Base field 4.4.17725.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 12 x^2 + 13 x + 41\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[29,29,-w^2 + 2 w + 8]$ |
| Dimension: | $29$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{29} - 5 x^{28} - 144 x^{27} + 604 x^{26} + 9377 x^{25} - 29883 x^{24} - 362472 x^{23} + 751116 x^{22} + 9086052 x^{21} - 8784522 x^{20} - 150435338 x^{19} - 7235931 x^{18} + 1598132639 x^{17} + 1545050122 x^{16} - 9935841081 x^{15} - 19040564543 x^{14} + 26927303857 x^{13} + 99852755298 x^{12} + 26949391194 x^{11} - 196373595187 x^{10} - 245837785679 x^9 - 11867548014 x^8 + 157436008180 x^7 + 85073299192 x^6 - 16754876144 x^5 - 22444223799 x^4 - 2418319572 x^3 + 1259429276 x^2 + 171019952 x + 4104048\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^3 + 3 w^2 + 5 w - 15]$ | $...$ |
| 9 | $[9, 3, -w^3 + 8 w + 8]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $...$ |
| 19 | $[19, 19, w + 1]$ | $...$ |
| 19 | $[19, 19, -w^2 + 6]$ | $...$ |
| 19 | $[19, 19, -w^2 + 2 w + 5]$ | $...$ |
| 19 | $[19, 19, -w + 2]$ | $...$ |
| 25 | $[25, 5, 2 w^2 - 2 w - 13]$ | $...$ |
| 29 | $[29, 29, -w^2 + 9]$ | $...$ |
| 29 | $[29, 29, -w^2 + 2 w + 6]$ | $...$ |
| 29 | $[29, 29, w^2 - 7]$ | $...$ |
| 29 | $[29, 29, -w^2 + 2 w + 8]$ | $-1$ |
| 31 | $[31, 31, -2 w^2 + w + 12]$ | $...$ |
| 31 | $[31, 31, 2 w^2 - 3 w - 11]$ | $...$ |
| 41 | $[41, 41, -w]$ | $...$ |
| 41 | $[41, 41, -w + 1]$ | $...$ |
| 49 | $[49, 7, w^3 + 2 w^2 - 10 w - 20]$ | $...$ |
| 49 | $[49, 7, w^3 - 5 w^2 - 3 w + 27]$ | $...$ |
| 61 | $[61, 61, 2 w^2 - 3 w - 14]$ | $...$ |
| 61 | $[61, 61, 2 w^2 - w - 15]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29,29,-w^2 + 2 w + 8]$ | $1$ |