Space of modular forms of level 4, weight 7, and Character 4.b

• Label: 4.7.b
• Level: $4$
• Weight: $7$
• Character orbit: 4.b
• Rep. character: $\chi_{4}(3,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(4, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

\( 2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.7.b.a	$4$	$7$	4.b	4.b	$2$	$2$	$2$	$0.920$	\(\Q(\sqrt{-15}) \)	None		$2$	$0$	\(4\)	\(0\)	\(20\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots\)