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

• Label: 3744.1.eh
• Level: $3744$
• Weight: $1$
• Character orbit: 3744.eh
• Rep. character: $\chi_{3744}(883,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $16$
• 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.eh (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 416 \)
Character field:			\(\Q(\zeta_{8})\)
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	48	24	24
Cusp forms	16	16	0
Eisenstein series	32	8	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3744.1.eh.a	$3744$	$1$	3744.eh	416.ae	$8$	$16$	$4$	$1.868$	\(\Q(\zeta_{32})\)	$D_{16}$	\(\Q(\sqrt{-39}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{6}q^{4}+(-\zeta_{32}-\zeta_{32}^{11}+\cdots)q^{5}+\cdots\)