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

• Label: 1344.2.b
• Level: $1344$
• Weight: $2$
• Character orbit: 1344.b
• Rep. character: $\chi_{1344}(895,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $8$
• Sturm bound: $512$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(512\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	280	32	248
Cusp forms	232	32	200
Eisenstein series	48	0	48

Trace form

\( 32 q + 32 q^{9} - 8 q^{21} - 32 q^{25} + 16 q^{29} - 16 q^{53} - 48 q^{77} + 32 q^{81} + 96 q^{85} + 16 q^{93}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.2.b.a	$1344$	$2$	1344.b	28.d	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-6}) \)	None					336.2.b.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
1344.2.b.b	$1344$	$2$	1344.b	28.d	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-3}) \)	None					336.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-\beta+2)q^{7}+q^{9}+2\beta q^{11}+\cdots\)
1344.2.b.c	$1344$	$2$	1344.b	28.d	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-3}) \)	None					336.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(\beta-2)q^{7}+q^{9}-2\beta q^{11}+\cdots\)
1344.2.b.d	$1344$	$2$	1344.b	28.d	$2$	$2$	$2$	$10.732$	\(\Q(\sqrt{-6}) \)	None					336.2.b.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
1344.2.b.e	$1344$	$2$	1344.b	28.d	$2$	$4$	$4$	$10.732$	4.0.2312.1	None					84.2.b.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1344.2.b.f	$1344$	$2$	1344.b	28.d	$2$	$4$	$4$	$10.732$	4.0.2312.1	None					84.2.b.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1344.2.b.g	$1344$	$2$	1344.b	28.d	$2$	$8$	$8$	$10.732$	8.0.836829184.2	None					672.2.b.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(4\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1344.2.b.h	$1344$	$2$	1344.b	28.d	$2$	$8$	$8$	$10.732$	8.0.836829184.2	None					672.2.b.a	$2$	$0$	\(0\)	\(8\)	\(0\)	\(-4\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots\)

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

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