Space of modular forms of level 243, weight 1, and Character 243.b

• Label: 243.1.b
• Level: $243$
• Weight: $1$
• Character orbit: 243.b
• Rep. character: $\chi_{243}(242,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	243.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(243, [\chi])\).

	Total	New	Old
Modular forms	10	1	9
Cusp forms	1	1	0
Eisenstein series	9	0	9

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	0	0

Trace form

\( q + q^{4} - q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(243, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
243.1.b.a	$243$	$1$	243.b	3.b	$2$	$1$	$1$	$0.121$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+q^{4}-q^{7}-q^{13}+q^{16}-q^{19}+q^{25}+\cdots\)