Space of modular forms of level 43, weight 9, and Character 43.b

• Label: 43.9.b
• Level: $43$
• Weight: $9$
• Character orbit: 43.b
• Rep. character: $\chi_{43}(42,\cdot)$
• Character field: $\Q$
• Dimension: $29$
• Newform subspaces: $2$
• Sturm bound: $33$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
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:			\(33\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(43, [\chi])\).

	Total	New	Old
Modular forms	31	31	0
Cusp forms	29	29	0
Eisenstein series	2	2	0

Trace form

\( 29 q - 4028 q^{4} - 1794 q^{6} - 74193 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.9.b.a	$43$	$9$	43.b	43.b	$2$	$1$	$1$	$17.517$	\(\Q\)	\(\Q(\sqrt{-43}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{4}+3^{8}q^{9}+10319q^{11}-54721q^{13}+\cdots\)
43.9.b.b	$43$	$9$	43.b	43.b	$2$	$28$	$28$	$17.517$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$