Space of modular forms of level 4, weight 6, and trivial character

• Label: 4.6.a
• Level: $4$
• Weight: $6$
• Character orbit: 4.a
• Rep. character: $\chi_{4}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	4.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(4))\).

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

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

\( q - 12 q^{3} + 54 q^{5} - 88 q^{7} - 99 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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
4.6.a.a	$4$	$6$	4.a	1.a	$1$	$1$	$1$	$0.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-12\)	\(54\)	\(-88\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)