Base field \(\Q(\sqrt{29}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 7\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[13, 13, w + 4]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - x^{2} - 12x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 4$ |
5 | $[5, 5, w - 2]$ | $-\frac{1}{4}e^{2} + \frac{1}{4}e + 4$ |
7 | $[7, 7, w]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 2$ |
7 | $[7, 7, -w + 1]$ | $\phantom{-}\frac{3}{4}e^{2} + \frac{1}{4}e - 5$ |
9 | $[9, 3, 3]$ | $-\frac{3}{4}e^{2} - \frac{5}{4}e + 7$ |
13 | $[13, 13, w + 4]$ | $-1$ |
13 | $[13, 13, w - 5]$ | $-\frac{3}{4}e^{2} - \frac{1}{4}e + 6$ |
23 | $[23, 23, -w - 5]$ | $\phantom{-}e^{2} - 8$ |
23 | $[23, 23, w - 6]$ | $\phantom{-}\frac{1}{4}e^{2} + \frac{3}{4}e$ |
29 | $[29, 29, 2w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 6$ |
53 | $[53, 53, 3w - 5]$ | $-\frac{1}{2}e^{2} - \frac{5}{2}e + 2$ |
53 | $[53, 53, -3w - 2]$ | $-2e^{2} - e + 18$ |
59 | $[59, 59, -3w - 1]$ | $\phantom{-}\frac{1}{4}e^{2} - \frac{1}{4}e - 1$ |
59 | $[59, 59, 3w - 4]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{5}{2}e - 10$ |
67 | $[67, 67, 3w - 13]$ | $\phantom{-}\frac{3}{4}e^{2} + \frac{13}{4}e - 9$ |
67 | $[67, 67, -3w - 10]$ | $-\frac{1}{2}e^{2} + \frac{3}{2}e + 10$ |
71 | $[71, 71, 2w - 11]$ | $\phantom{-}e^{2} + 2e - 12$ |
71 | $[71, 71, -2w - 9]$ | $-\frac{3}{4}e^{2} - \frac{5}{4}e + 6$ |
83 | $[83, 83, -w - 9]$ | $-\frac{1}{2}e^{2} - \frac{3}{2}e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w + 4]$ | $1$ |