Space of modular forms of level 43, weight 4, and Character 43.c

• Label: 43.4.c
• Level: $43$
• Weight: $4$
• Character orbit: 43.c
• Rep. character: $\chi_{43}(6,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(14\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(43, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	20	20	0
Eisenstein series	4	4	0

Trace form

\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.4.c.a	$43$	$4$	43.c	43.c	$3$	$20$	$10$	$2.537$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-5\)	\(-19\)	\(-51\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}+(-\beta _{4}-\beta _{6})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots\)