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 | $[5, 5, -w + 3]$ | $-e^{3} - e^{2} + 6e + 3$ |
5 | $[5, 5, w + 3]$ | $-e^{4} + 2e^{3} + 7e^{2} - 11e - 4$ |
7 | $[7, 7, -2w - 7]$ | $\phantom{-}e^{4} - 6e^{2} + 2e + 3$ |
9 | $[9, 3, 3]$ | $-2e^{4} + 2e^{3} + 12e^{2} - 13e - 7$ |
11 | $[11, 11, w + 5]$ | $\phantom{-}e^{4} - 2e^{3} - 8e^{2} + 12e + 7$ |
11 | $[11, 11, -w + 5]$ | $\phantom{-}e^{3} - 5e$ |
13 | $[13, 13, -w - 1]$ | $-1$ |
13 | $[13, 13, -w + 1]$ | $-2e^{4} + e^{3} + 12e^{2} - 9e - 2$ |
31 | $[31, 31, 2w - 5]$ | $\phantom{-}4e^{4} - 5e^{3} - 26e^{2} + 32e + 16$ |
31 | $[31, 31, -2w - 5]$ | $\phantom{-}e^{4} - 3e^{3} - 7e^{2} + 15e + 8$ |
43 | $[43, 43, 7w + 27]$ | $\phantom{-}3e^{4} - 3e^{3} - 17e^{2} + 17e + 5$ |
43 | $[43, 43, 3w + 13]$ | $\phantom{-}2e^{4} - e^{3} - 12e^{2} + 11e + 5$ |
47 | $[47, 47, 2w - 3]$ | $\phantom{-}e^{4} - 9e^{2} - e + 9$ |
47 | $[47, 47, -2w - 3]$ | $-e^{4} + e^{3} + 5e^{2} - 4e + 6$ |
61 | $[61, 61, 7w + 25]$ | $\phantom{-}e^{4} - e^{3} - 2e^{2} + 5e - 10$ |
61 | $[61, 61, -5w - 17]$ | $\phantom{-}3e^{4} - e^{3} - 18e^{2} + 10e + 13$ |
67 | $[67, 67, -w - 9]$ | $-2e^{4} + e^{3} + 13e^{2} - 9e - 13$ |
67 | $[67, 67, w - 9]$ | $\phantom{-}5e^{4} - 7e^{3} - 33e^{2} + 41e + 19$ |
101 | $[101, 101, 3w - 5]$ | $\phantom{-}3e^{3} + e^{2} - 20e + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w - 1]$ | $1$ |