Base field 4.4.19429.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - x + 5\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{2} + w + 4]$ |
Dimension: | $21$ |
CM: | no |
Base change: | no |
Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{21} - 4x^{20} - 41x^{19} + 164x^{18} + 713x^{17} - 2781x^{16} - 7026x^{15} + 25475x^{14} + 44091x^{13} - 137721x^{12} - 184581x^{11} + 448919x^{10} + 509507x^{9} - 862696x^{8} - 865464x^{7} + 921795x^{6} + 797999x^{5} - 504849x^{4} - 334707x^{3} + 115362x^{2} + 42552x - 2108\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $...$ |
7 | $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ | $...$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $-1$ |
13 | $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ | $...$ |
16 | $[16, 2, 2]$ | $...$ |
17 | $[17, 17, -w + 2]$ | $...$ |
19 | $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ | $...$ |
27 | $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ | $...$ |
31 | $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ | $...$ |
31 | $[31, 31, -w^{3} + w^{2} + 6w + 1]$ | $...$ |
41 | $[41, 41, w^{2} - w - 1]$ | $...$ |
43 | $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ | $...$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ | $...$ |
53 | $[53, 53, -w - 3]$ | $...$ |
53 | $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ | $...$ |
59 | $[59, 59, 2w^{2} - 3w - 6]$ | $...$ |
59 | $[59, 59, w^{3} - w^{2} - 7w - 3]$ | $...$ |
79 | $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ | $...$ |
79 | $[79, 79, w^{2} - 2w - 1]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{2} + w + 4]$ | $1$ |