Space of modular forms of level 8, weight 6, and trivial character

• 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: $0$

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

\( q + 20 q^{3} - 74 q^{5} - 24 q^{7} + 157 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
8.6.a.a	$8$	$6$	8.a	1.a	$1$	$1$	$1$	$1.283$	\(\Q\)	None	✓	✓	✓	✓	8.6.a.a	$1$	$0$	\(0\)	\(20\)	\(-74\)	\(-24\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)

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

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