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

• Label: 1728.1.b
• Level: $1728$
• Weight: $1$
• Character orbit: 1728.b
• Rep. character: $\chi_{1728}(1567,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1728.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(25\)

Dimensions

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

	Total	New	Old
Modular forms	48	8	40
Cusp forms	12	8	4
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	8	0	0	0

Trace form

\( 8 q + O(q^{10}) \)

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.b.a	$1728$	$1$	1728.b	8.d	$2$	$4$	$4$	$0.862$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-6}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1728.1.b.b	$1728$	$1$	1728.b	8.d	$2$	$4$	$4$	$0.862$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q-\zeta_{12}^{3}q^{7}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1728, [\chi]) \cong \)