Base field \(\Q(\sqrt{181}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 45\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[15,15,w - 6]$ |
Dimension: | $12$ |
CM: | no |
Base change: | no |
Newspace dimension: | $41$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{12} + 2x^{11} - 23x^{10} - 43x^{9} + 170x^{8} + 274x^{7} - 482x^{6} - 560x^{5} + 558x^{4} + 412x^{3} - 200x^{2} - 96x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w - 6]$ | $-1$ |
3 | $[3, 3, -w + 7]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $...$ |
5 | $[5, 5, 4w + 25]$ | $...$ |
5 | $[5, 5, -4w + 29]$ | $-1$ |
11 | $[11, 11, w - 8]$ | $...$ |
11 | $[11, 11, -w - 7]$ | $...$ |
13 | $[13, 13, 3w + 19]$ | $-\frac{187}{4932}e^{11} - \frac{565}{4932}e^{10} + \frac{1349}{1644}e^{9} + \frac{6173}{2466}e^{8} - \frac{2989}{548}e^{7} - \frac{20455}{1233}e^{6} + \frac{1856}{137}e^{5} + \frac{92041}{2466}e^{4} - \frac{46537}{2466}e^{3} - \frac{76441}{2466}e^{2} + \frac{13312}{1233}e + \frac{8168}{1233}$ |
13 | $[13, 13, 3w - 22]$ | $...$ |
29 | $[29, 29, 6w + 37]$ | $...$ |
29 | $[29, 29, 6w - 43]$ | $...$ |
37 | $[37, 37, 2w - 13]$ | $...$ |
37 | $[37, 37, 2w + 11]$ | $...$ |
43 | $[43, 43, -w - 1]$ | $...$ |
43 | $[43, 43, w - 2]$ | $...$ |
49 | $[49, 7, -7]$ | $...$ |
59 | $[59, 59, 5w - 37]$ | $...$ |
59 | $[59, 59, 5w + 32]$ | $...$ |
67 | $[67, 67, 21w + 131]$ | $...$ |
67 | $[67, 67, 21w - 152]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3,3,w + 6]$ | $1$ |
$5$ | $[5,5,-4w + 29]$ | $1$ |