Space of modular forms of level 1344, weight 1, and Character 1344.e

• Label: 1344.1.e
• Level: $1344$
• Weight: $1$
• Character orbit: 1344.e
• Rep. character: $\chi_{1344}(671,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $256$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1344.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 168 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(256\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1344, [\chi])\).

	Total	New	Old
Modular forms	32	8	24
Cusp forms	8	8	0
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.1.e.a	$1344$	$1$	1344.e	168.e	$2$	$2$	$2$	$0.671$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{21}) \)		$8$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-q^{3}-iq^{5}-iq^{7}+q^{9}+2iq^{15}+\cdots\)
1344.1.e.b	$1344$	$1$	1344.e	168.e	$2$	$2$	$2$	$0.671$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{42}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{3}-iq^{7}-q^{9}-q^{13}-iq^{19}+\cdots\)
1344.1.e.c	$1344$	$1$	1344.e	168.e	$2$	$2$	$2$	$0.671$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{42}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{3}-iq^{7}-q^{9}+q^{13}+iq^{19}+\cdots\)
1344.1.e.d	$1344$	$1$	1344.e	168.e	$2$	$2$	$2$	$0.671$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{21}) \)		$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{3}-iq^{5}+iq^{7}+q^{9}-2iq^{15}+\cdots\)