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

• Label: 1728.1.o
• Level: $1728$
• Weight: $1$
• Character orbit: 1728.o
• Rep. character: $\chi_{1728}(127,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• 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.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
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	108	8	100
Cusp forms	36	4	32
Eisenstein series	72	4	68

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	4	0	0

Trace form

\( 4 q + 2 q^{5} + O(q^{10}) \)

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.o.a	$1728$	$1$	1728.o	36.f	$6$	$4$	$2$	$0.862$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{5}q^{11}+\cdots\)

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

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