Base field \(\Q(\sqrt{3}, \sqrt{11})\)
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 62x^{2} + 625\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -\frac{1}{2}w^{3} + \frac{7}{2}w - 1]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{37}{50}e$ |
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{37}{50}e$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} - \frac{5}{2}w]$ | $-1$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $\phantom{-}\frac{1}{50}e^{3} - \frac{87}{50}e$ |
| 11 | $[11, 11, w^{2} + w - 1]$ | $-\frac{1}{50}e^{3} + \frac{87}{50}e$ |
| 25 | $[25, 5, \frac{1}{2}w^{3} - w^{2} - \frac{7}{2}w + 4]$ | $\phantom{-}6$ |
| 25 | $[25, 5, -\frac{1}{2}w^{3} - w^{2} + \frac{7}{2}w + 4]$ | $\phantom{-}6$ |
| 37 | $[37, 37, -w^{3} + 7w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{27}{2}$ |
| 37 | $[37, 37, -2w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{27}{2}$ |
| 37 | $[37, 37, 2w + 1]$ | $-\frac{1}{2}e^{2} + \frac{35}{2}$ |
| 37 | $[37, 37, -w^{3} + 7w - 1]$ | $-\frac{1}{2}e^{2} + \frac{35}{2}$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} - \frac{9}{2}w + 2]$ | $-2$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{9}{2}w + 2]$ | $-2$ |
| 83 | $[83, 83, \frac{1}{2}w^{3} + w^{2} - \frac{7}{2}w - 2]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{47}{10}e$ |
| 83 | $[83, 83, w^{2} + w - 5]$ | $\phantom{-}\frac{3}{50}e^{3} - \frac{61}{50}e$ |
| 83 | $[83, 83, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{47}{10}e$ |
| 83 | $[83, 83, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 2]$ | $\phantom{-}\frac{3}{50}e^{3} - \frac{61}{50}e$ |
| 97 | $[97, 97, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 8]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{23}{2}$ |
| 97 | $[97, 97, \frac{5}{2}w^{3} - w^{2} - \frac{31}{2}w + 6]$ | $-\frac{1}{2}e^{2} + \frac{39}{2}$ |
| 97 | $[97, 97, -\frac{11}{2}w^{3} + 4w^{2} + \frac{71}{2}w - 26]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{23}{2}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9,3,\frac{1}{2}w^{3}-\frac{5}{2}w]$ | $1$ |