Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[16, 2, 2]$ |
Dimension: | $10$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 45x^{8} + 738x^{6} - 5458x^{4} + 18300x^{2} - 22500\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2w + 1]$ | $-\frac{1}{150}e^{8} + \frac{3}{10}e^{6} - \frac{344}{75}e^{4} + \frac{2029}{75}e^{2} - 50$ |
7 | $[7, 7, -w^{2} + 2]$ | $-\frac{1}{150}e^{8} + \frac{3}{10}e^{6} - \frac{344}{75}e^{4} + \frac{2029}{75}e^{2} - 50$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-\frac{4}{225}e^{8} + \frac{31}{45}e^{6} - \frac{2002}{225}e^{4} + \frac{3269}{75}e^{2} - 66$ |
16 | $[16, 2, 2]$ | $-1$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{1}{75}e^{9} - \frac{49}{90}e^{7} + \frac{3403}{450}e^{5} - \frac{9274}{225}e^{3} + \frac{224}{3}e$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{75}e^{9} - \frac{49}{90}e^{7} + \frac{3403}{450}e^{5} - \frac{9274}{225}e^{3} + \frac{224}{3}e$ |
25 | $[25, 5, w^{2} - w - 3]$ | $-\frac{11}{450}e^{8} + \frac{89}{90}e^{6} - \frac{3109}{225}e^{4} + \frac{5848}{75}e^{2} - 144$ |
37 | $[37, 37, 2w - 1]$ | $\phantom{-}\frac{4}{225}e^{8} - \frac{31}{45}e^{6} + \frac{1927}{225}e^{4} - \frac{2794}{75}e^{2} + 46$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $-\frac{4}{225}e^{8} + \frac{31}{45}e^{6} - \frac{2002}{225}e^{4} + \frac{3269}{75}e^{2} - 66$ |
43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $-\frac{4}{225}e^{8} + \frac{31}{45}e^{6} - \frac{2002}{225}e^{4} + \frac{3269}{75}e^{2} - 66$ |
59 | $[59, 59, 2w - 5]$ | $-\frac{1}{225}e^{9} + \frac{13}{90}e^{7} - \frac{601}{450}e^{5} + \frac{533}{225}e^{3} + \frac{17}{3}e$ |
59 | $[59, 59, -2w - 3]$ | $-\frac{1}{225}e^{9} + \frac{13}{90}e^{7} - \frac{601}{450}e^{5} + \frac{533}{225}e^{3} + \frac{17}{3}e$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}\frac{1}{50}e^{8} - \frac{9}{10}e^{6} + \frac{344}{25}e^{4} - \frac{2029}{25}e^{2} + 152$ |
79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{1}{50}e^{8} - \frac{9}{10}e^{6} + \frac{344}{25}e^{4} - \frac{2029}{25}e^{2} + 152$ |
83 | $[83, 83, -w^{3} + 7w]$ | $\phantom{-}\frac{1}{30}e^{9} - \frac{4}{3}e^{7} + \frac{181}{10}e^{5} - \frac{483}{5}e^{3} + 171e$ |
83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}\frac{7}{450}e^{9} - \frac{29}{45}e^{7} + \frac{4141}{450}e^{5} - \frac{3901}{75}e^{3} + 93e$ |
83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $\phantom{-}\frac{7}{450}e^{9} - \frac{29}{45}e^{7} + \frac{4141}{450}e^{5} - \frac{3901}{75}e^{3} + 93e$ |
83 | $[83, 83, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{30}e^{9} - \frac{4}{3}e^{7} + \frac{181}{10}e^{5} - \frac{483}{5}e^{3} + 171e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$16$ | $[16, 2, 2]$ | $1$ |