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

• Label: 3744.1.gs
• Level: $3744$
• Weight: $1$
• Character orbit: 3744.gs
• Rep. character: $\chi_{3744}(865,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $672$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3744.gs (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(672\)
Trace bound:			\(17\)

Dimensions

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

	Total	New	Old
Modular forms	176	12	164
Cusp forms	48	12	36
Eisenstein series	128	0	128

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + 2 q^{5} - 6 q^{37} + 4 q^{41} - 4 q^{53} - 6 q^{61} + 4 q^{65} + 2 q^{73} - 10 q^{85} - 2 q^{89} + 2 q^{97}+O(q^{100}) \)

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.gs.a	$3744$	$1$	3744.gs	13.f	$12$	$4$	$1$	$1.868$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None		✓			3744.1.gs.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(\zeta_{12}-\zeta_{12}^{2})q^{5}-\zeta_{12}q^{13}+(1-\zeta_{12}^{4}+\cdots)q^{17}+\cdots\)
3744.1.gs.b	$3744$	$1$	3744.gs	13.f	$12$	$4$	$1$	$1.868$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None		✓			3744.1.gs.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}q^{13}+(-1+\cdots)q^{17}+\cdots\)
3744.1.gs.c	$3744$	$1$	3744.gs	13.f	$12$	$4$	$1$	$1.868$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None					416.1.bl.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(-\zeta_{12}^{4}-\zeta_{12}^{5})q^{5}+\zeta_{12}q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3744, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1872, [\chi])\)\(^{\oplus 2}\)