Base field 4.4.16357.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 9, w - 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 98x^{6} + 2825x^{4} - 20232x^{2} + 20736\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -w^{3} + 5w + 2]$ | $-\frac{1}{47520}e^{7} - \frac{19}{4752}e^{5} + \frac{2747}{9504}e^{3} - \frac{623}{220}e$ |
| 5 | $[5, 5, w - 1]$ | $-\frac{2}{495}e^{6} + \frac{23}{99}e^{4} - \frac{248}{99}e^{2} + \frac{346}{55}$ |
| 11 | $[11, 11, -w^{3} + 5w]$ | $-\frac{1}{47520}e^{7} - \frac{19}{4752}e^{5} + \frac{2747}{9504}e^{3} - \frac{843}{220}e$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 6w - 3]$ | $-\frac{13}{7920}e^{7} + \frac{83}{792}e^{5} - \frac{2437}{1584}e^{3} + \frac{1469}{330}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{990}e^{6} + \frac{23}{396}e^{4} - \frac{149}{396}e^{2} - \frac{271}{55}$ |
| 19 | $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ | $\phantom{-}\frac{7}{9504}e^{7} - \frac{127}{4752}e^{5} - \frac{2689}{9504}e^{3} + \frac{235}{132}e$ |
| 25 | $[25, 5, -w^{2} + w + 3]$ | $\phantom{-}0$ |
| 27 | $[27, 3, w^{3} - w^{2} - 5w + 4]$ | $-\frac{1}{23760}e^{7} - \frac{19}{2376}e^{5} + \frac{2747}{4752}e^{3} - \frac{623}{110}e$ |
| 31 | $[31, 31, -w - 3]$ | $\phantom{-}0$ |
| 37 | $[37, 37, -w^{3} - w^{2} + 6w + 4]$ | $\phantom{-}\frac{19}{11880}e^{7} - \frac{67}{594}e^{5} + \frac{5029}{2376}e^{3} - \frac{1999}{165}e$ |
| 41 | $[41, 41, w^{3} + w^{2} - 6w - 5]$ | $\phantom{-}\frac{1}{660}e^{7} - \frac{1}{22}e^{5} - \frac{151}{132}e^{3} + \frac{1522}{165}e$ |
| 43 | $[43, 43, w^{3} - 7w - 2]$ | $-\frac{4}{495}e^{6} + \frac{46}{99}e^{4} - \frac{496}{99}e^{2} + \frac{692}{55}$ |
| 47 | $[47, 47, -2w^{3} + 11w + 2]$ | $-\frac{31}{9504}e^{7} + \frac{1015}{4752}e^{5} - \frac{31991}{9504}e^{3} + \frac{1681}{132}e$ |
| 61 | $[61, 61, w^{2} - 3]$ | $-\frac{1}{660}e^{7} + \frac{1}{22}e^{5} + \frac{151}{132}e^{3} - \frac{1522}{165}e$ |
| 67 | $[67, 67, w^{2} + w - 4]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ | $\phantom{-}\frac{13}{15840}e^{7} - \frac{17}{1584}e^{5} - \frac{4559}{3168}e^{3} + \frac{8651}{660}e$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ | $\phantom{-}\frac{7}{396}e^{6} - \frac{353}{396}e^{4} + \frac{883}{198}e^{2} + \frac{162}{11}$ |
| 97 | $[97, 97, -w^{3} + 6w - 3]$ | $\phantom{-}\frac{31}{1980}e^{6} - \frac{307}{396}e^{4} + \frac{367}{99}e^{2} + \frac{268}{55}$ |
| 97 | $[97, 97, -3w^{3} + 16w]$ | $-\frac{17}{5280}e^{7} + \frac{39}{176}e^{5} - \frac{4165}{1056}e^{3} + \frac{13463}{660}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $1$ |