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

• Label: 243.2.e
• Level: $243$
• Weight: $2$
• Character orbit: 243.e
• Rep. character: $\chi_{243}(28,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $54$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(54\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	216	96	120
Cusp forms	108	48	60
Eisenstein series	108	48	60

Trace form

\( 48 q + 12 q^{4} + 12 q^{7} + O(q^{10}) \)

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.e.a	$243$	$2$	243.e	27.e	$9$	$12$	$2$	$1.940$	12.0.\(\cdots\).1	None					27.2.e.a	$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{2}-\beta _{8}-\beta _{11})q^{2}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
243.2.e.b	$243$	$2$	243.e	27.e	$9$	$12$	$2$	$1.940$	12.0.\(\cdots\).1	None					27.2.e.a	$2$	$0$	\(-3\)	\(0\)	\(3\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{4}+\beta _{8}-\beta _{9})q^{2}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
243.2.e.c	$243$	$2$	243.e	27.e	$9$	$12$	$2$	$1.940$	12.0.\(\cdots\).1	None					27.2.e.a	$2$	$0$	\(3\)	\(0\)	\(-3\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\beta _{5}-\beta _{8}+\beta _{9}-\beta _{11})q^{2}+(\beta _{1}+\cdots)q^{4}+\cdots\)
243.2.e.d	$243$	$2$	243.e	27.e	$9$	$12$	$2$	$1.940$	12.0.\(\cdots\).1	None					27.2.e.a	$2$	$0$	\(3\)	\(0\)	\(6\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{2}+\beta _{8}+\beta _{11})q^{2}+(-1-\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(243, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)