Base field \(\Q(\sqrt{3}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[73,73,-3w - 10]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 12x^{6} + 45x^{4} - 56x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{4}e^{7} - 2e^{5} + \frac{9}{4}e^{3} + 4e$ |
| 11 | $[11, 11, -2w + 1]$ | $-e^{7} + 10e^{5} - 27e^{3} + 18e$ |
| 11 | $[11, 11, 2w + 1]$ | $\phantom{-}\frac{1}{4}e^{7} - 3e^{5} + \frac{41}{4}e^{3} - 9e$ |
| 13 | $[13, 13, w + 4]$ | $-\frac{1}{2}e^{6} + 4e^{4} - \frac{13}{2}e^{2} + 2$ |
| 13 | $[13, 13, -w + 4]$ | $-e^{6} + 10e^{4} - 25e^{2} + 10$ |
| 23 | $[23, 23, -3w + 2]$ | $\phantom{-}2e^{3} - 10e$ |
| 23 | $[23, 23, 3w + 2]$ | $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + \frac{41}{2}e^{3} - 18e$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}2e^{6} - 18e^{4} + 36e^{2} - 2$ |
| 37 | $[37, 37, 2w - 7]$ | $\phantom{-}2e^{6} - 18e^{4} + 38e^{2} - 8$ |
| 37 | $[37, 37, -2w - 7]$ | $-\frac{1}{2}e^{6} + 4e^{4} - \frac{5}{2}e^{2} - 10$ |
| 47 | $[47, 47, -4w - 1]$ | $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + \frac{45}{2}e^{3} - 28e$ |
| 47 | $[47, 47, 4w - 1]$ | $\phantom{-}\frac{1}{4}e^{7} - 3e^{5} + \frac{49}{4}e^{3} - 15e$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}e^{6} - 10e^{4} + 23e^{2} - 2$ |
| 59 | $[59, 59, 5w - 4]$ | $\phantom{-}\frac{5}{4}e^{7} - 12e^{5} + \frac{117}{4}e^{3} - 16e$ |
| 59 | $[59, 59, -5w - 4]$ | $-\frac{1}{2}e^{7} + 4e^{5} - \frac{9}{2}e^{3} - 10e$ |
| 61 | $[61, 61, -w - 8]$ | $-2e^{2} + 6$ |
| 61 | $[61, 61, w - 8]$ | $\phantom{-}e^{6} - 8e^{4} + 15e^{2} - 6$ |
| 71 | $[71, 71, 5w - 2]$ | $-\frac{5}{4}e^{7} + 14e^{5} - \frac{181}{4}e^{3} + 42e$ |
| 71 | $[71, 71, -5w - 2]$ | $\phantom{-}\frac{3}{4}e^{7} - 9e^{5} + \frac{131}{4}e^{3} - 33e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $73$ | $[73,73,-3w - 10]$ | $1$ |