Base field 3.3.1489.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x - 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[29, 29, w^{2} - 2w - 5]$ |
Dimension: | $29$ |
CM: | no |
Base change: | no |
Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{29} + 18x^{28} + 40x^{27} - 1144x^{26} - 7483x^{25} + 17630x^{24} + 285639x^{23} + 339946x^{22} - 4802113x^{21} - 15535294x^{20} + 33814947x^{19} + 227547988x^{18} + 52881747x^{17} - 1638440244x^{16} - 2542894266x^{15} + 5360453206x^{14} + 17309247252x^{13} - 122125718x^{12} - 50920051656x^{11} - 49160503488x^{10} + 52898731876x^{9} + 120035190778x^{8} + 33311108292x^{7} - 83030399610x^{6} - 78767927441x^{5} - 11161181264x^{4} + 16478627548x^{3} + 8777157968x^{2} + 1500335424x + 76912384\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $...$ |
13 | $[13, 13, w^{2} - 3w - 5]$ | $...$ |
17 | $[17, 17, w - 1]$ | $...$ |
19 | $[19, 19, -w^{2} + 2w + 6]$ | $...$ |
19 | $[19, 19, -w^{2} + 2w + 10]$ | $...$ |
19 | $[19, 19, -w + 3]$ | $...$ |
23 | $[23, 23, w - 2]$ | $...$ |
27 | $[27, 3, 3]$ | $...$ |
29 | $[29, 29, w^{2} - 2w - 5]$ | $-1$ |
31 | $[31, 31, w^{2} - 3w - 6]$ | $...$ |
31 | $[31, 31, w^{2} - w - 8]$ | $...$ |
31 | $[31, 31, w^{2} - 2w - 4]$ | $...$ |
41 | $[41, 41, w^{2} - w - 5]$ | $...$ |
43 | $[43, 43, w^{2} - 3w - 10]$ | $...$ |
47 | $[47, 47, -w - 4]$ | $...$ |
47 | $[47, 47, w^{2} - w - 9]$ | $...$ |
47 | $[47, 47, -2w^{2} + 3w + 17]$ | $...$ |
49 | $[49, 7, w^{2} - w - 10]$ | $...$ |
53 | $[53, 53, w^{2} - w - 4]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$29$ | $[29, 29, w^{2} - 2w - 5]$ | $1$ |