Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[13, 13, -w]$ |
Dimension: | $22$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{22} + 4x^{21} - 32x^{20} - 142x^{19} + 400x^{18} + 2096x^{17} - 2383x^{16} - 16836x^{15} + 5530x^{14} + 80630x^{13} + 10902x^{12} - 235904x^{11} - 101418x^{10} + 411310x^{9} + 260130x^{8} - 388892x^{7} - 305939x^{6} + 149634x^{5} + 141979x^{4} + 3172x^{3} - 3849x^{2} + 170x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 1]$ | $...$ |
7 | $[7, 7, w^{2} + w - 7]$ | $...$ |
7 | $[7, 7, -w^{2} + 11]$ | $...$ |
7 | $[7, 7, -w^{2} + 9]$ | $...$ |
8 | $[8, 2, 2]$ | $...$ |
13 | $[13, 13, -w]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{2} - w + 4]$ | $...$ |
23 | $[23, 23, w^{2} + w - 10]$ | $...$ |
29 | $[29, 29, 2w^{2} - 21]$ | $...$ |
37 | $[37, 37, 2w^{2} + w - 17]$ | $...$ |
43 | $[43, 43, 3w^{2} + 3w - 22]$ | $...$ |
47 | $[47, 47, w^{2} - 6]$ | $...$ |
47 | $[47, 47, w^{2} - 3]$ | $...$ |
47 | $[47, 47, -w^{2} + 12]$ | $...$ |
53 | $[53, 53, w^{2} - w - 4]$ | $...$ |
61 | $[61, 61, w^{2} - 5]$ | $...$ |
67 | $[67, 67, w^{2} - w - 7]$ | $...$ |
73 | $[73, 73, 7w^{2} + 3w - 66]$ | $...$ |
79 | $[79, 79, 2w^{2} - 19]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w]$ | $-1$ |