Base field \(\Q(\sqrt{213}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 53\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, w - 8]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 80x^{4} + 1699x^{2} - 4192\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 8]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $-\frac{7}{482}e^{4} + \frac{255}{482}e^{2} - \frac{219}{241}$ |
| 11 | $[11, 11, -w + 7]$ | $-e$ |
| 11 | $[11, 11, -w - 6]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -2w + 15]$ | $-\frac{1}{482}e^{5} + \frac{1}{241}e^{3} + \frac{1349}{482}e$ |
| 17 | $[17, 17, -2w - 13]$ | $\phantom{-}\frac{1}{482}e^{5} - \frac{1}{241}e^{3} - \frac{1349}{482}e$ |
| 19 | $[19, 19, -w - 8]$ | $\phantom{-}\frac{11}{241}e^{4} - \frac{504}{241}e^{2} + \frac{3236}{241}$ |
| 19 | $[19, 19, -w + 9]$ | $\phantom{-}\frac{11}{241}e^{4} - \frac{504}{241}e^{2} + \frac{3236}{241}$ |
| 23 | $[23, 23, -w - 5]$ | $\phantom{-}\frac{5}{482}e^{5} - \frac{251}{482}e^{3} + \frac{1086}{241}e$ |
| 23 | $[23, 23, -w + 6]$ | $-\frac{5}{482}e^{5} + \frac{251}{482}e^{3} - \frac{1086}{241}e$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}\frac{19}{482}e^{4} - \frac{761}{482}e^{2} - \frac{886}{241}$ |
| 37 | $[37, 37, -w - 9]$ | $-\frac{19}{482}e^{4} + \frac{761}{482}e^{2} - \frac{78}{241}$ |
| 37 | $[37, 37, w - 10]$ | $-\frac{19}{482}e^{4} + \frac{761}{482}e^{2} - \frac{78}{241}$ |
| 41 | $[41, 41, -w - 3]$ | $-\frac{2}{241}e^{5} + \frac{249}{482}e^{3} - \frac{3521}{482}e$ |
| 41 | $[41, 41, w - 4]$ | $\phantom{-}\frac{2}{241}e^{5} - \frac{249}{482}e^{3} + \frac{3521}{482}e$ |
| 43 | $[43, 43, -2w + 17]$ | $-\frac{43}{482}e^{4} + \frac{1773}{482}e^{2} - \frac{1724}{241}$ |
| 43 | $[43, 43, -7w + 55]$ | $-\frac{43}{482}e^{4} + \frac{1773}{482}e^{2} - \frac{1724}{241}$ |
| 47 | $[47, 47, -w - 2]$ | $-\frac{5}{482}e^{5} + \frac{251}{482}e^{3} - \frac{845}{241}e$ |
| 47 | $[47, 47, w - 3]$ | $\phantom{-}\frac{5}{482}e^{5} - \frac{251}{482}e^{3} + \frac{845}{241}e$ |
| 49 | $[49, 7, -7]$ | $-\frac{16}{241}e^{4} + \frac{755}{241}e^{2} - \frac{3962}{241}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 8]$ | $1$ |