Space of modular forms of level 3891, weight 1, and Character 3891.i

• Label: 3891.1.i
• Level: $3891$
• Weight: $1$
• Character orbit: 3891.i
• Rep. character: $\chi_{3891}(365,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $432$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3891 = 3 \cdot 1297 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3891.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3891 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(432\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3891, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

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

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

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(3891, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3891.1.i.a	$3891$	$1$	3891.i	3891.i	$6$	$2$	$1$	$1.942$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓			3891.1.i.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
3891.1.i.b	$3891$	$1$	3891.i	3891.i	$6$	$4$	$2$	$1.942$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		✓	✓		3891.1.i.b	$4$	$0$	\(0\)	\(2\)	\(0\)	\(2\)	$1$		\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)