Base field 4.4.19821.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 8x^{2} + 6x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 13x^{4} - 2x^{3} + 42x^{2} + 16x - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ | $-1$ |
| 9 | $[9, 3, w + 1]$ | $-e + 2$ |
| 13 | $[13, 13, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 5w]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{4}e^{4} - 3e^{3} - \frac{3}{2}e^{2} + 9e + 1$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{3}{4}e^{4} - 3e^{3} + \frac{11}{2}e^{2} + 9e - 2$ |
| 17 | $[17, 17, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 3w + 5]$ | $-e^{3} + 7e$ |
| 19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 5]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + 6e^{3} - 3e^{2} - 17e - 2$ |
| 23 | $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 2]$ | $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + 2e^{3} + \frac{7}{2}e^{2} - 2e - 9$ |
| 25 | $[25, 5, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w]$ | $\phantom{-}e^{4} + e^{3} - 8e^{2} - 6e + 4$ |
| 25 | $[25, 5, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 3]$ | $-\frac{3}{4}e^{5} + \frac{1}{4}e^{4} + 7e^{3} - \frac{5}{2}e^{2} - 11e + 5$ |
| 29 | $[29, 29, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 4w - 3]$ | $\phantom{-}e^{2} - 6$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w]$ | $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + 3e^{3} + \frac{3}{2}e^{2} - 7e + 3$ |
| 37 | $[37, 37, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{3}{4}e^{4} - 4e^{3} + \frac{9}{2}e^{2} + 14e + 5$ |
| 41 | $[41, 41, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + 5w - 4]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{4}e^{4} - 4e^{3} - \frac{3}{2}e^{2} + 15e + 3$ |
| 43 | $[43, 43, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w]$ | $-\frac{1}{4}e^{5} + \frac{3}{4}e^{4} + 3e^{3} - \frac{13}{2}e^{2} - 7e + 5$ |
| 47 | $[47, 47, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w]$ | $\phantom{-}e^{3} - 6e - 6$ |
| 59 | $[59, 59, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 4]$ | $-\frac{1}{4}e^{5} - \frac{1}{4}e^{4} + 3e^{3} + \frac{7}{2}e^{2} - 9e - 3$ |
| 59 | $[59, 59, \frac{4}{3}w^{3} - \frac{5}{3}w^{2} - 10w + 9]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{1}{4}e^{4} - e^{3} + \frac{1}{2}e^{2} - 7e - 9$ |
| 67 | $[67, 67, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w]$ | $\phantom{-}\frac{1}{4}e^{5} + \frac{5}{4}e^{4} - e^{3} - \frac{21}{2}e^{2} - 5e + 11$ |
| 71 | $[71, 71, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{1}{2}e^{4} - 5e^{3} + 5e^{2} + 10e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - 2w + 2]$ | $1$ |