Base field 4.4.9909.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{3} + w^{2} + 3w - 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 15x^{4} - 2x^{3} + 45x^{2} + 38x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{15}{2}e^{3} + \frac{45}{2}e + 10$ |
| 7 | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $-\frac{1}{2}e^{5} + \frac{15}{2}e^{3} - \frac{45}{2}e - 10$ |
| 11 | $[11, 11, -w^{2} + w + 2]$ | $\phantom{-}\frac{3}{2}e^{5} - e^{4} - \frac{45}{2}e^{3} + 10e^{2} + \frac{133}{2}e + 26$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 3w - 1]$ | $-1$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}2e^{5} - e^{4} - 29e^{3} + 11e^{2} + 80e + 33$ |
| 17 | $[17, 17, -w^{3} + 5w + 2]$ | $\phantom{-}\frac{3}{2}e^{5} - e^{4} - \frac{43}{2}e^{3} + 12e^{2} + \frac{113}{2}e + 18$ |
| 29 | $[29, 29, -w^{2} + w + 1]$ | $\phantom{-}e^{2} + 2e - 8$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ | $-\frac{1}{2}e^{5} + e^{4} + \frac{15}{2}e^{3} - 10e^{2} - \frac{39}{2}e - 4$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w + 1]$ | $\phantom{-}\frac{3}{2}e^{5} - e^{4} - \frac{41}{2}e^{3} + 12e^{2} + \frac{95}{2}e + 14$ |
| 41 | $[41, 41, w^{2} - 5]$ | $-\frac{3}{2}e^{5} + e^{4} + \frac{41}{2}e^{3} - 12e^{2} - \frac{95}{2}e - 14$ |
| 47 | $[47, 47, w^{3} - w^{2} - 5w - 2]$ | $-\frac{1}{2}e^{5} + \frac{15}{2}e^{3} - \frac{49}{2}e - 18$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ | $-\frac{1}{2}e^{5} + e^{4} + \frac{15}{2}e^{3} - 12e^{2} - \frac{37}{2}e + 6$ |
| 53 | $[53, 53, w^{3} - 4w - 4]$ | $-2e^{3} - 2e^{2} + 19e + 12$ |
| 53 | $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ | $\phantom{-}e^{3} - 7e + 4$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $-e^{5} + 14e^{3} - 38e - 22$ |
| 71 | $[71, 71, w^{3} - w^{2} - 6w - 2]$ | $-e^{5} + 15e^{3} - 45e - 20$ |
| 103 | $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ | $\phantom{-}e^{5} - 16e^{3} - 2e^{2} + 54e + 32$ |
| 103 | $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ | $\phantom{-}2e^{5} - e^{4} - 28e^{3} + 12e^{2} + 70e + 24$ |
| 109 | $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ | $-4e^{5} + 2e^{4} + 56e^{3} - 24e^{2} - 144e - 50$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{3} + w^{2} + 3w - 1]$ | $1$ |