Base field \(\Q(\sqrt{241}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 60\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, -786w - 5708]$ |
| 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:
| \(x^{4} + 4x^{3} - 5x^{2} - 27x - 10\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -393w - 2854]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -393w + 3247]$ | $-1$ |
| 3 | $[3, 3, 4w - 33]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 4w + 29]$ | $-\frac{1}{3}e^{3} + \frac{8}{3}e - \frac{2}{3}$ |
| 5 | $[5, 5, 42w + 305]$ | $\phantom{-}\frac{2}{3}e^{3} + e^{2} - \frac{16}{3}e - \frac{11}{3}$ |
| 5 | $[5, 5, -42w + 347]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{8}{3}e - \frac{1}{3}$ |
| 29 | $[29, 29, 1820w + 13217]$ | $\phantom{-}\frac{4}{3}e^{3} + 2e^{2} - \frac{29}{3}e - \frac{25}{3}$ |
| 29 | $[29, 29, 1820w - 15037]$ | $\phantom{-}\frac{2}{3}e^{3} + e^{2} - \frac{16}{3}e - \frac{17}{3}$ |
| 41 | $[41, 41, -80w - 581]$ | $-\frac{1}{3}e^{3} - e^{2} + \frac{5}{3}e + \frac{25}{3}$ |
| 41 | $[41, 41, 80w - 661]$ | $-\frac{1}{3}e^{3} + e^{2} + \frac{8}{3}e - \frac{17}{3}$ |
| 47 | $[47, 47, 34w - 281]$ | $\phantom{-}\frac{1}{3}e^{3} + e^{2} - \frac{8}{3}e - \frac{10}{3}$ |
| 47 | $[47, 47, 34w + 247]$ | $-e^{3} - 3e^{2} + 8e + 16$ |
| 49 | $[49, 7, -7]$ | $-2e^{3} - e^{2} + 16e - 3$ |
| 53 | $[53, 53, 6w + 43]$ | $\phantom{-}e^{3} - 10e + 3$ |
| 53 | $[53, 53, 6w - 49]$ | $\phantom{-}\frac{2}{3}e^{3} - e^{2} - \frac{13}{3}e + \frac{37}{3}$ |
| 59 | $[59, 59, 10w + 73]$ | $-2e^{3} - 3e^{2} + 15e + 16$ |
| 59 | $[59, 59, 10w - 83]$ | $\phantom{-}\frac{2}{3}e^{3} - e^{2} - \frac{19}{3}e + \frac{4}{3}$ |
| 61 | $[61, 61, 4178w + 30341]$ | $-\frac{2}{3}e^{3} + \frac{16}{3}e - \frac{37}{3}$ |
| 61 | $[61, 61, 4178w - 34519]$ | $-e^{3} - e^{2} + 8e + 3$ |
| 67 | $[67, 67, -332w + 2743]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{17}{3}e - \frac{10}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -393w - 2854]$ | $-1$ |
| $2$ | $[2, 2, -393w + 3247]$ | $1$ |