Space of modular forms of level 243, weight 2, and Character 243.g

• Label: 243.2.g
• Level: $243$
• Weight: $2$
• Character orbit: 243.g
• Rep. character: $\chi_{243}(10,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $54$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(54\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(243, [\chi])\).

	Total	New	Old
Modular forms	540	180	360
Cusp forms	432	144	288
Eisenstein series	108	36	72

Trace form

\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(243, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
243.2.g.a	$243$	$2$	243.g	81.g	$27$	$144$	$8$	$1.940$		None			✓	✓	81.2.g.a	$2$	$0$	\(18\)	\(0\)	\(18\)	\(-18\)		$\mathrm{SU}(2)[C_{27}]$

Decomposition of \(S_{2}^{\mathrm{old}}(243, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(243, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)