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: | $[13, 13, w + 1]$ |
Dimension: | $14$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{14} - 2x^{13} - 40x^{12} + 62x^{11} + 606x^{10} - 696x^{9} - 4231x^{8} + 3602x^{7} + 13409x^{6} - 9268x^{5} - 17206x^{4} + 10308x^{3} + 7220x^{2} - 2620x - 1240\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, w]$ | $...$ |
8 | $[8, 2, 2]$ | $...$ |
11 | $[11, 11, w + 2]$ | $...$ |
13 | $[13, 13, w + 1]$ | $\phantom{-}1$ |
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 | $[29, 29, -w^{2} - 2w + 4]$ | $...$ |
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 |
---|---|---|
$13$ | $[13, 13, w + 1]$ | $-1$ |