Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} + w + 4]$ |
| Dimension: | $10$ |
| 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:
| \(x^{10} - 20x^{8} + 129x^{6} - 274x^{4} + 80x^{2} - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $-\frac{1}{14}e^{9} + \frac{9}{7}e^{7} - \frac{107}{14}e^{5} + \frac{114}{7}e^{3} - \frac{50}{7}e$ |
| 11 | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $-\frac{1}{14}e^{8} + \frac{25}{14}e^{6} - \frac{92}{7}e^{4} + \frac{191}{7}e^{2} - \frac{22}{7}$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}\frac{1}{14}e^{9} - \frac{9}{7}e^{7} + \frac{107}{14}e^{5} - \frac{114}{7}e^{3} + \frac{50}{7}e$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}\frac{1}{7}e^{8} - \frac{18}{7}e^{6} + \frac{100}{7}e^{4} - \frac{165}{7}e^{2} + \frac{2}{7}$ |
| 17 | $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ | $\phantom{-}\frac{3}{14}e^{9} - \frac{61}{14}e^{7} + \frac{199}{7}e^{5} - \frac{419}{7}e^{3} + \frac{87}{7}e$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{1}{2}e^{9} - \frac{21}{2}e^{7} + 70e^{5} - 147e^{3} + 25e$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $-\frac{5}{14}e^{9} + \frac{97}{14}e^{7} - \frac{299}{7}e^{5} + \frac{577}{7}e^{3} - \frac{68}{7}e$ |
| 27 | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $-\frac{3}{14}e^{9} + \frac{61}{14}e^{7} - \frac{199}{7}e^{5} + \frac{412}{7}e^{3} - \frac{45}{7}e$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ | $-\frac{1}{7}e^{9} + \frac{43}{14}e^{7} - \frac{291}{14}e^{5} + \frac{312}{7}e^{3} - \frac{100}{7}e$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}\frac{3}{7}e^{9} - \frac{115}{14}e^{7} + \frac{705}{14}e^{5} - \frac{698}{7}e^{3} + \frac{160}{7}e$ |
| 41 | $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ | $-\frac{1}{7}e^{9} + \frac{25}{7}e^{7} - \frac{191}{7}e^{5} + \frac{466}{7}e^{3} - \frac{205}{7}e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ | $-\frac{1}{7}e^{8} + \frac{18}{7}e^{6} - \frac{100}{7}e^{4} + \frac{165}{7}e^{2} - \frac{58}{7}$ |
| 59 | $[59, 59, w - 4]$ | $\phantom{-}e^{6} - 13e^{4} + 40e^{2} - 8$ |
| 67 | $[67, 67, 2w^{2} - 3w - 8]$ | $\phantom{-}\frac{1}{14}e^{8} - \frac{39}{14}e^{6} + \frac{176}{7}e^{4} - \frac{429}{7}e^{2} + \frac{78}{7}$ |
| 73 | $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ | $-\frac{12}{7}e^{9} + \frac{237}{7}e^{7} - \frac{1501}{7}e^{5} + \frac{3051}{7}e^{3} - \frac{521}{7}e$ |
| 89 | $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ | $-\frac{1}{7}e^{9} + \frac{25}{7}e^{7} - \frac{184}{7}e^{5} + \frac{382}{7}e^{3} + \frac{5}{7}e$ |
| 97 | $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ | $\phantom{-}\frac{4}{7}e^{8} - \frac{72}{7}e^{6} + \frac{421}{7}e^{4} - \frac{835}{7}e^{2} + \frac{134}{7}$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ | $-2e^{9} + 39e^{7} - 244e^{5} + 492e^{3} - 95e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + w + 4]$ | $-1$ |