Base field 4.4.8112.1
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13,13,-w^{3} + 4w + 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-3$ |
| 4 | $[4, 2, w^{2} - w - 1]$ | $-1$ |
| 9 | $[9, 3, -w^{2} + 2]$ | $-1$ |
| 13 | $[13, 13, w^{3} - 4w + 2]$ | $\phantom{-}2$ |
| 13 | $[13, 13, -w^{3} + 4w + 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{3} - 3w - 1]$ | $-7$ |
| 17 | $[17, 17, -w^{3} + 3w - 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{3} + w^{2} - 4w - 2]$ | $-4$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}8$ |
| 43 | $[43, 43, w^{2} + w - 4]$ | $\phantom{-}1$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}9$ |
| 53 | $[53, 53, w^{3} - 2w - 2]$ | $\phantom{-}8$ |
| 53 | $[53, 53, -w^{3} + 2w - 2]$ | $-12$ |
| 79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $-16$ |
| 79 | $[79, 79, -w^{3} - w^{2} + 4w + 1]$ | $-12$ |
| 101 | $[101, 101, -w^{3} + w^{2} + 3w - 5]$ | $-18$ |
| 101 | $[101, 101, w^{3} + w^{2} - 3w - 5]$ | $\phantom{-}6$ |
| 103 | $[103, 103, 2w^{2} - w - 4]$ | $-8$ |
| 103 | $[103, 103, 2w^{2} + w - 4]$ | $\phantom{-}12$ |
| 107 | $[107, 107, 2w^{2} + w - 5]$ | $\phantom{-}8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,-w^{3} + 4w + 2]$ | $-1$ |