Space of modular forms of level 43, weight 2, and Character 43.g

• Label: 43.2.g
• Level: $43$
• Weight: $2$
• Character orbit: 43.g
• Rep. character: $\chi_{43}(9,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(7\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(43, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	36	36	0
Eisenstein series	24	24	0

Trace form

\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.2.g.a	$43$	$2$	43.g	43.g	$21$	$36$	$3$	$0.343$		None		$2$	$0$	\(-10\)	\(-16\)	\(-17\)	\(6\)		$\mathrm{SU}(2)[C_{21}]$