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

• Label: 3871.1.m
• Level: $3871$
• Weight: $1$
• Character orbit: 3871.m
• Rep. character: $\chi_{3871}(1500,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $38$
• Newform subspaces: $6$
• Sturm bound: $373$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3871 = 7^{2} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3871.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 553 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(373\)
Trace bound:			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	54	46	8
Cusp forms	38	38	0
Eisenstein series	16	8	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	38	0	0	0

Trace form

38 * q + 2 * q^2 - 17 * q^4 - 8 * q^8 - 19 * q^9 + 2 * q^11 - 15 * q^16 + 2 * q^18 - 8 * q^22 + 2 * q^23 - 17 * q^25 + 6 * q^32 + 34 * q^36 + 6 * q^44 + 4 * q^46 - 12 * q^50 + 26 * q^64 + 4 * q^65 + 2 * q^67 + 4 * q^72 + q^79 - 19 * q^81 + 8 * q^88 - 12 * q^92 + 4 * q^95 - 4 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3871.1.m.a	$3871$	$1$	3871.m	553.m	$6$	$2$	$1$	$1.932$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-79}) \)	\(\Q(\sqrt{553}) \)		✓			3871.1.c.a	$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+3\zeta_{6}^{2}q^{4}-2q^{8}-\zeta_{6}q^{9}+\cdots\)
3871.1.m.b	$3871$	$1$	3871.m	553.m	$6$	$4$	$2$	$1.932$	\(\Q(\sqrt{-3}, \sqrt{5})\)	$D_{5}$	\(\Q(\sqrt{-79}) \)	None					79.1.b.a	$4$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
3871.1.m.c	$3871$	$1$	3871.m	553.m	$6$	$4$	$2$	$1.932$	\(\Q(\sqrt{-3}, \sqrt{5})\)	$D_{5}$	\(\Q(\sqrt{-79}) \)	None					79.1.b.a	$4$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
3871.1.m.d	$3871$	$1$	3871.m	553.m	$6$	$4$	$2$	$1.932$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-79}) \)	None		✓			3871.1.c.b	$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q-2\beta _{2}q^{2}+(-3-3\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
3871.1.m.e	$3871$	$1$	3871.m	553.m	$6$	$8$	$4$	$1.932$	8.0.324000000.2	$D_{10}$	\(\Q(\sqrt{-79}) \)	None		✓			3871.1.c.d	$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\beta _{2}+\beta _{6})q^{2}+\beta _{6}q^{4}+(-\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
3871.1.m.f	$3871$	$1$	3871.m	553.m	$6$	$16$	$8$	$1.932$	16.0.\(\cdots\).5	$D_{20}$	\(\Q(\sqrt{-79}) \)	None		✓	✓		3871.1.c.e	$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{7}-\beta _{8})q^{4}+\cdots\)