Base field 3.3.1825.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x + 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[29, 29, -w^{2} - 2w + 4]$ |
Dimension: | $34$ |
CM: | no |
Base change: | no |
Newspace dimension: | $84$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{34} - 116x^{32} + 6078x^{30} - 190173x^{28} + 3957311x^{26} - 57715613x^{24} + 605546674x^{22} - 4615423172x^{20} + 25482866419x^{18} - 100399896492x^{16} + 274179655892x^{14} - 495074364438x^{12} + 551342345602x^{10} - 348418762964x^{8} + 120513501530x^{6} - 21666075512x^{4} + 1776446840x^{2} - 46303704\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w + 2]$ | $...$ |
7 | $[7, 7, w]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $...$ |
11 | $[11, 11, w + 2]$ | $...$ |
13 | $[13, 13, w + 1]$ | $...$ |
17 | $[17, 17, -w^{2} - w + 4]$ | $...$ |
23 | $[23, 23, -w^{2} + 6]$ | $...$ |
23 | $[23, 23, -w^{2} - w + 3]$ | $...$ |
23 | $[23, 23, -w + 4]$ | $...$ |
27 | $[27, 3, 3]$ | $...$ |
29 | $[29, 29, -w^{2} - 2w + 4]$ | $-1$ |
31 | $[31, 31, w^{2} - 10]$ | $...$ |
41 | $[41, 41, w + 4]$ | $...$ |
41 | $[41, 41, w^{2} - 5]$ | $...$ |
41 | $[41, 41, -2w - 5]$ | $...$ |
43 | $[43, 43, w^{2} - w - 4]$ | $...$ |
47 | $[47, 47, w^{2} - w - 9]$ | $...$ |
49 | $[49, 7, w^{2} - w - 8]$ | $...$ |
53 | $[53, 53, 2w^{2} + w - 12]$ | $...$ |
59 | $[59, 59, w^{2} - 3]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29, 29, -w^{2} - 2w + 4]$ | $1$ |