Space of modular forms of level 1344, weight 2, and Character 1344.c

• Label: 1344.2.c
• Level: $1344$
• Weight: $2$
• Character orbit: 1344.c
• Rep. character: $\chi_{1344}(673,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $8$
• Sturm bound: $512$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(512\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(23\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1344, [\chi])\).

	Total	New	Old
Modular forms	280	24	256
Cusp forms	232	24	208
Eisenstein series	48	0	48

Trace form

\( 24 q - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.2.c.a	$1344$	$2$	1344.c	8.b	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.b	$1344$	$2$	1344.c	8.b	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.c	$1344$	$2$	1344.c	8.b	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
1344.2.c.d	$1344$	$2$	1344.c	8.b	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
1344.2.c.e	$1344$	$2$	1344.c	8.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}-q^{7}+\cdots\)
1344.2.c.f	$1344$	$2$	1344.c	8.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}-q^{7}+\cdots\)
1344.2.c.g	$1344$	$2$	1344.c	8.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+q^{7}+\cdots\)
1344.2.c.h	$1344$	$2$	1344.c	8.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \)