Space of modular forms of level 3744, weight 1, and Character 3744.dx

• Label: 3744.1.dx
• Level: $3744$
• Weight: $1$
• Character orbit: 3744.dx
• Rep. character: $\chi_{3744}(1889,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $672$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3744.dx (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(672\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3744, [\chi])\).

	Total	New	Old
Modular forms	96	8	88
Cusp forms	32	8	24
Eisenstein series	64	0	64

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

\( 8 q + 8 q^{25} + 12 q^{37} - 4 q^{49} + 4 q^{61}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3744.1.dx.a	$3744$	$1$	3744.dx	39.h	$6$	$8$	$4$	$1.868$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	3744.1.dx.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{24}+\zeta_{24}^{11})q^{5}-\zeta_{24}^{2}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 4}\)