Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, w + 3]$ |
| Dimension: | $12$ |
| 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:
| \(x^{12} - 20x^{10} + 140x^{8} - 424x^{6} + 550x^{4} - 236x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{25}{254}e^{10} - \frac{232}{127}e^{8} + \frac{1421}{127}e^{6} - \frac{3396}{127}e^{4} + \frac{3016}{127}e^{2} - \frac{578}{127}$ |
| 8 | $[8, 2, 2]$ | $-\frac{3}{254}e^{10} + \frac{38}{127}e^{8} - \frac{328}{127}e^{6} + \frac{1073}{127}e^{4} - \frac{875}{127}e^{2} - \frac{271}{127}$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $-\frac{17}{254}e^{11} + \frac{173}{127}e^{9} - \frac{1266}{127}e^{7} + \frac{4260}{127}e^{5} - \frac{6821}{127}e^{3} + \frac{4010}{127}e$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{26}{127}e^{11} + \frac{1021}{254}e^{9} - \frac{3484}{127}e^{7} + \frac{10259}{127}e^{5} - \frac{13177}{127}e^{3} + \frac{5886}{127}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{35}{254}e^{11} - \frac{675}{254}e^{9} + \frac{2218}{127}e^{7} - \frac{5999}{127}e^{5} + \frac{6229}{127}e^{3} - \frac{1241}{127}e$ |
| 19 | $[19, 19, w + 3]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $-\frac{11}{127}e^{11} + \frac{194}{127}e^{9} - \frac{1093}{127}e^{7} + \frac{2323}{127}e^{5} - \frac{2268}{127}e^{3} + \frac{1865}{127}e$ |
| 19 | $[19, 19, -w^{2} + 3w + 2]$ | $-\frac{39}{127}e^{11} + \frac{1595}{254}e^{9} - \frac{5734}{127}e^{7} + \frac{17738}{127}e^{5} - \frac{22623}{127}e^{3} + \frac{8448}{127}e$ |
| 23 | $[23, 23, w^{2} - w - 3]$ | $-\frac{55}{254}e^{11} + \frac{1097}{254}e^{9} - \frac{3812}{127}e^{7} + \frac{11332}{127}e^{5} - \frac{13925}{127}e^{3} + \frac{4726}{127}e$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{41}{127}e^{11} - \frac{1527}{254}e^{9} + \frac{4732}{127}e^{7} - \frac{11591}{127}e^{5} + \frac{10243}{127}e^{3} - \frac{1652}{127}e$ |
| 23 | $[23, 23, -w + 4]$ | $-\frac{11}{127}e^{10} + \frac{194}{127}e^{8} - \frac{1093}{127}e^{6} + \frac{2196}{127}e^{4} - \frac{871}{127}e^{2} - \frac{802}{127}$ |
| 31 | $[31, 31, w^{2} - 5]$ | $-\frac{25}{127}e^{10} + \frac{464}{127}e^{8} - \frac{2842}{127}e^{6} + \frac{6665}{127}e^{4} - \frac{5016}{127}e^{2} + \frac{648}{127}$ |
| 43 | $[43, 43, w^{2} - 3w - 3]$ | $-\frac{9}{127}e^{11} + \frac{329}{254}e^{9} - \frac{952}{127}e^{7} + \frac{1739}{127}e^{5} + \frac{592}{127}e^{3} - \frac{2515}{127}e$ |
| 49 | $[49, 7, w^{2} - 6]$ | $-\frac{44}{127}e^{10} + \frac{776}{127}e^{8} - \frac{4372}{127}e^{6} + \frac{9038}{127}e^{4} - \frac{6024}{127}e^{2} + \frac{856}{127}$ |
| 53 | $[53, 53, 2w - 5]$ | $-\frac{11}{254}e^{10} + \frac{97}{127}e^{8} - \frac{483}{127}e^{6} + \frac{336}{127}e^{4} + \frac{1406}{127}e^{2} - \frac{20}{127}$ |
| 61 | $[61, 61, 2w^{2} - 2w - 9]$ | $-\frac{157}{254}e^{11} + \frac{1523}{127}e^{9} - \frac{10138}{127}e^{7} + \frac{28256}{127}e^{5} - \frac{31991}{127}e^{3} + \frac{10752}{127}e$ |
| 71 | $[71, 71, 2w - 3]$ | $-\frac{27}{254}e^{10} + \frac{215}{127}e^{8} - \frac{920}{127}e^{6} + \frac{386}{127}e^{4} + \frac{2412}{127}e^{2} - \frac{788}{127}$ |
| 73 | $[73, 73, 2w^{2} - 5w - 5]$ | $\phantom{-}\frac{87}{254}e^{11} - \frac{848}{127}e^{9} + \frac{5702}{127}e^{7} - \frac{16258}{127}e^{5} + \frac{19279}{127}e^{3} - \frac{6619}{127}e$ |
| 83 | $[83, 83, w^{2} - w - 9]$ | $-\frac{34}{127}e^{10} + \frac{565}{127}e^{8} - \frac{2778}{127}e^{6} + \frac{3832}{127}e^{4} + \frac{402}{127}e^{2} - \frac{724}{127}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w + 3]$ | $-1$ |