Base field 4.4.13448.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[20, 10, w^{3} - 6w - 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - x^{5} - 8x^{4} + 4x^{3} + 15x^{2} - 3x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w + 1]$ | $-1$ |
| 5 | $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{1}{2}e^{3} - \frac{5}{2}e^{2} + \frac{1}{2}e + 2$ |
| 5 | $[5, 5, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 10w - 4]$ | $-1$ |
| 25 | $[25, 5, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 4]$ | $-\frac{1}{2}e^{5} + \frac{1}{2}e^{4} + \frac{9}{2}e^{3} - \frac{5}{2}e^{2} - 10e + 2$ |
| 37 | $[37, 37, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w]$ | $\phantom{-}\frac{3}{2}e^{5} - \frac{5}{2}e^{4} - \frac{19}{2}e^{3} + \frac{21}{2}e^{2} + 10e - 6$ |
| 37 | $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w]$ | $-\frac{3}{2}e^{5} + e^{4} + 12e^{3} - 2e^{2} - \frac{35}{2}e + 2$ |
| 43 | $[43, 43, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 2]$ | $\phantom{-}\frac{1}{2}e^{5} - 2e^{4} - e^{3} + 9e^{2} - \frac{5}{2}e - 4$ |
| 43 | $[43, 43, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + 10w + 2]$ | $-e^{5} + \frac{5}{2}e^{4} + \frac{11}{2}e^{3} - \frac{21}{2}e^{2} - \frac{17}{2}e + 4$ |
| 49 | $[49, 7, -w^{2} - w + 3]$ | $\phantom{-}e^{4} - e^{3} - 7e^{2} + 5e + 8$ |
| 49 | $[49, 7, -w^{2} + w + 3]$ | $\phantom{-}\frac{1}{2}e^{5} + \frac{1}{2}e^{4} - \frac{11}{2}e^{3} - \frac{5}{2}e^{2} + 11e + 2$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 2]$ | $-e^{5} + e^{4} + 8e^{3} - 7e^{2} - 13e + 8$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 2]$ | $\phantom{-}\frac{1}{2}e^{5} - 3e^{3} - e^{2} + \frac{3}{2}e + 2$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 2]$ | $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + e^{2} + \frac{11}{2}e - 4$ |
| 61 | $[61, 61, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 8w - 4]$ | $\phantom{-}e^{5} - 3e^{4} - 5e^{3} + 13e^{2} + 4e - 2$ |
| 73 | $[73, 73, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 2w]$ | $-2e^{5} + 4e^{4} + 11e^{3} - 18e^{2} - 9e + 16$ |
| 73 | $[73, 73, w^{2} - w + 1]$ | $-2e^{5} + 18e^{3} + 2e^{2} - 32e$ |
| 73 | $[73, 73, w^{2} + w + 1]$ | $\phantom{-}2e^{4} - 2e^{3} - 12e^{2} + 2e + 10$ |
| 73 | $[73, 73, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 2w]$ | $-e^{4} - e^{3} + 9e^{2} + e - 10$ |
| 81 | $[81, 3, -3]$ | $-e^{5} + 3e^{4} + 3e^{3} - 15e^{2} + 2e + 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w + 1]$ | $1$ |
| $5$ | $[5, 5, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 10w - 4]$ | $1$ |