | $[29, 29, w - 5]$ | $\phantom{-}\frac{3}{10}e^{3} - \frac{29}{10}e - \frac{2}{5}$ |
| 37 | $[37, 37, -w - 3]$ | $\phantom{-}\frac{1}{10}e^{3} - e^{2} - \frac{23}{10}e + \frac{61}{5}$ |
| 37 | $[37, 37, w - 4]$ | $-\frac{1}{2}e^{3} + e^{2} + \frac{15}{2}e - 5$ |
| 41 | $[41, 41, -w - 9]$ | $-\frac{1}{5}e^{3} + \frac{23}{5}e - \frac{17}{5}$ |
| 41 | $[41, 41, w - 10]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{23}{5}e - \frac{33}{5}$ |
| 43 | $[43, 43, -w - 2]$ | $-\frac{1}{10}e^{3} + \frac{1}{2}e^{2} + \frac{3}{10}e - \frac{97}{10}$ |
| 43 | $[43, 43, w - 3]$ | $-\frac{1}{10}e^{3} - \frac{1}{2}e^{2} + \frac{23}{10}e + \frac{13}{10}$ |
| 47 | $[47, 47, -w - 1]$ | $-e - 2$ |
| 47 | $[47, 47, w - 2]$ | $-\frac{1}{5}e^{3} + \frac{18}{5}e - \frac{2}{5}$ |
| 53 | $[53, 53, 2w - 13]$ | $-\frac{1}{10}e^{3} - \frac{1}{2}e^{2} - \frac{7}{10}e + \frac{43}{10}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $-1$ |