Base field \(\Q(\sqrt{14}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[13,13,w - 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - x^{4} - 7x^{3} + 6x^{2} + 7x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 4]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 3]$ | $\phantom{-}e^{4} - 2e^{3} - 7e^{2} + 11e + 4$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}e^{3} + e^{2} - 6e - 3$ |
| 7 | $[7, 7, -2w - 7]$ | $-e^{4} + 6e^{2} - 2e - 3$ |
| 9 | $[9, 3, 3]$ | $-2e^{4} + 2e^{3} + 12e^{2} - 13e - 7$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}e^{3} - 5e$ |
| 11 | $[11, 11, -w + 5]$ | $\phantom{-}e^{4} - 2e^{3} - 8e^{2} + 12e + 7$ |
| 13 | $[13, 13, -w - 1]$ | $\phantom{-}2e^{4} - e^{3} - 12e^{2} + 9e + 2$ |
| 13 | $[13, 13, -w + 1]$ | $\phantom{-}1$ |
| 31 | $[31, 31, 2w - 5]$ | $-e^{4} + 3e^{3} + 7e^{2} - 15e - 8$ |
| 31 | $[31, 31, -2w - 5]$ | $-4e^{4} + 5e^{3} + 26e^{2} - 32e - 16$ |
| 43 | $[43, 43, 7w + 27]$ | $\phantom{-}2e^{4} - e^{3} - 12e^{2} + 11e + 5$ |
| 43 | $[43, 43, 3w + 13]$ | $\phantom{-}3e^{4} - 3e^{3} - 17e^{2} + 17e + 5$ |
| 47 | $[47, 47, 2w - 3]$ | $\phantom{-}e^{4} - e^{3} - 5e^{2} + 4e - 6$ |
| 47 | $[47, 47, -2w - 3]$ | $-e^{4} + 9e^{2} + e - 9$ |
| 61 | $[61, 61, 7w + 25]$ | $-3e^{4} + e^{3} + 18e^{2} - 10e - 13$ |
| 61 | $[61, 61, -5w - 17]$ | $-e^{4} + e^{3} + 2e^{2} - 5e + 10$ |
| 67 | $[67, 67, -w - 9]$ | $\phantom{-}5e^{4} - 7e^{3} - 33e^{2} + 41e + 19$ |
| 67 | $[67, 67, w - 9]$ | $-2e^{4} + e^{3} + 13e^{2} - 9e - 13$ |
| 101 | $[101, 101, 3w - 5]$ | $-3e^{4} + 2e^{3} + 19e^{2} - 12e - 20$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,w - 1]$ | $-1$ |