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

• Label: 2664.1.m
• Level: $2664$
• Weight: $1$
• Character orbit: 2664.m
• Rep. character: $\chi_{2664}(739,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• 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.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 296 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
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	32	14	18
Cusp forms	24	12	12
Eisenstein series	8	2	6

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

\( 12 q + 4 q^{4} + O(q^{10}) \)

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.m.a	$2664$	$1$	2664.m	296.h	$2$	$2$	$2$	$1.330$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-74}) \)	None	✓				296.1.h.a	$2$	$0$	\(-2\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{2}+q^{4}+(1-\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
2664.1.m.b	$2664$	$1$	2664.m	296.h	$2$	$2$	$2$	$1.330$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-74}) \)	None	✓				296.1.h.a	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
2664.1.m.c	$2664$	$1$	2664.m	296.h	$2$	$8$	$8$	$1.330$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-111}) \)	None		✓	✓		2664.1.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+(-\zeta_{16}^{3}+\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2664, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2664, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 2}\)