Properties

Label 3.3.697.1-31.1-c
Base field 3.3.697.1
Weight $[2, 2, 2]$
Level norm $31$
Level $[31, 31, w^{2} - 2w - 8]$
Dimension $10$
CM no
Base change no

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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 $[67, 67, 2w - 1]$ $\phantom{-}\frac{3}{1856}e^{9} - \frac{23}{464}e^{7} + \frac{133}{464}e^{5} + \frac{53}{29}e^{3} - \frac{215}{29}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, w^{2} - 2w - 8]$ $-1$