Base field 3.3.1573.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[13, 13, w + 3]$ |
Dimension: | $22$ |
CM: | no |
Base change: | no |
Newspace dimension: | $37$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{22} - 34x^{20} - 2x^{19} + 493x^{18} + 61x^{17} - 3981x^{16} - 767x^{15} + 19582x^{14} + 5172x^{13} - 60165x^{12} - 20259x^{11} + 113419x^{10} + 46291x^{9} - 122611x^{8} - 57818x^{7} + 64770x^{6} + 32397x^{5} - 11178x^{4} - 3666x^{3} + 1063x^{2} - 65x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w]$ | $\phantom{-}e$ |
4 | $[4, 2, w^{2} - w - 7]$ | $...$ |
5 | $[5, 5, w - 1]$ | $...$ |
7 | $[7, 7, w + 1]$ | $...$ |
11 | $[11, 11, -w^{2} + 5]$ | $...$ |
13 | $[13, 13, w + 3]$ | $\phantom{-}1$ |
13 | $[13, 13, -2w + 1]$ | $...$ |
19 | $[19, 19, 2w^{2} - w - 15]$ | $...$ |
25 | $[25, 5, w^{2} - 7]$ | $...$ |
27 | $[27, 3, 3]$ | $...$ |
31 | $[31, 31, w^{2} - 2w - 1]$ | $...$ |
37 | $[37, 37, -3w^{2} + 2w + 23]$ | $...$ |
41 | $[41, 41, -2w - 1]$ | $...$ |
47 | $[47, 47, w^{2} - 3]$ | $...$ |
49 | $[49, 7, w^{2} - 2w - 5]$ | $...$ |
59 | $[59, 59, 2w - 3]$ | $...$ |
67 | $[67, 67, w - 5]$ | $...$ |
71 | $[71, 71, w^{2} - 2w - 11]$ | $...$ |
73 | $[73, 73, w^{2} + 1]$ | $...$ |
83 | $[83, 83, -4w^{2} + 3w + 27]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w + 3]$ | $-1$ |