Space of modular forms of level 3888, weight 1, and Character 3888.o

• Label: 3888.1.o
• Level: $3888$
• Weight: $1$
• Character orbit: 3888.o
• Rep. character: $\chi_{3888}(1135,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $6$
• Sturm bound: $648$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 3888 = 2^{4} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3888.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(648\)
Trace bound:			\(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3888, [\chi])\).

	Total	New	Old
Modular forms	164	12	152
Cusp forms	56	12	44
Eisenstein series	108	0	108

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q + 6 q^{25} + 6 q^{49}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3888, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3888.1.o.a	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3888.1.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$1$		\(q+(-1+\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(-\zeta_{6}+\cdots)q^{19}+\cdots\)
3888.1.o.b	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3888.1.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$1$		\(q+(-1+\zeta_{6}^{2})q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+\cdots\)
3888.1.o.c	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3888.1.g.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{19}+\zeta_{6}q^{25}+\cdots\)
3888.1.o.d	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3888.1.g.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{13}+(-\zeta_{6}-\zeta_{6}^{2})q^{19}+\zeta_{6}q^{25}+\cdots\)
3888.1.o.e	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3888.1.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
3888.1.o.f	$3888$	$1$	3888.o	36.f	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3888.1.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$1$		\(q+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3888, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3888, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)