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: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 33x^{8} + 368x^{6} - 1722x^{4} + 3500x^{2} - 2500\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 2]$ | $-e$ |
7 | $[7, 7, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{61}{50}e^{8} - \frac{1813}{50}e^{6} + \frac{8249}{25}e^{4} - \frac{25421}{25}e^{2} + 926$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}\frac{61}{50}e^{8} - \frac{1813}{50}e^{6} + \frac{8249}{25}e^{4} - \frac{25421}{25}e^{2} + 926$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{8}{25}e^{8} - \frac{239}{25}e^{6} + \frac{2194}{25}e^{4} - \frac{6851}{25}e^{2} + 250$ |
16 | $[16, 2, 2]$ | $-1$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}\frac{42}{25}e^{9} - \frac{2497}{50}e^{7} + \frac{22737}{50}e^{5} - \frac{35099}{25}e^{3} + 1282e$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $-\frac{42}{25}e^{9} + \frac{2497}{50}e^{7} - \frac{22737}{50}e^{5} + \frac{35099}{25}e^{3} - 1282e$ |
25 | $[25, 5, w^{2} - w - 3]$ | $\phantom{-}\frac{107}{50}e^{8} - \frac{3181}{50}e^{6} + \frac{14488}{25}e^{4} - \frac{44802}{25}e^{2} + 1638$ |
37 | $[37, 37, 2w - 1]$ | $-\frac{23}{25}e^{8} + \frac{684}{25}e^{6} - \frac{6239}{25}e^{4} + \frac{19356}{25}e^{2} - 710$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{53}{25}e^{8} - \frac{1574}{25}e^{6} + \frac{14304}{25}e^{4} - \frac{43991}{25}e^{2} + 1600$ |
43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}\frac{53}{25}e^{8} - \frac{1574}{25}e^{6} + \frac{14304}{25}e^{4} - \frac{43991}{25}e^{2} + 1600$ |
59 | $[59, 59, 2w - 5]$ | $\phantom{-}\frac{34}{25}e^{9} - \frac{2019}{50}e^{7} + \frac{18349}{50}e^{5} - \frac{28248}{25}e^{3} + 1031e$ |
59 | $[59, 59, -2w - 3]$ | $-\frac{34}{25}e^{9} + \frac{2019}{50}e^{7} - \frac{18349}{50}e^{5} + \frac{28248}{25}e^{3} - 1031e$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}\frac{307}{50}e^{8} - \frac{9131}{50}e^{6} + \frac{41613}{25}e^{4} - \frac{128727}{25}e^{2} + 4724$ |
79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}\frac{307}{50}e^{8} - \frac{9131}{50}e^{6} + \frac{41613}{25}e^{4} - \frac{128727}{25}e^{2} + 4724$ |
83 | $[83, 83, -w^{3} + 7w]$ | $-\frac{67}{50}e^{9} + \frac{993}{25}e^{7} - \frac{17981}{50}e^{5} + \frac{27412}{25}e^{3} - 981e$ |
83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}\frac{39}{50}e^{9} - \frac{581}{25}e^{7} + \frac{10627}{50}e^{5} - \frac{16554}{25}e^{3} + 613e$ |
83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $-\frac{39}{50}e^{9} + \frac{581}{25}e^{7} - \frac{10627}{50}e^{5} + \frac{16554}{25}e^{3} - 613e$ |
83 | $[83, 83, w^{2} - 2w - 6]$ | $\phantom{-}\frac{67}{50}e^{9} - \frac{993}{25}e^{7} + \frac{17981}{50}e^{5} - \frac{27412}{25}e^{3} + 981e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$16$ | $[16, 2, 2]$ | $1$ |