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

• Label: 4.43.b
• Level: $4$
• Weight: $43$
• Character orbit: 4.b
• Rep. character: $\chi_{4}(3,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 43 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	22	22	0
Cusp forms	20	20	0
Eisenstein series	2	2	0

Trace form

\( 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 6838718638036512 q^{6} - 27661415389266953664 q^{8} - 733170595646091132876 q^{9} + O(q^{10}) \)

Decomposition of \(S_{43}^{\mathrm{new}}(4, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.43.b.a	$4$	$43$	4.b	4.b	$2$	$20$	$20$	$44.691$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(802164\)	\(0\)	\(13\!\cdots\!00\)	\(0\)	$2^{380}\cdot 3^{41}\cdot 5^{10}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(40108+\beta _{1})q^{2}+(2^{4}-78\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)