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: | yes |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 45 x^8 + 738 x^6 - 5458 x^4 + 18300 x^2 - 22500\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^2 + 2 w + 1]$ | $-\frac{1}{150} e^8 + \frac{3}{10} e^6 - \frac{344}{75} e^4 + \frac{2029}{75} e^2 - 50$ |
| 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 | $[9, 3, w^3 - w^2 - 4 w]$ | $-\frac{4}{225} e^8 + \frac{31}{45} e^6 - \frac{2002}{225} e^4 + \frac{3269}{75} e^2 - 66$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 17 | $[17, 17, -w^3 + 2 w^2 + 3 w - 2]$ | $\phantom{-}\frac{1}{75} e^9 - \frac{49}{90} e^7 + \frac{3403}{450} e^5 - \frac{9274}{225} e^3 + \frac{224}{3} e$ |
| 17 | $[17, 17, -w^3 + w^2 + 4 w - 2]$ | $\phantom{-}\frac{1}{75} e^9 - \frac{49}{90} e^7 + \frac{3403}{450} e^5 - \frac{9274}{225} e^3 + \frac{224}{3} e$ |
| 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 | $[37, 37, 2 w - 1]$ | $\phantom{-}\frac{4}{225} e^8 - \frac{31}{45} e^6 + \frac{1927}{225} e^4 - \frac{2794}{75} e^2 + 46$ |
| 43 | $[43, 43, -w^3 + 2 w^2 + 2 w - 2]$ | $-\frac{4}{225} e^8 + \frac{31}{45} e^6 - \frac{2002}{225} e^4 + \frac{3269}{75} e^2 - 66$ |
| 43 | $[43, 43, w^3 - w^2 - 3 w + 1]$ | $-\frac{4}{225} e^8 + \frac{31}{45} e^6 - \frac{2002}{225} e^4 + \frac{3269}{75} e^2 - 66$ |
| 59 | $[59, 59, 2 w - 5]$ | $-\frac{1}{225} e^9 + \frac{13}{90} e^7 - \frac{601}{450} e^5 + \frac{533}{225} e^3 + \frac{17}{3} e$ |
| 59 | $[59, 59, -2 w - 3]$ | $-\frac{1}{225} e^9 + \frac{13}{90} e^7 - \frac{601}{450} e^5 + \frac{533}{225} e^3 + \frac{17}{3} e$ |
| 79 | $[79, 79, -w^3 + 2 w^2 + 5 w - 4]$ | $\phantom{-}\frac{1}{50} e^8 - \frac{9}{10} e^6 + \frac{344}{25} e^4 - \frac{2029}{25} e^2 + 152$ |
| 79 | $[79, 79, -w^3 + w^2 + 6 w - 2]$ | $\phantom{-}\frac{1}{50} e^8 - \frac{9}{10} e^6 + \frac{344}{25} e^4 - \frac{2029}{25} e^2 + 152$ |
| 83 | $[83, 83, -w^3 + 7 w]$ | $\phantom{-}\frac{1}{30} e^9 - \frac{4}{3} e^7 + \frac{181}{10} e^5 - \frac{483}{5} e^3 + 171 e$ |
| 83 | $[83, 83, -w^3 + 2 w^2 + 4 w - 2]$ | $\phantom{-}\frac{7}{450} e^9 - \frac{29}{45} e^7 + \frac{4141}{450} e^5 - \frac{3901}{75} e^3 + 93 e$ |
| 83 | $[83, 83, -w^3 + w^2 + 5 w - 3]$ | $\phantom{-}\frac{7}{450} e^9 - \frac{29}{45} e^7 + \frac{4141}{450} e^5 - \frac{3901}{75} e^3 + 93 e$ |
| 83 | $[83, 83, w^2 - 2 w - 6]$ | $\phantom{-}\frac{1}{30} e^9 - \frac{4}{3} e^7 + \frac{181}{10} e^5 - \frac{483}{5} e^3 + 171 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |