Base field \(\Q(\sqrt{157}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 39\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[9, 9, -w + 6]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} - 11x^{4} + 28x^{2} - 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 6]$ | $\phantom{-}0$ |
3 | $[3, 3, -w + 7]$ | $\phantom{-}\frac{1}{4}e^{4} - \frac{11}{4}e^{2} + 5$ |
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
11 | $[11, 11, -3w - 17]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{25}{4}e^{2} + 7$ |
11 | $[11, 11, 3w - 20]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{11}{4}e^{3} + 7e$ |
13 | $[13, 13, 2w - 13]$ | $-\frac{1}{4}e^{4} + \frac{11}{4}e^{2} - 2$ |
13 | $[13, 13, 2w + 11]$ | $\phantom{-}\frac{5}{4}e^{4} - \frac{43}{4}e^{2} + 13$ |
17 | $[17, 17, w + 7]$ | $-\frac{1}{4}e^{4} + \frac{11}{4}e^{2} - 4$ |
17 | $[17, 17, -w + 8]$ | $-\frac{1}{4}e^{5} + \frac{11}{4}e^{3} - 6e$ |
19 | $[19, 19, -w - 4]$ | $-e^{3} + 5e$ |
19 | $[19, 19, -w + 5]$ | $-\frac{3}{4}e^{5} + \frac{29}{4}e^{3} - 10e$ |
25 | $[25, 5, 5]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 7e$ |
31 | $[31, 31, -6w - 35]$ | $\phantom{-}\frac{1}{4}e^{5} - \frac{7}{4}e^{3}$ |
31 | $[31, 31, -6w + 41]$ | $-\frac{1}{2}e^{5} + \frac{7}{2}e^{3}$ |
37 | $[37, 37, -w - 1]$ | $\phantom{-}e^{3} - 8e$ |
37 | $[37, 37, w - 2]$ | $\phantom{-}\frac{3}{4}e^{5} - \frac{29}{4}e^{3} + 13e$ |
47 | $[47, 47, 3w + 16]$ | $-\frac{3}{2}e^{5} + \frac{29}{2}e^{3} - 22e$ |
47 | $[47, 47, -3w + 19]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{21}{4}e^{2} + 8$ |
49 | $[49, 7, -7]$ | $-\frac{1}{4}e^{4} + \frac{3}{4}e^{2} + 2$ |
67 | $[67, 67, 3w - 22]$ | $-\frac{5}{4}e^{4} + \frac{51}{4}e^{2} - 22$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 6]$ | $1$ |