Space of modular forms of level 1344, weight 4, and Character 1344.p

• Label: 1344.4.p
• Level: $1344$
• Weight: $4$
• Character orbit: 1344.p
• Rep. character: $\chi_{1344}(223,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $1024$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1344.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1024\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1344, [\chi])\).

	Total	New	Old
Modular forms	792	96	696
Cusp forms	744	96	648
Eisenstein series	48	0	48

Trace form

\( 96 q - 864 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1344, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.4.p.a	$1344$	$4$	1344.p	56.e	$2$	$16$	$16$	$79.299$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{17}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}-\beta _{7}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
1344.4.p.b	$1344$	$4$	1344.p	56.e	$2$	$16$	$16$	$79.299$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{17}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+\beta _{7}q^{5}+(\beta _{1}-\beta _{5})q^{7}-9q^{9}+\cdots\)
1344.4.p.c	$1344$	$4$	1344.p	56.e	$2$	$32$	$32$	$79.299$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1344.4.p.d	$1344$	$4$	1344.p	56.e	$2$	$32$	$32$	$79.299$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)