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

• Label: 243.2.c
• Level: $243$
• Weight: $2$
• Character orbit: 243.c
• Rep. character: $\chi_{243}(82,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $54$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(54\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	72	24	48
Cusp forms	36	24	12
Eisenstein series	36	0	36

Trace form

\( 24 q - 12 q^{4} + 3 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
243.2.c.a	$243$	$2$	243.c	9.c	$3$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{4}+(-5+5\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
243.2.c.b	$243$	$2$	243.c	9.c	$3$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{4}+(4-4\zeta_{6})q^{7}+7\zeta_{6}q^{13}+\cdots\)
243.2.c.c	$243$	$2$	243.c	9.c	$3$	$4$	$2$	$1.940$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-4+4\beta _{1})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
243.2.c.d	$243$	$2$	243.c	9.c	$3$	$4$	$2$	$1.940$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
243.2.c.e	$243$	$2$	243.c	9.c	$3$	$6$	$3$	$1.940$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\cdots)q^{4}+\cdots\)
243.2.c.f	$243$	$2$	243.c	9.c	$3$	$6$	$3$	$1.940$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(3\)	\(0\)	\(6\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)

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

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