Base field \(\Q(\sqrt{357}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 89\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[9, 3, 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $114$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4096\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
4 | $[4, 2, 2]$ | $\phantom{-}3$ |
7 | $[7, 7, w + 3]$ | $\phantom{-}0$ |
11 | $[11, 11, w + 3]$ | $\phantom{-}\frac{1}{128}e^{3} + \frac{1}{2}e$ |
11 | $[11, 11, w + 7]$ | $-\frac{1}{128}e^{3} - \frac{1}{2}e$ |
17 | $[17, 17, w + 8]$ | $-\frac{1}{128}e^{3} + \frac{1}{2}e$ |
23 | $[23, 23, w + 4]$ | $-\frac{1}{128}e^{3} - \frac{1}{2}e$ |
23 | $[23, 23, w + 18]$ | $\phantom{-}\frac{1}{128}e^{3} + \frac{1}{2}e$ |
25 | $[25, 5, 5]$ | $\phantom{-}6$ |
29 | $[29, 29, w + 1]$ | $-\frac{1}{128}e^{3} - \frac{1}{2}e$ |
29 | $[29, 29, w + 27]$ | $\phantom{-}\frac{1}{128}e^{3} + \frac{1}{2}e$ |
31 | $[31, 31, w + 13]$ | $\phantom{-}0$ |
31 | $[31, 31, w + 17]$ | $\phantom{-}0$ |
43 | $[43, 43, -w - 11]$ | $\phantom{-}4$ |
43 | $[43, 43, w - 12]$ | $\phantom{-}4$ |
47 | $[47, 47, -w - 6]$ | $\phantom{-}\frac{1}{64}e^{3} - e$ |
47 | $[47, 47, w - 7]$ | $\phantom{-}\frac{1}{64}e^{3} - e$ |
59 | $[59, 59, -w - 5]$ | $-\frac{1}{64}e^{3} + e$ |
59 | $[59, 59, w - 6]$ | $-\frac{1}{64}e^{3} + e$ |
61 | $[61, 61, w + 16]$ | $-\frac{3}{32}e^{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $1$ |