Space of modular forms of level 43, weight 11, and Character 43.b

• Label: 43.11.b
• Level: $43$
• Weight: $11$
• Character orbit: 43.b
• Rep. character: $\chi_{43}(42,\cdot)$
• Character field: $\Q$
• Dimension: $35$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(43, [\chi])\).

	Total	New	Old
Modular forms	37	37	0
Cusp forms	35	35	0
Eisenstein series	2	2	0

Trace form

\( 35 q - 15132 q^{4} + 12798 q^{6} - 731667 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.11.b.a	$43$	$11$	43.b	43.b	$2$	$1$	$1$	$27.320$	\(\Q\)	\(\Q(\sqrt{-43}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{10}q^{4}+3^{10}q^{9}-18501q^{11}+\cdots\)
43.11.b.b	$43$	$11$	43.b	43.b	$2$	$34$	$34$	$27.320$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$