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: | $[19,19,-w + 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} + 20x^{6} + 124x^{4} + 256x^{2} + 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{16}e^{7} + \frac{9}{8}e^{5} + \frac{11}{2}e^{3} + 6e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 4 | $[4, 2, 2]$ | $-\frac{1}{4}e^{4} - \frac{5}{2}e^{2} - 3$ |
| 5 | $[5, 5, w + 2]$ | $-\frac{1}{8}e^{5} - \frac{7}{4}e^{3} - 6e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{1}{16}e^{7} + e^{5} + \frac{15}{4}e^{3} + e$ |
| 7 | $[7, 7, w + 6]$ | $\phantom{-}\frac{1}{16}e^{7} + \frac{9}{8}e^{5} + 6e^{3} + 9e$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{1}{16}e^{7} - e^{5} - \frac{17}{4}e^{3} - 5e$ |
| 19 | $[19, 19, w + 1]$ | $-\frac{1}{8}e^{6} - 2e^{4} - 9e^{2} - 12$ |
| 19 | $[19, 19, w - 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, w + 9]$ | $\phantom{-}\frac{1}{16}e^{7} + \frac{9}{8}e^{5} + 6e^{3} + 12e$ |
| 23 | $[23, 23, w + 13]$ | $-\frac{1}{16}e^{7} - e^{5} - \frac{13}{4}e^{3} + 2e$ |
| 37 | $[37, 37, w + 11]$ | $\phantom{-}\frac{1}{8}e^{7} + \frac{19}{8}e^{5} + \frac{49}{4}e^{3} + 11e$ |
| 37 | $[37, 37, w + 25]$ | $-\frac{1}{8}e^{7} - \frac{9}{4}e^{5} - 12e^{3} - 20e$ |
| 59 | $[59, 59, 3w + 10]$ | $-\frac{1}{2}e^{4} - 6e^{2} - 12$ |
| 59 | $[59, 59, 3w - 13]$ | $-\frac{1}{2}e^{4} - 6e^{2} - 12$ |
| 73 | $[73, 73, w + 15]$ | $\phantom{-}\frac{1}{8}e^{7} + \frac{5}{2}e^{5} + 14e^{3} + 19e$ |
| 73 | $[73, 73, w + 57]$ | $\phantom{-}\frac{1}{2}e^{3} + 7e$ |
| 89 | $[89, 89, -w - 10]$ | $\phantom{-}\frac{3}{4}e^{4} + 10e^{2} + 22$ |
| 89 | $[89, 89, w - 11]$ | $\phantom{-}\frac{1}{4}e^{6} + \frac{7}{2}e^{4} + 12e^{2} + 6$ |
| 97 | $[97, 97, w + 22]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{5}{2}e^{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19,19,-w + 2]$ | $-1$ |