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

• Label: 1344.4.b
• Level: $1344$
• Weight: $4$
• Character orbit: 1344.b
• Rep. character: $\chi_{1344}(895,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $1024$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1344.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1024\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(19\)

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

\( 96 q + 864 q^{9} - 120 q^{21} - 2400 q^{25} - 400 q^{29} - 1024 q^{37} - 752 q^{53} + 3504 q^{77} + 7776 q^{81} - 4704 q^{85} + 3696 q^{93}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.4.b.a	$1344$	$4$	1344.b	28.d	$2$	$2$	$2$	$79.299$	\(\Q(\sqrt{-3}) \)	None					336.4.b.b	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(-28\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3 q^{3}-8\beta q^{5}+(-7\beta-14)q^{7}+\cdots\)
1344.4.b.b	$1344$	$4$	1344.b	28.d	$2$	$2$	$2$	$79.299$	\(\Q(\sqrt{-6}) \)	None					336.4.b.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(34\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+\beta q^{5}+(17-3\beta )q^{7}+9q^{9}+\cdots\)
1344.4.b.c	$1344$	$4$	1344.b	28.d	$2$	$2$	$2$	$79.299$	\(\Q(\sqrt{-6}) \)	None					336.4.b.a	$2$	$1$	\(0\)	\(6\)	\(0\)	\(-34\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+\beta q^{5}+(-17+3\beta )q^{7}+9q^{9}+\cdots\)
1344.4.b.d	$1344$	$4$	1344.b	28.d	$2$	$2$	$2$	$79.299$	\(\Q(\sqrt{-3}) \)	None					336.4.b.b	$2$	$0$	\(0\)	\(6\)	\(0\)	\(28\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 q^{3}-8\beta q^{5}+(7\beta+14)q^{7}+9 q^{9}+\cdots\)
1344.4.b.e	$1344$	$4$	1344.b	28.d	$2$	$8$	$8$	$79.299$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					336.4.b.e	$2$	$0$	\(0\)	\(-24\)	\(0\)	\(4\)	$2^{15}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+\beta _{5}q^{5}-\beta _{3}q^{7}+9q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1344.4.b.f	$1344$	$4$	1344.b	28.d	$2$	$8$	$8$	$79.299$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					336.4.b.e	$2$	$0$	\(0\)	\(24\)	\(0\)	\(-4\)	$2^{15}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+9q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1344.4.b.g	$1344$	$4$	1344.b	28.d	$2$	$12$	$12$	$79.299$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					84.4.b.a	$2$	$0$	\(0\)	\(-36\)	\(0\)	\(-10\)	$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}-\beta _{7}q^{5}+(-1-\beta _{2})q^{7}+9q^{9}+\cdots\)
1344.4.b.h	$1344$	$4$	1344.b	28.d	$2$	$12$	$12$	$79.299$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					84.4.b.a	$2$	$0$	\(0\)	\(36\)	\(0\)	\(10\)	$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}-\beta _{7}q^{5}+(1+\beta _{2})q^{7}+9q^{9}+\cdots\)
1344.4.b.i	$1344$	$4$	1344.b	28.d	$2$	$24$	$24$	$79.299$		None					672.4.b.a	$2$	$0$	\(0\)	\(-72\)	\(0\)	\(20\)		$\mathrm{SU}(2)[C_{2}]$
1344.4.b.j	$1344$	$4$	1344.b	28.d	$2$	$24$	$24$	$79.299$		None					672.4.b.a	$2$	$0$	\(0\)	\(72\)	\(0\)	\(-20\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)