Base field 6.6.810448.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[25, 5, w^{4} - 2w^{3} - 2w^{2} + 3w + 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 3x^{6} - 18x^{5} + 50x^{4} + 89x^{3} - 191x^{2} - 164x + 128\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}e$ |
| 25 | $[25, 5, w^{4} - 2w^{3} - 2w^{2} + 3w + 1]$ | $-1$ |
| 25 | $[25, 5, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - 2w + 2]$ | $\phantom{-}\frac{3}{26}e^{6} - \frac{4}{13}e^{5} - \frac{24}{13}e^{4} + \frac{54}{13}e^{3} + \frac{173}{26}e^{2} - \frac{106}{13}e - \frac{82}{13}$ |
| 25 | $[25, 5, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $\phantom{-}\frac{3}{26}e^{6} - \frac{4}{13}e^{5} - \frac{24}{13}e^{4} + \frac{54}{13}e^{3} + \frac{173}{26}e^{2} - \frac{106}{13}e - \frac{82}{13}$ |
| 27 | $[27, 3, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{1}{26}e^{6} + \frac{7}{26}e^{5} + \frac{3}{26}e^{4} - \frac{101}{26}e^{3} + \frac{60}{13}e^{2} + \frac{122}{13}e - \frac{120}{13}$ |
| 27 | $[27, 3, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 6w - 4]$ | $-\frac{1}{26}e^{6} + \frac{7}{26}e^{5} + \frac{3}{26}e^{4} - \frac{101}{26}e^{3} + \frac{60}{13}e^{2} + \frac{122}{13}e - \frac{120}{13}$ |
| 37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 3w + 2]$ | $\phantom{-}\frac{2}{13}e^{6} - \frac{1}{13}e^{5} - \frac{32}{13}e^{4} + \frac{7}{13}e^{3} + \frac{98}{13}e^{2} + \frac{58}{13}e + \frac{38}{13}$ |
| 37 | $[37, 37, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 5w + 5]$ | $-\frac{6}{13}e^{6} + \frac{3}{13}e^{5} + \frac{109}{13}e^{4} - \frac{21}{13}e^{3} - \frac{463}{13}e^{2} - \frac{148}{13}e + \frac{198}{13}$ |
| 37 | $[37, 37, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} - 2]$ | $\phantom{-}\frac{2}{13}e^{6} - \frac{1}{13}e^{5} - \frac{32}{13}e^{4} + \frac{7}{13}e^{3} + \frac{98}{13}e^{2} + \frac{58}{13}e + \frac{38}{13}$ |
| 67 | $[67, 67, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 2]$ | $\phantom{-}\frac{3}{26}e^{6} - \frac{4}{13}e^{5} - \frac{24}{13}e^{4} + \frac{54}{13}e^{3} + \frac{121}{26}e^{2} - \frac{106}{13}e + \frac{100}{13}$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 7w - 5]$ | $\phantom{-}\frac{2}{13}e^{6} - \frac{1}{13}e^{5} - \frac{32}{13}e^{4} + \frac{7}{13}e^{3} + \frac{124}{13}e^{2} + \frac{32}{13}e - \frac{92}{13}$ |
| 67 | $[67, 67, -2w^{5} + 6w^{4} + 4w^{3} - 16w^{2} - 3w + 5]$ | $\phantom{-}\frac{1}{13}e^{6} + \frac{6}{13}e^{5} - \frac{29}{13}e^{4} - \frac{107}{13}e^{3} + \frac{205}{13}e^{2} + \frac{406}{13}e - \frac{124}{13}$ |
| 67 | $[67, 67, -2w^{5} + 4w^{4} + 8w^{3} - 12w^{2} - 9w + 6]$ | $\phantom{-}\frac{1}{13}e^{6} + \frac{6}{13}e^{5} - \frac{29}{13}e^{4} - \frac{107}{13}e^{3} + \frac{205}{13}e^{2} + \frac{406}{13}e - \frac{124}{13}$ |
| 67 | $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 6w + 4]$ | $\phantom{-}\frac{2}{13}e^{6} - \frac{1}{13}e^{5} - \frac{32}{13}e^{4} + \frac{7}{13}e^{3} + \frac{124}{13}e^{2} + \frac{32}{13}e - \frac{92}{13}$ |
| 67 | $[67, 67, w^{5} - 4w^{4} + 10w^{2} - 2w - 3]$ | $\phantom{-}\frac{3}{26}e^{6} - \frac{4}{13}e^{5} - \frac{24}{13}e^{4} + \frac{54}{13}e^{3} + \frac{121}{26}e^{2} - \frac{106}{13}e + \frac{100}{13}$ |
| 107 | $[107, 107, w^{5} - 3w^{4} - w^{3} + 7w^{2} - 3w - 2]$ | $\phantom{-}\frac{9}{26}e^{6} + \frac{1}{13}e^{5} - \frac{85}{13}e^{4} - \frac{33}{13}e^{3} + \frac{805}{26}e^{2} + \frac{254}{13}e - \frac{220}{13}$ |
| 107 | $[107, 107, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 5]$ | $-\frac{4}{13}e^{6} + \frac{2}{13}e^{5} + \frac{64}{13}e^{4} - \frac{14}{13}e^{3} - \frac{222}{13}e^{2} - \frac{90}{13}e + \frac{132}{13}$ |
| 107 | $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 13w^{2} + 6w - 4]$ | $-\frac{3}{13}e^{6} - \frac{5}{13}e^{5} + \frac{61}{13}e^{4} + \frac{100}{13}e^{3} - \frac{303}{13}e^{2} - \frac{464}{13}e + \frac{164}{13}$ |
| 107 | $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 15w^{2} + 4w - 6]$ | $-\frac{3}{13}e^{6} - \frac{5}{13}e^{5} + \frac{61}{13}e^{4} + \frac{100}{13}e^{3} - \frac{303}{13}e^{2} - \frac{464}{13}e + \frac{164}{13}$ |
| 107 | $[107, 107, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $-\frac{4}{13}e^{6} + \frac{2}{13}e^{5} + \frac{64}{13}e^{4} - \frac{14}{13}e^{3} - \frac{222}{13}e^{2} - \frac{90}{13}e + \frac{132}{13}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, w^{4} - 2w^{3} - 2w^{2} + 3w + 1]$ | $1$ |