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

• Label: 1344.2.j
• Level: $1344$
• Weight: $2$
• Character orbit: 1344.j
• Rep. character: $\chi_{1344}(1247,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $9$
• Sturm bound: $512$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(512\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(19\), \(23\), \(47\)

Dimensions

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

	Total	New	Old
Modular forms	280	48	232
Cusp forms	232	48	184
Eisenstein series	48	0	48

Trace form

\( 48 q + O(q^{10}) \)

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.j.a	$1344$	$2$	1344.j	24.f	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{7}-3q^{9}+2\zeta_{12}^{2}q^{11}+\cdots\)
1344.2.j.b	$1344$	$2$	1344.j	24.f	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}-3q^{9}+2\zeta_{12}^{2}q^{11}+\cdots\)
1344.2.j.c	$1344$	$2$	1344.j	24.f	$2$	$4$	$4$	$10.732$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}-\beta _{2}q^{7}+3\beta _{2}q^{9}+\cdots\)
1344.2.j.d	$1344$	$2$	1344.j	24.f	$2$	$4$	$4$	$10.732$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+3\beta _{2}q^{9}+\cdots\)
1344.2.j.e	$1344$	$2$	1344.j	24.f	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{3}q^{3}-2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
1344.2.j.f	$1344$	$2$	1344.j	24.f	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{3}-2\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\cdots\)
1344.2.j.g	$1344$	$2$	1344.j	24.f	$2$	$8$	$8$	$10.732$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{24}^{2})q^{3}+(-\zeta_{24}^{3}+\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)
1344.2.j.h	$1344$	$2$	1344.j	24.f	$2$	$8$	$8$	$10.732$	8.0.40960000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}-\beta _{5})q^{3}-\beta _{7}q^{5}+\beta _{1}q^{7}+(2+\cdots)q^{9}+\cdots\)
1344.2.j.i	$1344$	$2$	1344.j	24.f	$2$	$8$	$8$	$10.732$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\zeta_{24}^{2})q^{3}+(-\zeta_{24}^{3}+\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)