Space of modular forms of level 3871, weight 1, and Character 3871.c

• Label: 3871.1.c
• Level: $3871$
• Weight: $1$
• Character orbit: 3871.c
• Rep. character: $\chi_{3871}(2843,\cdot)$
• Character field: $\Q$
• Dimension: $17$
• Newform subspaces: $5$
• Sturm bound: $373$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3871 = 7^{2} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3871.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(373\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3871, [\chi])\).

	Total	New	Old
Modular forms	31	22	9
Cusp forms	23	17	6
Eisenstein series	8	5	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	17	0	0	0

Trace form

\( 17 q - q^{2} + 16 q^{4} + q^{5} - 2 q^{8} + 17 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3871, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3871.1.c.a	$3871$	$1$	3871.c	79.b	$2$	$1$	$1$	$1.932$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-79}) \)	\(\Q(\sqrt{553}) \)	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+2q^{2}+3q^{4}+4q^{8}+q^{9}-2q^{11}+\cdots\)
3871.1.c.b	$3871$	$1$	3871.c	79.b	$2$	$2$	$2$	$1.932$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-79}) \)	None	✓	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-2q^{2}+3q^{4}-\beta q^{5}-4q^{8}+q^{9}+\cdots\)
3871.1.c.c	$3871$	$1$	3871.c	79.b	$2$	$2$	$2$	$1.932$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-79}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\beta q^{2}+\beta q^{4}+(1-\beta )q^{5}-q^{8}+q^{9}+\cdots\)
3871.1.c.d	$3871$	$1$	3871.c	79.b	$2$	$4$	$4$	$1.932$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-79}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-1-\beta _{2})q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
3871.1.c.e	$3871$	$1$	3871.c	79.b	$2$	$8$	$8$	$1.932$	\(\Q(\zeta_{40})^+\)	$D_{20}$	\(\Q(\sqrt{-79}) \)	None	✓	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{4}q^{2}-\beta _{4}q^{4}+\beta _{7}q^{5}+q^{8}+q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3871, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3871, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(553, [\chi])\)\(^{\oplus 2}\)