Base field 3.3.1129.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} - w + 4]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 24x^{8} + 202x^{6} - 704x^{4} + 864x^{2} - 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}\frac{1}{32}e^{8} - \frac{5}{8}e^{6} + \frac{61}{16}e^{4} - \frac{27}{4}e^{2}$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{64}e^{9} - \frac{5}{16}e^{7} + \frac{61}{32}e^{5} - \frac{27}{8}e^{3} - e$ |
| 8 | $[8, 2, 2]$ | $-\frac{1}{8}e^{8} + \frac{9}{4}e^{6} - \frac{47}{4}e^{4} + \frac{33}{2}e^{2} + 2$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $-\frac{1}{64}e^{9} + \frac{5}{16}e^{7} - \frac{69}{32}e^{5} + \frac{51}{8}e^{3} - \frac{13}{2}e$ |
| 13 | $[13, 13, w^{2} - w - 7]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{9}{4}e^{5} + \frac{45}{4}e^{3} - \frac{27}{2}e$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{16}e^{9} - \frac{9}{8}e^{7} + \frac{45}{8}e^{5} - \frac{21}{4}e^{3} - 9e$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}1$ |
| 29 | $[29, 29, 2w^{2} - 2w - 11]$ | $-\frac{3}{32}e^{9} + \frac{15}{8}e^{7} - \frac{195}{16}e^{5} + \frac{121}{4}e^{3} - \frac{51}{2}e$ |
| 31 | $[31, 31, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{16}e^{7} - \frac{5}{4}e^{5} + \frac{61}{8}e^{3} - \frac{23}{2}e$ |
| 37 | $[37, 37, -2w^{2} + 3w + 7]$ | $-\frac{3}{32}e^{9} + 2e^{7} - \frac{223}{16}e^{5} + \frac{71}{2}e^{3} - 23e$ |
| 41 | $[41, 41, w^{2} - 2]$ | $\phantom{-}\frac{5}{64}e^{9} - \frac{23}{16}e^{7} + \frac{249}{32}e^{5} - \frac{85}{8}e^{3} - \frac{19}{2}e$ |
| 59 | $[59, 59, 2w^{2} - 13]$ | $\phantom{-}\frac{1}{4}e^{6} - 4e^{4} + \frac{33}{2}e^{2} - 6$ |
| 61 | $[61, 61, w^{2} + w - 10]$ | $-2e^{2} + 6$ |
| 67 | $[67, 67, 2w^{2} - w - 11]$ | $\phantom{-}\frac{1}{4}e^{7} - \frac{9}{2}e^{5} + \frac{45}{2}e^{3} - 28e$ |
| 73 | $[73, 73, -w^{2} - 1]$ | $-\frac{5}{16}e^{8} + \frac{23}{4}e^{6} - \frac{249}{8}e^{4} + \frac{101}{2}e^{2} - 18$ |
| 83 | $[83, 83, w^{2} - w - 10]$ | $-\frac{5}{16}e^{8} + 6e^{6} - \frac{281}{8}e^{4} + 66e^{2} - 14$ |
| 89 | $[89, 89, -w^{2} + 4w - 2]$ | $-\frac{3}{16}e^{8} + \frac{7}{2}e^{6} - \frac{155}{8}e^{4} + 32e^{2} - 7$ |
| 97 | $[97, 97, w^{2} - 2w - 7]$ | $\phantom{-}\frac{1}{8}e^{7} - \frac{3}{2}e^{5} + \frac{5}{4}e^{3} + 14e$ |
| 97 | $[97, 97, -w^{2} - 4w - 5]$ | $-\frac{3}{16}e^{8} + \frac{13}{4}e^{6} - \frac{127}{8}e^{4} + \frac{45}{2}e^{2} - 16$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} - w + 4]$ | $-1$ |