Properties

Label 8.6.a
Level $8$
Weight $6$
Character orbit 8.a
Rep. character $\chi_{8}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 8.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(8))\).

Total New Old
Modular forms 7 1 6
Cusp forms 3 1 2
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim.
\(-\)\(1\)

Trace form

\( q + 20 q^{3} - 74 q^{5} - 24 q^{7} + 157 q^{9} + O(q^{10}) \) \( q + 20 q^{3} - 74 q^{5} - 24 q^{7} + 157 q^{9} + 124 q^{11} + 478 q^{13} - 1480 q^{15} - 1198 q^{17} + 3044 q^{19} - 480 q^{21} + 184 q^{23} + 2351 q^{25} - 1720 q^{27} - 3282 q^{29} - 5728 q^{31} + 2480 q^{33} + 1776 q^{35} + 10326 q^{37} + 9560 q^{39} - 8886 q^{41} - 9188 q^{43} - 11618 q^{45} + 23664 q^{47} - 16231 q^{49} - 23960 q^{51} + 11686 q^{53} - 9176 q^{55} + 60880 q^{57} + 16876 q^{59} - 18482 q^{61} - 3768 q^{63} - 35372 q^{65} - 15532 q^{67} + 3680 q^{69} - 31960 q^{71} - 4886 q^{73} + 47020 q^{75} - 2976 q^{77} + 44560 q^{79} - 72551 q^{81} + 67364 q^{83} + 88652 q^{85} - 65640 q^{87} + 71994 q^{89} - 11472 q^{91} - 114560 q^{93} - 225256 q^{95} + 48866 q^{97} + 19468 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(8))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
8.6.a.a 8.a 1.a $1$ $1.283$ \(\Q\) None \(0\) \(20\) \(-74\) \(-24\) $-$ $\mathrm{SU}(2)$ \(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)