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

• Label: 3891.1.c
• Level: $3891$
• Weight: $1$
• Character orbit: 3891.c
• Rep. character: $\chi_{3891}(3890,\cdot)$
• Character field: $\Q$
• Dimension: $21$
• Newform subspaces: $7$
• Sturm bound: $432$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3891 = 3 \cdot 1297 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3891.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3891 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(432\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	23	23	0
Cusp forms	21	21	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	21	0	0	0

Trace form

\( 21 q - 2 q^{3} - q^{4} - 4 q^{7} + 10 q^{9} + O(q^{10}) \)

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	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3891.1.c.a	$3891$	$1$	3891.c	3891.c	$2$	$1$	$1$	$1.942$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3891}) \)	None	✓	✓	3891.1.c.a	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
3891.1.c.b	$3891$	$1$	3891.c	3891.c	$2$	$1$	$1$	$1.942$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3891}) \)	\(\Q(\sqrt{1297}) \)	✓	✓	3891.1.c.b	$4$	$0$	\(0\)	\(1\)	\(0\)	\(2\)	$1$		\(q+q^{3}+q^{4}+2q^{7}+q^{9}+q^{12}-2q^{13}+\cdots\)
3891.1.c.c	$3891$	$1$	3891.c	3891.c	$2$	$1$	$1$	$1.942$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3891}) \)	None	✓	✓	3891.1.c.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)	$1$		\(q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
3891.1.c.d	$3891$	$1$	3891.c	3891.c	$2$	$2$	$2$	$1.942$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-3891}) \)	None	✓	✓	3891.1.c.d	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)	$1$		\(q-q^{3}+q^{4}-\beta q^{5}-2q^{7}+q^{9}-\beta q^{11}+\cdots\)
3891.1.c.e	$3891$	$1$	3891.c	3891.c	$2$	$2$	$2$	$1.942$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-3891}) \)	None	✓	✓	3891.1.c.e	$4$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$1$		\(q+q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}+\beta q^{11}+\cdots\)
3891.1.c.f	$3891$	$1$	3891.c	3891.c	$2$	$4$	$4$	$1.942$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-3891}) \)	None	✓	✓	3891.1.c.f	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$1$		\(q-q^{3}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)
3891.1.c.g	$3891$	$1$	3891.c	3891.c	$2$	$10$	$10$	$1.942$	\(\Q(\zeta_{22})\)	$D_{22}$	None	\(\Q(\sqrt{1297}) \)		✓	3891.1.c.g	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q+(-\zeta_{22}-\zeta_{22}^{10})q^{2}-\zeta_{22}^{5}q^{3}+\cdots\)