Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[15,15,-w + 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 9x^{3} - 14x^{2} + 16x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 3e - 1$ |
| 5 | $[5, 5, w + 2]$ | $-1$ |
| 7 | $[7, 7, w]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 4e^{2} + 2e - 4$ |
| 7 | $[7, 7, w + 6]$ | $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 4e + 2$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2}$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} + \frac{1}{2}e^{3} - 3e^{2} - 2e$ |
| 19 | $[19, 19, w - 2]$ | $-\frac{1}{2}e^{4} + e^{3} + \frac{7}{2}e^{2} - 7e + 2$ |
| 23 | $[23, 23, w + 9]$ | $-e^{4} + 8e^{2} - 4$ |
| 23 | $[23, 23, w + 13]$ | $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + 2e - 2$ |
| 37 | $[37, 37, w + 11]$ | $\phantom{-}\frac{1}{2}e^{4} - e^{3} - \frac{11}{2}e^{2} + 6e + 8$ |
| 37 | $[37, 37, w + 25]$ | $-e^{3} + 7e - 2$ |
| 59 | $[59, 59, 3w + 10]$ | $-\frac{1}{2}e^{4} - \frac{1}{2}e^{3} + 5e^{2} + 6e - 8$ |
| 59 | $[59, 59, 3w - 13]$ | $\phantom{-}\frac{3}{2}e^{4} + \frac{1}{2}e^{3} - 13e^{2} - 2e + 16$ |
| 73 | $[73, 73, w + 15]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - 5e^{2} + 12e + 10$ |
| 73 | $[73, 73, w + 57]$ | $\phantom{-}e^{3} + 4e^{2} - 4e - 18$ |
| 89 | $[89, 89, -w - 10]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} + 3e - 4$ |
| 89 | $[89, 89, w - 11]$ | $-\frac{1}{2}e^{4} + \frac{3}{2}e^{3} + 4e^{2} - 10e - 6$ |
| 97 | $[97, 97, w + 22]$ | $-\frac{1}{2}e^{4} + \frac{1}{2}e^{3} + 2e^{2} - 7e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w + 3]$ | $1$ |
| $5$ | $[5,5,-w + 3]$ | $1$ |