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: | $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 31x^{8} + 340x^{6} - 1568x^{4} + 2880x^{2} - 1728\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{5} + 2w^{4} + 4w^{3} - 5w^{2} - 5w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{5} + 3w^{4} + 3w^{3} - 10w^{2} - 3w + 5]$ | $\phantom{-}\frac{1}{36}e^{9} - \frac{53}{72}e^{7} + \frac{473}{72}e^{5} - \frac{397}{18}e^{3} + 20e$ |
| 25 | $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ | $-1$ |
| 37 | $[37, 37, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{1}{72}e^{9} - \frac{11}{36}e^{7} + \frac{133}{72}e^{5} - \frac{23}{18}e^{3} - 8e$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{1}{72}e^{9} - \frac{11}{36}e^{7} + \frac{133}{72}e^{5} - \frac{23}{18}e^{3} - 8e$ |
| 49 | $[49, 7, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 3]$ | $-\frac{1}{8}e^{7} + \frac{19}{8}e^{5} - 12e^{3} + 12e$ |
| 49 | $[49, 7, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 4]$ | $-\frac{1}{8}e^{7} + \frac{19}{8}e^{5} - 12e^{3} + 12e$ |
| 53 | $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 3w + 1]$ | $-\frac{5}{144}e^{9} + \frac{155}{144}e^{7} - \frac{407}{36}e^{5} + \frac{809}{18}e^{3} - 49e$ |
| 53 | $[53, 53, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $-\frac{5}{144}e^{9} + \frac{155}{144}e^{7} - \frac{407}{36}e^{5} + \frac{809}{18}e^{3} - 49e$ |
| 61 | $[61, 61, -3w^{5} + 6w^{4} + 12w^{3} - 16w^{2} - 12w + 5]$ | $-\frac{1}{4}e^{6} + \frac{19}{4}e^{4} - 24e^{2} + 22$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 7w^{3} + 16w^{2} + 7w - 7]$ | $-\frac{5}{144}e^{9} + \frac{173}{144}e^{7} - \frac{949}{72}e^{5} + \frac{454}{9}e^{3} - 51e$ |
| 61 | $[61, 61, -2w^{5} + 5w^{4} + 7w^{3} - 15w^{2} - 8w + 6]$ | $-\frac{5}{144}e^{9} + \frac{173}{144}e^{7} - \frac{949}{72}e^{5} + \frac{454}{9}e^{3} - 51e$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 3]$ | $-\frac{1}{4}e^{6} + \frac{19}{4}e^{4} - 24e^{2} + 22$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{1}{24}e^{8} - \frac{37}{24}e^{6} + \frac{215}{12}e^{4} - \frac{217}{3}e^{2} + 79$ |
| 67 | $[67, 67, w^{5} - 3w^{4} - 3w^{3} + 10w^{2} + 2w - 3]$ | $-\frac{1}{144}e^{9} + \frac{31}{144}e^{7} - \frac{85}{36}e^{5} + \frac{89}{9}e^{3} - 6e$ |
| 67 | $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 5]$ | $-\frac{1}{144}e^{9} + \frac{31}{144}e^{7} - \frac{85}{36}e^{5} + \frac{89}{9}e^{3} - 6e$ |
| 71 | $[71, 71, w^{5} - 2w^{4} - 4w^{3} + 7w^{2} + 2w - 4]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{19}{4}e^{4} + 22e^{2} - 12$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{19}{4}e^{4} + 22e^{2} - 12$ |
| 81 | $[81, 3, -w^{4} + 2w^{3} + 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{1}{12}e^{8} - \frac{19}{12}e^{6} + \frac{28}{3}e^{4} - \frac{77}{3}e^{2} + 38$ |
| 101 | $[101, 101, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 3]$ | $-\frac{1}{36}e^{9} + \frac{53}{72}e^{7} - \frac{509}{72}e^{5} + \frac{266}{9}e^{3} - 43e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, -w^{3} + 2w^{2} + 2w - 3]$ | $1$ |