Base field 3.3.697.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[31, 31, w^{2} - 2w - 8]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} - 48x^{8} + 812x^{6} - 5552x^{4} + 11904x^{2} - 512\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $-\frac{5}{1856}e^{8} + \frac{3}{29}e^{6} - \frac{531}{464}e^{4} + \frac{333}{116}e^{2} + \frac{107}{29}$ |
11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{3}{928}e^{8} - \frac{23}{232}e^{6} + \frac{191}{232}e^{4} - \frac{39}{29}e^{2} + \frac{34}{29}$ |
11 | $[11, 11, -w + 2]$ | $-\frac{1}{464}e^{9} + \frac{71}{928}e^{7} - \frac{195}{232}e^{5} + \frac{759}{232}e^{3} - \frac{403}{58}e$ |
11 | $[11, 11, w - 1]$ | $-\frac{5}{3712}e^{9} + \frac{77}{928}e^{7} - \frac{1575}{928}e^{5} + \frac{1515}{116}e^{3} - \frac{1575}{58}e$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $-\frac{5}{3712}e^{9} + \frac{3}{58}e^{7} - \frac{647}{928}e^{5} + \frac{971}{232}e^{3} - \frac{309}{29}e$ |
17 | $[17, 17, -w^{2} + w + 8]$ | $\phantom{-}\frac{11}{928}e^{8} - \frac{47}{116}e^{6} + \frac{913}{232}e^{4} - \frac{489}{58}e^{2} - \frac{30}{29}$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $-\frac{9}{1856}e^{9} + \frac{167}{928}e^{7} - \frac{979}{464}e^{5} + \frac{1947}{232}e^{3} - \frac{595}{58}e$ |
19 | $[19, 19, -w^{2} + 6]$ | $-\frac{1}{928}e^{9} + \frac{21}{928}e^{7} + \frac{33}{232}e^{5} - \frac{1085}{232}e^{3} + \frac{1089}{58}e$ |
23 | $[23, 23, -w^{2} + 3]$ | $\phantom{-}\frac{5}{3712}e^{9} - \frac{3}{58}e^{7} + \frac{531}{928}e^{5} - \frac{333}{232}e^{3} - \frac{39}{29}e$ |
25 | $[25, 5, w^{2} - 7]$ | $\phantom{-}\frac{1}{1856}e^{9} - \frac{27}{464}e^{7} + \frac{721}{464}e^{5} - \frac{1621}{116}e^{3} + \frac{895}{29}e$ |
27 | $[27, 3, -3]$ | $\phantom{-}\frac{1}{116}e^{8} - \frac{71}{232}e^{6} + \frac{195}{58}e^{4} - \frac{643}{58}e^{2} - \frac{6}{29}$ |
31 | $[31, 31, w^{2} - 2w - 8]$ | $\phantom{-}1$ |
37 | $[37, 37, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{464}e^{8} - \frac{25}{232}e^{6} + \frac{199}{116}e^{4} - \frac{545}{58}e^{2} + \frac{332}{29}$ |
41 | $[41, 41, -w - 4]$ | $-\frac{3}{928}e^{8} + \frac{23}{232}e^{6} - \frac{191}{232}e^{4} + \frac{10}{29}e^{2} + \frac{256}{29}$ |
41 | $[41, 41, w^{2} - 2w - 7]$ | $-\frac{21}{1856}e^{8} + \frac{95}{232}e^{6} - \frac{2091}{464}e^{4} + \frac{1677}{116}e^{2} - \frac{32}{29}$ |
47 | $[47, 47, 2w^{2} - 3w - 7]$ | $-\frac{5}{1856}e^{9} + \frac{125}{928}e^{7} - \frac{1111}{464}e^{5} + \frac{3885}{232}e^{3} - \frac{1787}{58}e$ |
53 | $[53, 53, -w^{2} + w + 9]$ | $\phantom{-}\frac{17}{1856}e^{8} - \frac{35}{116}e^{6} + \frac{1179}{464}e^{4} - \frac{123}{116}e^{2} - \frac{242}{29}$ |
61 | $[61, 61, 3w^{2} - 2w - 17]$ | $\phantom{-}\frac{31}{3712}e^{9} - \frac{315}{928}e^{7} + \frac{4313}{928}e^{5} - \frac{717}{29}e^{3} + \frac{2573}{58}e$ |
67 | $[67, 67, 2w - 1]$ | $\phantom{-}\frac{3}{1856}e^{9} - \frac{23}{464}e^{7} + \frac{133}{464}e^{5} + \frac{53}{29}e^{3} - \frac{215}{29}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$31$ | $[31, 31, w^{2} - 2w - 8]$ | $-1$ |