Base field \(\Q(\sqrt{70}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6, 6, -w - 8]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $48$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + x^{5} - 8x^{4} - 5x^{3} + 15x^{2} + 6x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -3w + 25]$ | $-e^{3} - e^{2} + 4e + 3$ |
| 7 | $[7, 7, w]$ | $\phantom{-}\frac{2}{3}e^{5} + \frac{1}{3}e^{4} - 5e^{3} - \frac{1}{3}e^{2} + \frac{26}{3}e - \frac{1}{3}$ |
| 11 | $[11, 11, w - 9]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - 3e^{3} - \frac{14}{3}e^{2} + \frac{22}{3}e + \frac{16}{3}$ |
| 11 | $[11, 11, -w - 9]$ | $-\frac{1}{3}e^{5} + \frac{1}{3}e^{4} + 3e^{3} - \frac{7}{3}e^{2} - \frac{16}{3}e + \frac{2}{3}$ |
| 17 | $[17, 17, w + 6]$ | $-e^{5} - 2e^{4} + 6e^{3} + 8e^{2} - 7e - 2$ |
| 17 | $[17, 17, w + 11]$ | $\phantom{-}\frac{2}{3}e^{5} + \frac{1}{3}e^{4} - 5e^{3} + \frac{2}{3}e^{2} + \frac{23}{3}e - \frac{7}{3}$ |
| 23 | $[23, 23, w + 1]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{3}e^{4} - 3e^{3} + \frac{1}{3}e^{2} + \frac{13}{3}e + \frac{13}{3}$ |
| 23 | $[23, 23, w + 22]$ | $-e^{5} + 9e^{3} - 15e - 4$ |
| 31 | $[31, 31, 4w - 33]$ | $\phantom{-}\frac{2}{3}e^{5} + \frac{7}{3}e^{4} - 2e^{3} - \frac{34}{3}e^{2} - \frac{7}{3}e + \frac{26}{3}$ |
| 31 | $[31, 31, 4w + 33]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - 2e^{3} - \frac{8}{3}e^{2} + \frac{16}{3}e + \frac{13}{3}$ |
| 37 | $[37, 37, w + 12]$ | $-\frac{8}{3}e^{5} - \frac{7}{3}e^{4} + 20e^{3} + \frac{28}{3}e^{2} - \frac{101}{3}e - \frac{17}{3}$ |
| 37 | $[37, 37, w + 25]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{4}{3}e^{4} - 5e^{3} + \frac{22}{3}e^{2} + \frac{31}{3}e - \frac{5}{3}$ |
| 53 | $[53, 53, w + 21]$ | $-\frac{1}{3}e^{5} - \frac{5}{3}e^{4} - e^{3} + \frac{20}{3}e^{2} + \frac{35}{3}e - \frac{13}{3}$ |
| 53 | $[53, 53, w + 32]$ | $-\frac{2}{3}e^{5} + \frac{2}{3}e^{4} + 7e^{3} - \frac{5}{3}e^{2} - \frac{41}{3}e - \frac{5}{3}$ |
| 61 | $[61, 61, -w - 3]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{8}{3}e^{4} + 3e^{3} - \frac{29}{3}e^{2} - \frac{47}{3}e + \frac{4}{3}$ |
| 61 | $[61, 61, w - 3]$ | $-e^{5} + e^{4} + 9e^{3} - 5e^{2} - 16e - 4$ |
| 73 | $[73, 73, w + 17]$ | $\phantom{-}\frac{10}{3}e^{5} + \frac{5}{3}e^{4} - 26e^{3} - \frac{11}{3}e^{2} + \frac{124}{3}e + \frac{7}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $3$ | $[3, 3, w + 2]$ | $-1$ |