Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 24x^{10} + 212x^{8} - 858x^{6} + 1553x^{4} - 973x^{2} + 162\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}\frac{2}{73}e^{10} - \frac{31}{73}e^{8} + \frac{124}{73}e^{6} - \frac{78}{73}e^{4} - \frac{112}{73}e^{2} - \frac{124}{73}$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $-\frac{128}{657}e^{11} + \frac{856}{219}e^{9} - \frac{17353}{657}e^{7} + \frac{15899}{219}e^{5} - \frac{48385}{657}e^{3} + \frac{14798}{657}e$ |
| 7 | $[7, 7, -w^{2} + 11]$ | $-\frac{2}{73}e^{10} + \frac{31}{73}e^{8} - \frac{124}{73}e^{6} + \frac{78}{73}e^{4} + \frac{185}{73}e^{2} - \frac{168}{73}$ |
| 7 | $[7, 7, -w^{2} + 9]$ | $-\frac{128}{657}e^{11} + \frac{856}{219}e^{9} - \frac{17353}{657}e^{7} + \frac{15899}{219}e^{5} - \frac{48385}{657}e^{3} + \frac{14798}{657}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w]$ | $-\frac{100}{657}e^{11} + \frac{614}{219}e^{9} - \frac{10580}{657}e^{7} + \frac{6775}{219}e^{5} - \frac{2795}{657}e^{3} - \frac{7451}{657}e$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $-\frac{232}{657}e^{11} + \frac{1442}{219}e^{9} - \frac{25334}{657}e^{7} + \frac{16813}{219}e^{5} - \frac{12923}{657}e^{3} - \frac{3647}{657}e$ |
| 23 | $[23, 23, w^{2} + w - 10]$ | $\phantom{-}\frac{24}{73}e^{10} - \frac{445}{73}e^{8} + \frac{2583}{73}e^{6} - \frac{5097}{73}e^{4} + \frac{1430}{73}e^{2} + \frac{264}{73}$ |
| 29 | $[29, 29, 2w^{2} - 21]$ | $-\frac{76}{219}e^{11} + \frac{490}{73}e^{9} - \frac{9311}{219}e^{7} + \frac{7558}{73}e^{5} - \frac{17060}{219}e^{3} + \frac{2887}{219}e$ |
| 37 | $[37, 37, 2w^{2} + w - 17]$ | $-\frac{64}{657}e^{11} + \frac{428}{219}e^{9} - \frac{8348}{657}e^{7} + \frac{6307}{219}e^{5} - \frac{4811}{657}e^{3} - \frac{10997}{657}e$ |
| 43 | $[43, 43, 3w^{2} + 3w - 22]$ | $-\frac{128}{657}e^{11} + \frac{856}{219}e^{9} - \frac{17353}{657}e^{7} + \frac{15899}{219}e^{5} - \frac{47728}{657}e^{3} + \frac{10199}{657}e$ |
| 47 | $[47, 47, w^{2} - 6]$ | $\phantom{-}\frac{47}{73}e^{11} - \frac{911}{73}e^{9} + \frac{5761}{73}e^{7} - \frac{13732}{73}e^{5} + \frac{9048}{73}e^{3} - \frac{432}{73}e$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{17}{219}e^{11} + \frac{100}{73}e^{9} - \frac{1492}{219}e^{7} + \frac{367}{73}e^{5} + \frac{5624}{219}e^{3} - \frac{3034}{219}e$ |
| 47 | $[47, 47, -w^{2} + 12]$ | $-\frac{27}{73}e^{10} + \frac{528}{73}e^{8} - \frac{3353}{73}e^{6} + \frac{7842}{73}e^{4} - \frac{4839}{73}e^{2} + \frac{1236}{73}$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-\frac{82}{219}e^{11} + \frac{521}{73}e^{9} - \frac{9683}{219}e^{7} + \frac{7636}{73}e^{5} - \frac{16505}{219}e^{3} + \frac{1945}{219}e$ |
| 61 | $[61, 61, w^{2} - 5]$ | $\phantom{-}\frac{167}{657}e^{11} - \frac{1021}{219}e^{9} + \frac{17143}{657}e^{7} - \frac{9617}{219}e^{5} - \frac{6797}{657}e^{3} + \frac{4027}{657}e$ |
| 67 | $[67, 67, w^{2} - w - 7]$ | $\phantom{-}\frac{139}{657}e^{11} - \frac{779}{219}e^{9} + \frac{10370}{657}e^{7} - \frac{493}{219}e^{5} - \frac{52387}{657}e^{3} + \frac{28247}{657}e$ |
| 73 | $[73, 73, 7w^{2} + 3w - 66]$ | $\phantom{-}\frac{39}{73}e^{10} - \frac{714}{73}e^{8} + \frac{4097}{73}e^{6} - \frac{8237}{73}e^{4} + \frac{3291}{73}e^{2} + \frac{502}{73}$ |
| 79 | $[79, 79, 2w^{2} - 19]$ | $\phantom{-}\frac{344}{657}e^{11} - \frac{2191}{219}e^{9} + \frac{40600}{657}e^{7} - \frac{31190}{219}e^{5} + \frac{61255}{657}e^{3} - \frac{13736}{657}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $8$ | $[8, 2, 2]$ | $-1$ |