Base field 3.3.564.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} + w + 1]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - x^{9} - 14x^{8} + 12x^{7} + 67x^{6} - 44x^{5} - 126x^{4} + 50x^{3} + 80x^{2} - 20x - 12\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $\phantom{-}e^{4} - 6e^{2} + 4$ |
| 3 | $[3, 3, w - 2]$ | $-\frac{1}{2}e^{9} + \frac{13}{2}e^{7} - \frac{55}{2}e^{5} - \frac{1}{2}e^{4} + 41e^{3} + 3e^{2} - 16e - 2$ |
| 13 | $[13, 13, w^{2} - 2w - 2]$ | $-e^{7} + 11e^{5} + e^{4} - 34e^{3} - 6e^{2} + 22e + 2$ |
| 17 | $[17, 17, -w^{2} + 2]$ | $-\frac{1}{2}e^{9} - e^{8} + \frac{13}{2}e^{7} + 12e^{6} - \frac{57}{2}e^{5} - \frac{89}{2}e^{4} + 48e^{3} + 51e^{2} - 26e - 12$ |
| 19 | $[19, 19, -w^{2} + w + 1]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -w + 4]$ | $-\frac{1}{2}e^{9} + \frac{15}{2}e^{7} + e^{6} - \frac{75}{2}e^{5} - \frac{21}{2}e^{4} + 68e^{3} + 29e^{2} - 28e - 10$ |
| 41 | $[41, 41, -w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{2}e^{9} - \frac{1}{2}e^{8} - 6e^{7} + 6e^{6} + \frac{43}{2}e^{5} - 22e^{4} - 22e^{3} + 23e^{2} + 8e$ |
| 41 | $[41, 41, -2w^{2} - 3w + 4]$ | $\phantom{-}e^{8} - e^{7} - 12e^{6} + 12e^{5} + 46e^{4} - 40e^{3} - 60e^{2} + 26e + 18$ |
| 41 | $[41, 41, 2w + 1]$ | $-\frac{1}{2}e^{9} + \frac{13}{2}e^{7} + e^{6} - \frac{55}{2}e^{5} - \frac{21}{2}e^{4} + 39e^{3} + 29e^{2} - 6e - 12$ |
| 43 | $[43, 43, -w^{2} - w + 5]$ | $\phantom{-}e^{8} + 2e^{7} - 10e^{6} - 22e^{5} + 24e^{4} + 66e^{3} + 4e^{2} - 32e - 4$ |
| 47 | $[47, 47, -w^{2} + 8]$ | $\phantom{-}\frac{1}{2}e^{9} + \frac{1}{2}e^{8} - 6e^{7} - 5e^{6} + \frac{45}{2}e^{5} + 13e^{4} - 28e^{3} - e^{2} + 12e - 6$ |
| 47 | $[47, 47, 2w^{2} - w - 8]$ | $\phantom{-}e^{9} - e^{8} - 14e^{7} + 10e^{6} + 66e^{5} - 23e^{4} - 114e^{3} - 10e^{2} + 42e + 12$ |
| 53 | $[53, 53, w^{2} + w - 7]$ | $-e^{9} + e^{8} + 12e^{7} - 12e^{6} - 44e^{5} + 42e^{4} + 46e^{3} - 36e^{2} - 2e + 6$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-\frac{3}{2}e^{9} + \frac{41}{2}e^{7} + e^{6} - \frac{187}{2}e^{5} - \frac{29}{2}e^{4} + 156e^{3} + 51e^{2} - 64e - 18$ |
| 61 | $[61, 61, -3w^{2} + 14]$ | $\phantom{-}e^{9} - 14e^{7} - 2e^{6} + 65e^{5} + 21e^{4} - 110e^{3} - 60e^{2} + 48e + 26$ |
| 61 | $[61, 61, 4w^{2} - 2w - 19]$ | $-\frac{1}{2}e^{9} - e^{8} + \frac{13}{2}e^{7} + 13e^{6} - \frac{59}{2}e^{5} - \frac{111}{2}e^{4} + 54e^{3} + 83e^{2} - 30e - 28$ |
| 61 | $[61, 61, -2w^{2} + 7]$ | $\phantom{-}2e^{9} - 26e^{7} - e^{6} + 111e^{5} + 13e^{4} - 170e^{3} - 42e^{2} + 70e + 14$ |
| 67 | $[67, 67, -2w^{2} - w + 8]$ | $\phantom{-}e^{5} - 2e^{4} - 8e^{3} + 10e^{2} + 12e - 4$ |
| 71 | $[71, 71, w^{2} + 2w - 4]$ | $\phantom{-}\frac{1}{2}e^{9} - \frac{1}{2}e^{8} - 5e^{7} + 6e^{6} + \frac{23}{2}e^{5} - 21e^{4} + 8e^{3} + 17e^{2} - 20e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} + w + 1]$ | $-1$ |