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: | $[25, 5, w^2 - w - 3]$ |
| Dimension: | $20$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $50$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{20} - 72 x^{18} + 2108 x^{16} - 32352 x^{14} + 280256 x^{12} - 1377024 x^{10} + 3659776 x^8 - 4729344 x^6 + 2489088 x^4 - 285696 x^2 + 9216\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $...$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^2 + 2 w + 1]$ | $...$ |
| 7 | $[7, 7, -w^2 + 2]$ | $...$ |
| 9 | $[9, 3, w^3 - w^2 - 4 w]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, -w^3 + 2 w^2 + 3 w - 2]$ | $...$ |
| 17 | $[17, 17, -w^3 + w^2 + 4 w - 2]$ | $...$ |
| 25 | $[25, 5, w^2 - w - 3]$ | $-1$ |
| 37 | $[37, 37, 2 w - 1]$ | $...$ |
| 43 | $[43, 43, -w^3 + 2 w^2 + 2 w - 2]$ | $...$ |
| 43 | $[43, 43, w^3 - w^2 - 3 w + 1]$ | $...$ |
| 59 | $[59, 59, 2 w - 5]$ | $...$ |
| 59 | $[59, 59, -2 w - 3]$ | $...$ |
| 79 | $[79, 79, -w^3 + 2 w^2 + 5 w - 4]$ | $...$ |
| 79 | $[79, 79, -w^3 + w^2 + 6 w - 2]$ | $...$ |
| 83 | $[83, 83, -w^3 + 7 w]$ | $...$ |
| 83 | $[83, 83, -w^3 + 2 w^2 + 4 w - 2]$ | $...$ |
| 83 | $[83, 83, -w^3 + w^2 + 5 w - 3]$ | $...$ |
| 83 | $[83, 83, w^2 - 2 w - 6]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, w^2 - w - 3]$ | $1$ |