Base field \(\Q(\sqrt{481}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 120\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $80$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - x^{3} - 12x^{2} + 8x + 29\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -2w - 21]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 2w - 23]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{12}{5}e + \frac{1}{5}$ |
| 5 | $[5, 5, w]$ | $\phantom{-}e^{2} - 6$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{1}{5}e^{3} - e^{2} + \frac{7}{5}e + \frac{34}{5}$ |
| 13 | $[13, 13, w + 6]$ | $-\frac{3}{5}e^{3} + \frac{21}{5}e + \frac{7}{5}$ |
| 19 | $[19, 19, w + 2]$ | $-\frac{2}{5}e^{3} + \frac{14}{5}e + \frac{18}{5}$ |
| 19 | $[19, 19, w + 16]$ | $-\frac{2}{5}e^{3} + \frac{14}{5}e + \frac{18}{5}$ |
| 31 | $[31, 31, w + 13]$ | $-\frac{1}{5}e^{3} + \frac{17}{5}e + \frac{14}{5}$ |
| 31 | $[31, 31, w + 17]$ | $\phantom{-}\frac{1}{5}e^{3} - \frac{17}{5}e + \frac{16}{5}$ |
| 37 | $[37, 37, w + 18]$ | $\phantom{-}\frac{6}{5}e^{3} - \frac{42}{5}e - \frac{9}{5}$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}\frac{6}{5}e^{3} - \frac{42}{5}e - \frac{19}{5}$ |
| 53 | $[53, 53, -234w + 2683]$ | $-\frac{2}{5}e^{3} + 2e^{2} + \frac{4}{5}e - \frac{52}{5}$ |
| 53 | $[53, 53, -234w - 2449]$ | $-\frac{6}{5}e^{3} - 2e^{2} + \frac{52}{5}e + \frac{74}{5}$ |
| 59 | $[59, 59, w + 1]$ | $-\frac{4}{5}e^{3} - 2e^{2} + \frac{18}{5}e + \frac{86}{5}$ |
| 59 | $[59, 59, w + 57]$ | $-\frac{4}{5}e^{3} + 2e^{2} + \frac{38}{5}e - \frac{44}{5}$ |
| 89 | $[89, 89, w + 41]$ | $-\frac{6}{5}e^{3} + 2e^{2} + \frac{42}{5}e - \frac{66}{5}$ |
| 89 | $[89, 89, w + 47]$ | $-\frac{8}{5}e^{3} - 2e^{2} + \frac{56}{5}e + \frac{62}{5}$ |
| 97 | $[97, 97, w + 26]$ | $\phantom{-}\frac{4}{5}e^{3} - 2e^{2} - \frac{38}{5}e + \frac{14}{5}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $2$ | $[2, 2, w + 1]$ | $-1$ |