Base field 5.5.170701.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ |
Dimension: | $21$ |
CM: | no |
Base change: | no |
Newspace dimension: | $51$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{21} + 11x^{20} + 11x^{19} - 281x^{18} - 909x^{17} + 2329x^{16} + 13358x^{15} - 3002x^{14} - 90434x^{13} - 63642x^{12} + 322521x^{11} + 420012x^{10} - 586572x^{9} - 1162449x^{8} + 377329x^{7} + 1591850x^{6} + 299252x^{5} - 982940x^{4} - 500699x^{3} + 164319x^{2} + 159518x + 27425\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 2]$ | $...$ |
8 | $[8, 2, -2w^{4} + 3w^{3} + 10w^{2} - 5w - 3]$ | $...$ |
11 | $[11, 11, w^{4} - w^{3} - 6w^{2} + 2]$ | $...$ |
13 | $[13, 13, -w^{4} + 2w^{3} + 5w^{2} - 5w - 3]$ | $...$ |
23 | $[23, 23, -w^{2} + 2]$ | $...$ |
23 | $[23, 23, -w + 2]$ | $...$ |
31 | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $-1$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $...$ |
47 | $[47, 47, -w^{4} + 2w^{3} + 5w^{2} - 4w - 4]$ | $...$ |
53 | $[53, 53, w^{2} - w - 4]$ | $...$ |
53 | $[53, 53, -w^{4} + 2w^{3} + 4w^{2} - 4w - 3]$ | $...$ |
53 | $[53, 53, -w^{3} + w^{2} + 4w - 1]$ | $...$ |
71 | $[71, 71, w^{4} - w^{3} - 7w^{2} + 3w + 6]$ | $...$ |
71 | $[71, 71, -2w^{4} + 2w^{3} + 11w^{2} - 2]$ | $...$ |
71 | $[71, 71, -w^{4} + 3w^{3} + 3w^{2} - 9w - 1]$ | $...$ |
73 | $[73, 73, 2w^{4} - 4w^{3} - 9w^{2} + 10w + 5]$ | $...$ |
79 | $[79, 79, 2w^{4} - 3w^{3} - 11w^{2} + 4w + 8]$ | $...$ |
83 | $[83, 83, -3w^{4} + 5w^{3} + 15w^{2} - 9w - 10]$ | $...$ |
89 | $[89, 89, w^{3} - w^{2} - 5w + 1]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 6w - 4]$ | $1$ |