Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[31, 31, w^{2} - w - 8]$ |
Dimension: | $25$ |
CM: | no |
Base change: | no |
Newspace dimension: | $59$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{25} - x^{24} - 71x^{23} + 84x^{22} + 2135x^{21} - 2893x^{20} - 35579x^{19} + 54260x^{18} + 359657x^{17} - 613930x^{16} - 2255633x^{15} + 4348134x^{14} + 8512119x^{13} - 19208563x^{12} - 17074590x^{11} + 50641475x^{10} + 9795370x^{9} - 71486921x^{8} + 19540613x^{7} + 41242839x^{6} - 25750511x^{5} - 1822618x^{4} + 5139140x^{3} - 1526080x^{2} + 178864x - 7456\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -w - 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 2]$ | $...$ |
7 | $[7, 7, w + 3]$ | $...$ |
7 | $[7, 7, -w + 2]$ | $...$ |
7 | $[7, 7, -w + 1]$ | $...$ |
8 | $[8, 2, 2]$ | $...$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $...$ |
19 | $[19, 19, -w^{2} + 5]$ | $...$ |
23 | $[23, 23, -w^{2} - w + 3]$ | $...$ |
27 | $[27, 3, 3]$ | $...$ |
29 | $[29, 29, w^{2} - w - 3]$ | $...$ |
31 | $[31, 31, w^{2} - w - 8]$ | $-1$ |
37 | $[37, 37, -w - 4]$ | $...$ |
43 | $[43, 43, 2w^{2} - 4w - 3]$ | $...$ |
47 | $[47, 47, w^{2} - 3]$ | $...$ |
53 | $[53, 53, 2w^{2} - w - 11]$ | $...$ |
59 | $[59, 59, w^{2} - 2w - 4]$ | $...$ |
67 | $[67, 67, w^{2} + w - 8]$ | $...$ |
71 | $[71, 71, w^{2} + w - 11]$ | $...$ |
73 | $[73, 73, -w^{2} + 4w - 2]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, w^{2} - w - 8]$ | $1$ |