Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 4 x^2 + 5 x + 1\); 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:
| \(x^{10} - 33 x^8 + 368 x^6 - 1722 x^4 + 3500 x^2 - 2500\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $-e$ |
| 7 | $[7, 7, -w^2 + 2 w + 1]$ | $\phantom{-}\frac{61}{50} e^8 - \frac{1813}{50} e^6 + \frac{8249}{25} e^4 - \frac{25421}{25} e^2 + 926$ |
| 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 | $[9, 3, w^3 - w^2 - 4 w]$ | $\phantom{-}\frac{8}{25} e^8 - \frac{239}{25} e^6 + \frac{2194}{25} e^4 - \frac{6851}{25} e^2 + 250$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 17 | $[17, 17, -w^3 + 2 w^2 + 3 w - 2]$ | $\phantom{-}\frac{42}{25} e^9 - \frac{2497}{50} e^7 + \frac{22737}{50} e^5 - \frac{35099}{25} e^3 + 1282 e$ |
| 17 | $[17, 17, -w^3 + w^2 + 4 w - 2]$ | $-\frac{42}{25} e^9 + \frac{2497}{50} e^7 - \frac{22737}{50} e^5 + \frac{35099}{25} e^3 - 1282 e$ |
| 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 | $[37, 37, 2 w - 1]$ | $-\frac{23}{25} e^8 + \frac{684}{25} e^6 - \frac{6239}{25} e^4 + \frac{19356}{25} e^2 - 710$ |
| 43 | $[43, 43, -w^3 + 2 w^2 + 2 w - 2]$ | $\phantom{-}\frac{53}{25} e^8 - \frac{1574}{25} e^6 + \frac{14304}{25} e^4 - \frac{43991}{25} e^2 + 1600$ |
| 43 | $[43, 43, w^3 - w^2 - 3 w + 1]$ | $\phantom{-}\frac{53}{25} e^8 - \frac{1574}{25} e^6 + \frac{14304}{25} e^4 - \frac{43991}{25} e^2 + 1600$ |
| 59 | $[59, 59, 2 w - 5]$ | $\phantom{-}\frac{34}{25} e^9 - \frac{2019}{50} e^7 + \frac{18349}{50} e^5 - \frac{28248}{25} e^3 + 1031 e$ |
| 59 | $[59, 59, -2 w - 3]$ | $-\frac{34}{25} e^9 + \frac{2019}{50} e^7 - \frac{18349}{50} e^5 + \frac{28248}{25} e^3 - 1031 e$ |
| 79 | $[79, 79, -w^3 + 2 w^2 + 5 w - 4]$ | $\phantom{-}\frac{307}{50} e^8 - \frac{9131}{50} e^6 + \frac{41613}{25} e^4 - \frac{128727}{25} e^2 + 4724$ |
| 79 | $[79, 79, -w^3 + w^2 + 6 w - 2]$ | $\phantom{-}\frac{307}{50} e^8 - \frac{9131}{50} e^6 + \frac{41613}{25} e^4 - \frac{128727}{25} e^2 + 4724$ |
| 83 | $[83, 83, -w^3 + 7 w]$ | $-\frac{67}{50} e^9 + \frac{993}{25} e^7 - \frac{17981}{50} e^5 + \frac{27412}{25} e^3 - 981 e$ |
| 83 | $[83, 83, -w^3 + 2 w^2 + 4 w - 2]$ | $\phantom{-}\frac{39}{50} e^9 - \frac{581}{25} e^7 + \frac{10627}{50} e^5 - \frac{16554}{25} e^3 + 613 e$ |
| 83 | $[83, 83, -w^3 + w^2 + 5 w - 3]$ | $-\frac{39}{50} e^9 + \frac{581}{25} e^7 - \frac{10627}{50} e^5 + \frac{16554}{25} e^3 - 613 e$ |
| 83 | $[83, 83, w^2 - 2 w - 6]$ | $\phantom{-}\frac{67}{50} e^9 - \frac{993}{25} e^7 + \frac{17981}{50} e^5 - \frac{27412}{25} e^3 + 981 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |