Base field 6.6.1387029.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - x^{2} - 4x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[21, 21, 2w^{5} - 5w^{4} - 6w^{3} + 14w^{2} + 3w - 4]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} - 6x^{5} - 81x^{4} + 404x^{3} + 444x^{2} - 2016x - 2144\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{5} + 2w^{4} + 4w^{3} - 5w^{2} - 5w + 1]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ | $\phantom{-}1$ |
| 25 | $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ | $\phantom{-}2$ |
| 37 | $[37, 37, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{3}{136}e^{5} - \frac{11}{102}e^{4} - \frac{725}{408}e^{3} + \frac{439}{68}e^{2} + \frac{637}{102}e - \frac{607}{51}$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}e$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 3]$ | $\phantom{-}\frac{5}{918}e^{5} - \frac{16}{459}e^{4} - \frac{331}{918}e^{3} + \frac{1015}{459}e^{2} - \frac{1591}{459}e - \frac{1160}{459}$ |
| 49 | $[49, 7, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 4]$ | $-\frac{5}{918}e^{5} + \frac{16}{459}e^{4} + \frac{331}{918}e^{3} - \frac{1015}{459}e^{2} + \frac{1591}{459}e + \frac{2996}{459}$ |
| 53 | $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $-\frac{11}{3672}e^{5} - \frac{13}{918}e^{4} + \frac{1279}{3672}e^{3} + \frac{2357}{1836}e^{2} - \frac{5395}{918}e - \frac{739}{459}$ |
| 53 | $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}\frac{1}{1836}e^{5} - \frac{95}{918}e^{4} + \frac{607}{1836}e^{3} + \frac{4003}{459}e^{2} - \frac{8926}{459}e - \frac{20924}{459}$ |
| 61 | $[61, 61, -3w^{5} + 6w^{4} + 12w^{3} - 16w^{2} - 12w + 5]$ | $\phantom{-}\frac{101}{3672}e^{5} - \frac{131}{918}e^{4} - \frac{7849}{3672}e^{3} + \frac{15913}{1836}e^{2} + \frac{2551}{918}e - \frac{7541}{459}$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 7w^{3} + 16w^{2} + 7w - 7]$ | $\phantom{-}\frac{10}{459}e^{5} - \frac{103}{1836}e^{4} - \frac{1783}{918}e^{3} + \frac{3847}{1836}e^{2} + \frac{7100}{459}e + \frac{4081}{459}$ |
| 61 | $[61, 61, -2w^{5} + 5w^{4} + 7w^{3} - 15w^{2} - 8w + 6]$ | $-\frac{35}{3672}e^{5} + \frac{28}{459}e^{4} + \frac{2623}{3672}e^{3} - \frac{7105}{1836}e^{2} + \frac{749}{918}e + \frac{2183}{459}$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 3]$ | $-\frac{5}{918}e^{5} + \frac{16}{459}e^{4} + \frac{331}{918}e^{3} - \frac{1015}{459}e^{2} + \frac{2050}{459}e + \frac{2078}{459}$ |
| 64 | $[64, 2, -2]$ | $-\frac{5}{408}e^{5} - \frac{1}{204}e^{4} + \frac{167}{136}e^{3} + \frac{181}{102}e^{2} - \frac{1661}{102}e - \frac{283}{17}$ |
| 67 | $[67, 67, w^{5} - 3w^{4} - 3w^{3} + 10w^{2} + 2w - 3]$ | $-\frac{10}{459}e^{5} + \frac{103}{1836}e^{4} + \frac{1783}{918}e^{3} - \frac{3847}{1836}e^{2} - \frac{6641}{459}e - \frac{5917}{459}$ |
| 67 | $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 5]$ | $\phantom{-}\frac{29}{918}e^{5} - \frac{155}{918}e^{4} - \frac{2287}{918}e^{3} + \frac{9479}{918}e^{2} + \frac{2492}{459}e - \frac{9482}{459}$ |
| 71 | $[71, 71, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 2w - 4]$ | $-\frac{23}{1836}e^{5} + \frac{43}{918}e^{4} + \frac{1951}{1836}e^{3} - \frac{1187}{459}e^{2} - \frac{2323}{459}e + \frac{3280}{459}$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ | $\phantom{-}\frac{41}{1836}e^{5} - \frac{293}{1836}e^{4} - \frac{2959}{1836}e^{3} + \frac{19859}{1836}e^{2} - \frac{1826}{459}e - \frac{15007}{459}$ |
| 81 | $[81, 3, -w^{4} + 2w^{3} + 2w^{2} - 3w + 2]$ | $-\frac{1}{102}e^{5} + \frac{23}{204}e^{4} + \frac{28}{51}e^{3} - \frac{1679}{204}e^{2} + \frac{461}{51}e + \frac{1813}{51}$ |
| 101 | $[101, 101, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 3]$ | $-\frac{10}{459}e^{5} + \frac{103}{1836}e^{4} + \frac{1783}{918}e^{3} - \frac{3847}{1836}e^{2} - \frac{8018}{459}e - \frac{4081}{459}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{5} + 2w^{4} + 4w^{3} - 5w^{2} - 5w + 1]$ | $-1$ |
| $7$ | $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ | $-1$ |