Space of modular forms of level 43, weight 10, and Character 43.g

• Label: 43.10.g
• Level: $43$
• Weight: $10$
• Character orbit: 43.g
• Rep. character: $\chi_{43}(9,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $384$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(43, [\chi])\).

	Total	New	Old
Modular forms	408	408	0
Cusp forms	384	384	0
Eisenstein series	24	24	0

Trace form

\( 384 q + 56 q^{2} - 321 q^{3} - 16052 q^{4} - 695 q^{5} + 1274 q^{6} + 32650 q^{7} - 50022 q^{8} + 373611 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.10.g.a	$43$	$10$	43.g	43.g	$21$	$384$	$32$	$22.147$		None		$2$	$0$	\(56\)	\(-321\)	\(-695\)	\(32650\)		$\mathrm{SU}(2)[C_{21}]$