Space of modular forms of level 729, weight 2, and Character 729.g

• Label: 729.2.g
• Level: $729$
• Weight: $2$
• Character orbit: 729.g
• Rep. character: $\chi_{729}(28,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $576$
• Newform subspaces: $4$
• Sturm bound: $162$
• Trace bound: $20$

Defining parameters

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(162\)
Trace bound:			\(20\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(729, [\chi])\).

	Total	New	Old
Modular forms	1620	720	900
Cusp forms	1296	576	720
Eisenstein series	324	144	180

Trace form

\( 576 q + 36 q^{4} + 36 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(729, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
729.2.g.a	$729$	$2$	729.g	81.g	$27$	$144$	$8$	$5.821$		None					81.2.g.a	$2$	$0$	\(-9\)	\(0\)	\(-9\)	\(9\)		$\mathrm{SU}(2)[C_{27}]$
729.2.g.b	$729$	$2$	729.g	81.g	$27$	$144$	$8$	$5.821$		None					81.2.g.a	$2$	$0$	\(-9\)	\(0\)	\(-9\)	\(9\)		$\mathrm{SU}(2)[C_{27}]$
729.2.g.c	$729$	$2$	729.g	81.g	$27$	$144$	$8$	$5.821$		None					81.2.g.a	$2$	$0$	\(9\)	\(0\)	\(9\)	\(9\)		$\mathrm{SU}(2)[C_{27}]$
729.2.g.d	$729$	$2$	729.g	81.g	$27$	$144$	$8$	$5.821$		None					81.2.g.a	$2$	$0$	\(9\)	\(0\)	\(9\)	\(9\)		$\mathrm{SU}(2)[C_{27}]$

Decomposition of \(S_{2}^{\mathrm{old}}(729, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(729, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 2}\)