Base field 4.4.14272.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 8x^{2} + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-\frac{1}{3}e^{3} + \frac{5}{3}e$ |
| 4 | $[4, 2, -w^{3} + 3w^{2} + w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{3} + 3w^{2} + 2w - 5]$ | $-e^{2} + 2$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e$ |
| 13 | $[13, 13, -w + 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{3} - 3w^{2} - 2w + 2]$ | $\phantom{-}e^{3} - 6e$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}e^{2} - 5$ |
| 19 | $[19, 19, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{10}{3}e$ |
| 23 | $[23, 23, w^{2} - 2w - 1]$ | $-\frac{2}{3}e^{3} + \frac{7}{3}e$ |
| 27 | $[27, 3, w^{3} - 2w^{2} - 5w - 1]$ | $-\frac{1}{3}e^{3} + \frac{11}{3}e$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 5w - 1]$ | $-\frac{4}{3}e^{3} + \frac{20}{3}e$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}2e$ |
| 41 | $[41, 41, 2w^{3} - 5w^{2} - 6w + 4]$ | $-\frac{1}{3}e^{3} + \frac{11}{3}e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w - 2]$ | $-e^{2} - 5$ |
| 59 | $[59, 59, w - 4]$ | $\phantom{-}3e^{2} - 15$ |
| 67 | $[67, 67, 2w^{2} - 3w - 8]$ | $-2e^{2} - 1$ |
| 73 | $[73, 73, 2w^{3} - 5w^{2} - 6w + 5]$ | $\phantom{-}2e^{3} - 17e$ |
| 89 | $[89, 89, -2w^{3} + 6w^{2} + 5w - 7]$ | $-\frac{2}{3}e^{3} + \frac{13}{3}e$ |
| 97 | $[97, 97, -2w^{3} + 6w^{2} + 3w - 7]$ | $\phantom{-}e^{2} - 4$ |
| 97 | $[97, 97, -w^{3} + 3w^{2} + 3w - 1]$ | $\phantom{-}\frac{8}{3}e^{3} - \frac{46}{3}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w + 2]$ | $-1$ |