Space of modular forms of level 3783, weight 1, and Character 3783.ba

• Label: 3783.1.ba
• Level: $3783$
• Weight: $1$
• Character orbit: 3783.ba
• Rep. character: $\chi_{3783}(35,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $457$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3783 = 3 \cdot 13 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3783.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3783 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(457\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3783, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	6	6	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	4	0	0

Trace form

\( 6 q + 2 q^{3} + 6 q^{4} - 4 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3783, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3783.1.ba.a	$3783$	$1$	3783.ba	3783.aa	$6$	$2$	$1$	$1.888$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓			3783.1.ba.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$1$		\(q+q^{3}+q^{4}-\zeta_{6}q^{7}+q^{9}+q^{12}+q^{13}+\cdots\)
3783.1.ba.b	$3783$	$1$	3783.ba	3783.aa	$6$	$4$	$2$	$1.888$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		✓	✓		3783.1.ba.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{12}^{3}q^{3}+q^{4}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{7}+\cdots\)