Space of modular forms of level 3864, weight 1, and Character 3864.cx

• Label: 3864.1.cx
• Level: $3864$
• Weight: $1$
• Character orbit: 3864.cx
• Rep. character: $\chi_{3864}(125,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $768$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3864.cx (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3864 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(768\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3864, [\chi])\).

	Total	New	Old
Modular forms	160	160	0
Cusp forms	80	80	0
Eisenstein series	80	80	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	80	0	0	0

Trace form

\( 80 q + 8 q^{4} - 8 q^{16} - 36 q^{18} - 8 q^{25} - 44 q^{30} - 8 q^{39} + 8 q^{49} + 8 q^{64} - 8 q^{72} + 8 q^{78} - 36 q^{81}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3864, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3864.1.cx.a	$3864$	$1$	3864.cx	3864.bx	$22$	$40$	$4$	$1.928$	\(\Q(\zeta_{88})\)	$D_{44}$	\(\Q(\sqrt{-14}) \)	None		✓			3864.1.cx.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{88}^{42}q^{2}-\zeta_{88}^{23}q^{3}-\zeta_{88}^{40}q^{4}+\cdots\)
3864.1.cx.b	$3864$	$1$	3864.cx	3864.bx	$22$	$40$	$4$	$1.928$	\(\Q(\zeta_{88})\)	$D_{44}$	\(\Q(\sqrt{-14}) \)	None		✓			3864.1.cx.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{88}^{6}q^{2}-\zeta_{88}^{11}q^{3}+\zeta_{88}^{12}q^{4}+\cdots\)