Base field \(\Q(\sqrt{15}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 15\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15, 15, w]$ |
| 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:
| \(x^{4} + 24x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}\frac{1}{16}e^{3} + \frac{5}{4}e$ |
| 3 | $[3, 3, w]$ | $-\frac{1}{16}e^{3} - \frac{5}{4}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}\frac{1}{16}e^{3} + \frac{5}{4}e$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 6]$ | $-\frac{1}{4}e^{3} - 6e$ |
| 11 | $[11, 11, -w - 2]$ | $\phantom{-}\frac{1}{4}e^{2} + 5$ |
| 11 | $[11, 11, w - 2]$ | $-\frac{1}{4}e^{2} - 1$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}\frac{1}{8}e^{3} + \frac{9}{2}e$ |
| 17 | $[17, 17, w + 10]$ | $-\frac{3}{8}e^{3} - \frac{19}{2}e$ |
| 43 | $[43, 43, w + 12]$ | $\phantom{-}\frac{1}{4}e^{3} + 7e$ |
| 43 | $[43, 43, w + 31]$ | $-\frac{1}{4}e^{3} - 7e$ |
| 53 | $[53, 53, w + 11]$ | $\phantom{-}\frac{1}{8}e^{3} + \frac{5}{2}e$ |
| 53 | $[53, 53, w + 42]$ | $\phantom{-}\frac{1}{8}e^{3} + \frac{5}{2}e$ |
| 59 | $[59, 59, 2w - 1]$ | $-\frac{1}{4}e^{2} - 1$ |
| 59 | $[59, 59, -2w - 1]$ | $\phantom{-}\frac{1}{4}e^{2} + 5$ |
| 61 | $[61, 61, 2w - 11]$ | $\phantom{-}\frac{1}{2}e^{2} + 12$ |
| 61 | $[61, 61, -2w - 11]$ | $-\frac{1}{2}e^{2}$ |
| 67 | $[67, 67, w + 22]$ | $-\frac{1}{4}e^{3} - 3e$ |
| 67 | $[67, 67, w + 45]$ | $-\frac{3}{4}e^{3} - 17e$ |
| 71 | $[71, 71, 3w - 8]$ | $-8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $\frac{1}{16}e^{3} + \frac{5}{4}e$ |
| $5$ | $[5, 5, w]$ | $-\frac{1}{16}e^{3} - \frac{5}{4}e$ |