Space of modular forms of level 4, weight 11, and Character 4.b

• Label: 4.11.b
• Level: $4$
• Weight: $11$
• Character orbit: 4.b
• Rep. character: $\chi_{4}(3,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
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:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(4, [\chi])\).

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

Trace form

\( 4 q - 12 q^{2} + 16 q^{4} - 1560 q^{5} + 7200 q^{6} - 36288 q^{8} - 28764 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(4, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.11.b.a	$4$	$11$	4.b	4.b	$2$	$4$	$4$	$2.541$	4.0.26777625.2	None		$2$	$0$	\(-12\)	\(0\)	\(-1560\)	\(0\)	$2^{12}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3+\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots\)