Space of modular forms of level 2664, weight 1, and Character 2664.bw

• Label: 2664.1.bw
• Level: $2664$
• Weight: $1$
• Character orbit: 2664.bw
• Rep. character: $\chi_{2664}(1627,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $456$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2664.bw (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2664 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(456\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2664, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q - 10 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2664, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2664.1.bw.a	$2664$	$1$	2664.bw	2664.aw	$6$	$2$	$1$	$1.330$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-74}) \)	None		✓			2664.1.bw.a	$4$	$0$	\(-1\)	\(2\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\)
2664.1.bw.b	$2664$	$1$	2664.bw	2664.aw	$6$	$2$	$1$	$1.330$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-74}) \)	None		✓			2664.1.bw.a	$4$	$0$	\(1\)	\(2\)	\(2\)	\(0\)	$1$		\(q+\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
2664.1.bw.c	$2664$	$1$	2664.bw	2664.aw	$6$	$8$	$4$	$1.330$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-74}) \)	None		✓			2664.1.bw.c	$4$	$0$	\(-4\)	\(-2\)	\(2\)	\(0\)	$1$		\(q+\zeta_{30}^{10}q^{2}+\zeta_{30}^{12}q^{3}-\zeta_{30}^{5}q^{4}+\cdots\)
2664.1.bw.d	$2664$	$1$	2664.bw	2664.aw	$6$	$8$	$4$	$1.330$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-74}) \)	None		✓			2664.1.bw.c	$4$	$0$	\(4\)	\(-2\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{30}^{10}q^{2}+\zeta_{30}^{12}q^{3}-\zeta_{30}^{5}q^{4}+\cdots\)