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

• Label: 1344.4.c
• Level: $1344$
• Weight: $4$
• Character orbit: 1344.c
• Rep. character: $\chi_{1344}(673,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $8$
• Sturm bound: $1024$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(1024\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	792	72	720
Cusp forms	744	72	672
Eisenstein series	48	0	48

Trace form

\( 72 q - 648 q^{9} + O(q^{10}) \)

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.c.a	$1344$	$4$	1344.c	8.b	$2$	$6$	$6$	$79.299$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-42\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}-7q^{7}-9q^{9}+\cdots\)
1344.4.c.b	$1344$	$4$	1344.c	8.b	$2$	$6$	$6$	$79.299$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-42\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}-7q^{7}-9q^{9}+\cdots\)
1344.4.c.c	$1344$	$4$	1344.c	8.b	$2$	$6$	$6$	$79.299$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(42\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+7q^{7}-9q^{9}+\cdots\)
1344.4.c.d	$1344$	$4$	1344.c	8.b	$2$	$6$	$6$	$79.299$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(42\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+7q^{7}-9q^{9}+\cdots\)
1344.4.c.e	$1344$	$4$	1344.c	8.b	$2$	$12$	$12$	$79.299$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-84\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}-7q^{7}-9q^{9}+\cdots\)
1344.4.c.f	$1344$	$4$	1344.c	8.b	$2$	$12$	$12$	$79.299$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-84\)	$2^{22}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{2}q^{3}+(\beta _{2}+\beta _{11})q^{5}-7q^{7}-9q^{9}+\cdots\)
1344.4.c.g	$1344$	$4$	1344.c	8.b	$2$	$12$	$12$	$79.299$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(84\)	$2^{22}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{2}q^{3}+(\beta _{2}+\beta _{11})q^{5}+7q^{7}-9q^{9}+\cdots\)
1344.4.c.h	$1344$	$4$	1344.c	8.b	$2$	$12$	$12$	$79.299$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(84\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+7q^{7}-9q^{9}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \)