Base field 6.6.1202933.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 6x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[35, 35, 2w^{5} - 11w^{3} - 4w^{2} + 7w + 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 42x^{3} - 24x^{2} + 288x + 324\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $-1$ |
| 7 | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $-1$ |
| 19 | $[19, 19, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 4w]$ | $\phantom{-}e$ |
| 23 | $[23, 23, -w^{2} + w + 2]$ | $-\frac{1}{18}e^{4} - \frac{1}{9}e^{3} + \frac{7}{3}e^{2} + \frac{1}{3}e - 13$ |
| 25 | $[25, 5, w^{5} + w^{4} - 6w^{3} - 7w^{2} + 4w + 2]$ | $\phantom{-}e + 2$ |
| 41 | $[41, 41, 2w^{5} - w^{4} - 10w^{3} + 6w - 1]$ | $\phantom{-}\frac{1}{18}e^{4} + \frac{4}{9}e^{3} - \frac{2}{3}e^{2} - \frac{25}{3}e - 5$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{1}{9}e^{3} - \frac{16}{3}e^{2} + \frac{25}{3}e + 32$ |
| 53 | $[53, 53, w^{5} - 5w^{3} - 3w^{2} + w + 3]$ | $-e - 4$ |
| 59 | $[59, 59, 2w^{5} - 11w^{3} - 4w^{2} + 8w]$ | $-\frac{1}{3}e^{3} - \frac{5}{3}e^{2} + 8e + 24$ |
| 61 | $[61, 61, w^{2} - 2w - 2]$ | $\phantom{-}e + 4$ |
| 64 | $[64, 2, -2]$ | $-\frac{1}{18}e^{4} + \frac{2}{9}e^{3} + 3e^{2} - \frac{26}{3}e - 17$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + w - 3]$ | $\phantom{-}\frac{1}{18}e^{4} - \frac{2}{9}e^{3} - 3e^{2} + \frac{29}{3}e + 15$ |
| 67 | $[67, 67, -2w^{4} + w^{3} + 10w^{2} - 6]$ | $-\frac{1}{9}e^{4} - \frac{2}{9}e^{3} + \frac{11}{3}e^{2} - \frac{1}{3}e - 12$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e^{2} - 7e - 20$ |
| 73 | $[73, 73, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 2]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e^{2} - 8e - 15$ |
| 79 | $[79, 79, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 5w - 1]$ | $-\frac{1}{9}e^{4} + \frac{1}{9}e^{3} + \frac{16}{3}e^{2} - \frac{31}{3}e - 27$ |
| 83 | $[83, 83, 2w^{5} - 11w^{3} - 4w^{2} + 6w]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{1}{9}e^{3} - \frac{16}{3}e^{2} + \frac{28}{3}e + 28$ |
| 89 | $[89, 89, -2w^{5} + 11w^{3} + 4w^{2} - 7w - 2]$ | $-\frac{1}{9}e^{4} - \frac{2}{9}e^{3} + \frac{11}{3}e^{2} - \frac{4}{3}e - 5$ |
| 97 | $[97, 97, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{1}{9}e^{3} - \frac{16}{3}e^{2} + \frac{28}{3}e + 26$ |
| 97 | $[97, 97, w^{5} - w^{4} - 6w^{3} + 3w^{2} + 7w - 1]$ | $\phantom{-}\frac{1}{9}e^{4} - \frac{1}{9}e^{3} - \frac{16}{3}e^{2} + \frac{28}{3}e + 30$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w^{4} + w^{3} + 4w^{2} - 2w - 1]$ | $1$ |
| $7$ | $[7, 7, w^{5} - w^{4} - 5w^{3} + 3w^{2} + 4w - 3]$ | $1$ |