Base field 4.4.1957.1
Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} - x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[61, 61, -w^{3} + w^{2} + w - 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 2x^{5} - 15x^{4} + 26x^{3} + 58x^{2} - 72x - 47\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 3w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{1}{6}e^{5} - 2e^{3} - \frac{2}{3}e^{2} + \frac{29}{6}e + \frac{19}{6}$ |
| 16 | $[16, 2, 2]$ | $-\frac{1}{6}e^{5} - \frac{1}{2}e^{4} + \frac{5}{2}e^{3} + \frac{17}{3}e^{2} - \frac{25}{3}e - \frac{61}{6}$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w]$ | $\phantom{-}\frac{1}{3}e^{5} - 5e^{3} - \frac{1}{3}e^{2} + \frac{47}{3}e + \frac{10}{3}$ |
| 23 | $[23, 23, w^{3} + w^{2} - 4w - 2]$ | $-e^{2} + e + 5$ |
| 27 | $[27, 3, -2w^{3} + w^{2} + 6w - 1]$ | $-e^{3} + 7e + 2$ |
| 31 | $[31, 31, -w^{3} + 5w]$ | $-\frac{1}{3}e^{5} + \frac{9}{2}e^{3} - \frac{1}{6}e^{2} - \frac{41}{3}e + \frac{19}{6}$ |
| 37 | $[37, 37, -w^{3} + 5w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - 6e + \frac{15}{2}$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $-\frac{1}{3}e^{5} + \frac{1}{2}e^{4} + 4e^{3} - \frac{31}{6}e^{2} - \frac{49}{6}e + \frac{49}{6}$ |
| 43 | $[43, 43, -w^{2} + 2w + 3]$ | $-\frac{1}{3}e^{5} + 5e^{3} + \frac{1}{3}e^{2} - \frac{47}{3}e - \frac{4}{3}$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 2w + 2]$ | $-\frac{1}{3}e^{5} + 4e^{3} + \frac{4}{3}e^{2} - \frac{29}{3}e - \frac{13}{3}$ |
| 47 | $[47, 47, 3w^{3} - w^{2} - 10w - 2]$ | $-\frac{1}{2}e^{4} + \frac{9}{2}e^{2} + \frac{1}{2}e - \frac{13}{2}$ |
| 53 | $[53, 53, -w^{3} + w^{2} + 2w - 3]$ | $-\frac{1}{3}e^{5} + \frac{1}{2}e^{4} + 5e^{3} - \frac{25}{6}e^{2} - \frac{97}{6}e + \frac{7}{6}$ |
| 59 | $[59, 59, -2w^{3} + w^{2} + 8w + 1]$ | $-\frac{1}{3}e^{5} + 5e^{3} + \frac{7}{3}e^{2} - \frac{53}{3}e - \frac{28}{3}$ |
| 59 | $[59, 59, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}e^{3} - e^{2} - 6e + 5$ |
| 61 | $[61, 61, -w^{3} + w^{2} + w - 2]$ | $-1$ |
| 67 | $[67, 67, 2w^{3} - 5w - 2]$ | $\phantom{-}\frac{1}{6}e^{5} - 2e^{3} - \frac{2}{3}e^{2} + \frac{29}{6}e + \frac{7}{6}$ |
| 71 | $[71, 71, 2w^{2} - w - 3]$ | $\phantom{-}\frac{1}{3}e^{5} - \frac{1}{2}e^{4} - 4e^{3} + \frac{31}{6}e^{2} + \frac{37}{6}e - \frac{49}{6}$ |
| 73 | $[73, 73, 2w^{2} - w - 5]$ | $\phantom{-}\frac{1}{3}e^{5} - 4e^{3} - \frac{4}{3}e^{2} + \frac{29}{3}e + \frac{7}{3}$ |
| 73 | $[73, 73, w^{3} - 2w^{2} - 2w + 5]$ | $\phantom{-}e^{4} - e^{3} - 10e^{2} + 7e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $61$ | $[61, 61, -w^{3} + w^{2} + w - 2]$ | $1$ |