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: | $[3, 3, -2w - 21]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $126$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 8x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e$ |
| 3 | $[3, 3, -2w - 21]$ | $-1$ |
| 3 | $[3, 3, 2w - 23]$ | $-1$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{11}{3}e$ |
| 5 | $[5, 5, w + 4]$ | $-\frac{1}{3}e^{3} - \frac{2}{3}e$ |
| 13 | $[13, 13, w + 6]$ | $-e^{3} - 5e$ |
| 19 | $[19, 19, w + 2]$ | $\phantom{-}3e$ |
| 19 | $[19, 19, w + 16]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{16}{3}e$ |
| 31 | $[31, 31, w + 13]$ | $-\frac{1}{3}e^{3} + \frac{1}{3}e$ |
| 31 | $[31, 31, w + 17]$ | $-e^{3} - 5e$ |
| 37 | $[37, 37, w + 18]$ | $-\frac{2}{3}e^{3} - \frac{7}{3}e$ |
| 49 | $[49, 7, -7]$ | $-2e^{2} - 2$ |
| 53 | $[53, 53, -234w + 2683]$ | $-e^{2} - 8$ |
| 53 | $[53, 53, -234w - 2449]$ | $-2e^{2} - 10$ |
| 59 | $[59, 59, w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e$ |
| 59 | $[59, 59, w + 57]$ | $\phantom{-}3e^{3} + 16e$ |
| 89 | $[89, 89, w + 41]$ | $-\frac{1}{3}e^{3} - \frac{5}{3}e$ |
| 89 | $[89, 89, w + 47]$ | $-\frac{2}{3}e^{3} - \frac{10}{3}e$ |
| 97 | $[97, 97, w + 26]$ | $-6e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -2w - 21]$ | $1$ |