Base field 4.4.12357.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 20x^{8} + 135x^{6} - 376x^{4} + 408x^{2} - 144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{1}{12}e^{8} + \frac{5}{3}e^{6} - \frac{43}{4}e^{4} + \frac{149}{6}e^{2} - 15$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-2$ |
| 11 | $[11, 11, -w^{2} - w + 1]$ | $-\frac{1}{8}e^{9} + \frac{5}{2}e^{7} - \frac{131}{8}e^{5} + \frac{79}{2}e^{3} - 24e$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{2}e^{4} + \frac{11}{2}e^{2} - 11$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{6}e^{9} - \frac{10}{3}e^{7} + 22e^{5} - \frac{331}{6}e^{3} + 38e$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w - 4]$ | $-\frac{1}{24}e^{9} + \frac{7}{12}e^{7} - \frac{13}{8}e^{5} - \frac{25}{12}e^{3} + 5e$ |
| 31 | $[31, 31, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{1}{2}e^{6} - \frac{15}{2}e^{4} + 27e^{2} - 17$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $-\frac{1}{12}e^{9} + \frac{5}{3}e^{7} - \frac{45}{4}e^{5} + \frac{91}{3}e^{3} - 27e$ |
| 43 | $[43, 43, w^{3} + w^{2} - 5w - 4]$ | $-\frac{1}{2}e^{6} + 8e^{4} - \frac{67}{2}e^{2} + 29$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w - 1]$ | $-\frac{1}{4}e^{7} + \frac{7}{2}e^{5} - \frac{41}{4}e^{3} - e$ |
| 53 | $[53, 53, -w^{2} - w + 4]$ | $\phantom{-}\frac{3}{8}e^{9} - \frac{27}{4}e^{7} + \frac{301}{8}e^{5} - \frac{291}{4}e^{3} + 31e$ |
| 59 | $[59, 59, -w^{3} + 4w - 2]$ | $\phantom{-}\frac{1}{24}e^{9} - \frac{13}{12}e^{7} + \frac{73}{8}e^{5} - \frac{335}{12}e^{3} + 27e$ |
| 67 | $[67, 67, -2w^{3} + w^{2} + 8w + 1]$ | $\phantom{-}\frac{1}{2}e^{8} - \frac{17}{2}e^{6} + 43e^{4} - 73e^{2} + 32$ |
| 89 | $[89, 89, -2w^{3} + 3w^{2} + 8w - 8]$ | $\phantom{-}\frac{1}{8}e^{9} - 2e^{7} + \frac{67}{8}e^{5} - 5e^{3} - 12e$ |
| 89 | $[89, 89, w^{3} - 5w + 1]$ | $\phantom{-}\frac{1}{4}e^{9} - \frac{19}{4}e^{7} + \frac{115}{4}e^{5} - \frac{249}{4}e^{3} + 33e$ |
| 97 | $[97, 97, w^{3} - 6w - 1]$ | $\phantom{-}\frac{3}{4}e^{8} - 14e^{6} + \frac{333}{4}e^{4} - 183e^{2} + 103$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 4w - 10]$ | $-\frac{1}{2}e^{8} + 9e^{6} - \frac{101}{2}e^{4} + 102e^{2} - 62$ |
| 101 | $[101, 101, -w^{3} + 6w - 2]$ | $\phantom{-}\frac{19}{24}e^{9} - \frac{181}{12}e^{7} + \frac{743}{8}e^{5} - \frac{2561}{12}e^{3} + 134e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{3} + w^{2} + 5w - 2]$ | $-1$ |