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

• Label: 3888.1.q
• Level: $3888$
• Weight: $1$
• Character orbit: 3888.q
• Rep. character: $\chi_{3888}(161,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $648$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3888 = 2^{4} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3888.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(648\)
Trace bound:			\(13\)

Dimensions

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

	Total	New	Old
Modular forms	164	10	154
Cusp forms	56	10	46
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	6	0	4	0

Trace form

\( 10 q - 2 q^{13} + 4 q^{19} - q^{25} - 5 q^{31} - q^{43} - q^{49} + 8 q^{55} - 2 q^{61} - 2 q^{67} + 4 q^{73} + 2 q^{79} - 4 q^{85} + 6 q^{91} + 2 q^{97}+O(q^{100}) \)

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.q.a	$3888$	$1$	3888.q	9.d	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					972.1.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{13}-q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
3888.1.q.b	$3888$	$1$	3888.q	9.d	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					243.1.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
3888.1.q.c	$3888$	$1$	3888.q	9.d	$6$	$2$	$1$	$1.940$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None					972.1.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
3888.1.q.d	$3888$	$1$	3888.q	9.d	$6$	$4$	$2$	$1.940$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None			✓		1944.1.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3888, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1944, [\chi])\)\(^{\oplus 2}\)