Space of modular forms of level 1728, weight 1, and Character 1728.g

• Label: 1728.1.g
• Level: $1728$
• Weight: $1$
• Character orbit: 1728.g
• Rep. character: $\chi_{1728}(703,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1728.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1728, [\chi])\).

	Total	New	Old
Modular forms	52	2	50
Cusp forms	16	2	14
Eisenstein series	36	0	36

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1728, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1728.1.g.a	$1728$	$1$	1728.g	4.b	$2$	$2$	$2$	$0.862$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 2}\)