Base field 4.4.8789.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 6 x^2 - 2 x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29, 29, w^3 - 2 w^2 - 5 w]$ |
| Dimension: | $13$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{13} - 6 x^{12} - 24 x^{11} + 194 x^{10} + 33 x^9 - 1825 x^8 + 1785 x^7 + 5153 x^6 - 8740 x^5 - 4 x^4 + 5872 x^3 - 2464 x^2 - 64 x + 64\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w^3 + 2 w^2 + 3 w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $...$ |
| 11 | $[11, 11, -w^3 + 2 w^2 + 4 w]$ | $...$ |
| 13 | $[13, 13, -2 w^3 + 3 w^2 + 10 w - 2]$ | $...$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 17 | $[17, 17, -w^3 + 2 w^2 + 5 w - 3]$ | $...$ |
| 17 | $[17, 17, -w^3 + w^2 + 5 w]$ | $...$ |
| 17 | $[17, 17, -w^2 + 2 w + 1]$ | $...$ |
| 19 | $[19, 19, w^2 - w - 2]$ | $...$ |
| 29 | $[29, 29, w^3 - 2 w^2 - 5 w]$ | $-1$ |
| 29 | $[29, 29, w^2 - w - 3]$ | $...$ |
| 31 | $[31, 31, -w^3 + 2 w^2 + 3 w - 2]$ | $...$ |
| 43 | $[43, 43, 2 w^3 - 3 w^2 - 11 w]$ | $...$ |
| 47 | $[47, 47, w^3 - 7 w - 4]$ | $...$ |
| 53 | $[53, 53, -2 w^3 + 3 w^2 + 9 w - 1]$ | $...$ |
| 61 | $[61, 61, -w - 3]$ | $...$ |
| 73 | $[73, 73, -w^3 + 2 w^2 + 3 w - 3]$ | $...$ |
| 73 | $[73, 73, w^3 - w^2 - 7 w - 1]$ | $...$ |
| 81 | $[81, 3, -3]$ | $...$ |
| 83 | $[83, 83, -2 w^3 + 3 w^2 + 9 w + 1]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, w^3 - 2 w^2 - 5 w]$ | $1$ |