Space of modular forms of level 43, weight 3, and Character 43.d

• Label: 43.3.d
• Level: $43$
• Weight: $3$
• Character orbit: 43.d
• Rep. character: $\chi_{43}(7,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $11$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(11\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(43, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	12	12	0
Eisenstein series	4	4	0

Trace form

\( 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.3.d.a	$43$	$3$	43.d	43.d	$6$	$12$	$6$	$1.172$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(9\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)