Space of modular forms of level 3887, weight 1, and Character 3887.j

• Label: 3887.1.j
• Level: $3887$
• Weight: $1$
• Character orbit: 3887.j
• Rep. character: $\chi_{3887}(2851,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $364$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3887 = 13^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3887.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 299 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(364\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3887, [\chi])\).

	Total	New	Old
Modular forms	72	52	20
Cusp forms	44	32	12
Eisenstein series	28	20	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q + 2 q^{3} + 10 q^{4} + 9 q^{6} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3887, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3887.1.j.a	$3887$	$1$	3887.j	299.j	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-23}) \)	None			299.1.c.c	$4$	$0$	\(-3\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+(-1+\zeta_{6}^{2})q^{2}-\zeta_{6}q^{3}+(1-\zeta_{6}+\cdots)q^{4}+\cdots\)
3887.1.j.b	$3887$	$1$	3887.j	299.j	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-299}) \)	\(\Q(\sqrt{13}) \)			299.1.c.a	$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+3\zeta_{6}^{2}q^{9}-2q^{12}+\cdots\)
3887.1.j.c	$3887$	$1$	3887.j	299.j	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-23}) \)	None			299.1.c.c	$4$	$0$	\(3\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+(1-\zeta_{6}^{2})q^{2}-\zeta_{6}q^{3}+(1-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
3887.1.j.d	$3887$	$1$	3887.j	299.j	$6$	$4$	$2$	$1.940$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-299}) \)	None			299.1.c.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-1-\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots\)
3887.1.j.e	$3887$	$1$	3887.j	299.j	$6$	$4$	$2$	$1.940$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-23}) \)	None			23.1.b.a	$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{6}+\zeta_{12}^{3}q^{8}+\cdots\)
3887.1.j.f	$3887$	$1$	3887.j	299.j	$6$	$6$	$3$	$1.940$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-23}) \)	None			299.1.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{18}+\zeta_{18}^{2})q^{2}+(-\zeta_{18}^{4}-\zeta_{18}^{8}+\cdots)q^{3}+\cdots\)
3887.1.j.g	$3887$	$1$	3887.j	299.j	$6$	$12$	$6$	$1.940$	\(\Q(\zeta_{36})\)	$D_{9}$	\(\Q(\sqrt{-23}) \)	None			299.1.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$		\(q+(-\zeta_{36}^{11}+\zeta_{36}^{13})q^{2}+(\zeta_{36}^{8}+\zeta_{36}^{16}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3887, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3887, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(299, [\chi])\)\(^{\oplus 2}\)