Space of modular forms of level 3724, weight 1, and Character 3724.n

• Label: 3724.1.n
• Level: $3724$
• Weight: $1$
• Character orbit: 3724.n
• Rep. character: $\chi_{3724}(1831,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $560$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3724.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 532 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(560\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3724, [\chi])\).

	Total	New	Old
Modular forms	44	20	24
Cusp forms	12	4	8
Eisenstein series	32	16	16

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

\( 4 q + 2 q^{4} - 2 q^{6} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3724, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3724.1.n.a	$3724$	$1$	3724.n	532.n	$6$	$4$	$2$	$1.859$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3724, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3724, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)