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

• Label: 1344.2.bk
• Level: $1344$
• Weight: $2$
• Character orbit: 1344.bk
• Rep. character: $\chi_{1344}(289,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $12$
• Sturm bound: $512$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bk (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(512\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(11\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	560	64	496
Cusp forms	464	64	400
Eisenstein series	96	0	96

Trace form

\( 64 q + 32 q^{9} + O(q^{10}) \)

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.bk.a	$1344$	$2$	1344.bk	56.p	$6$	$4$	$2$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-4+2\zeta_{12}^{2})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
1344.2.bk.b	$1344$	$2$	1344.bk	56.p	$6$	$4$	$2$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-2+\zeta_{12}^{2})q^{5}+(3\zeta_{12}+\cdots)q^{7}+\cdots\)
1344.2.bk.c	$1344$	$2$	1344.bk	56.p	$6$	$4$	$2$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1344.2.bk.d	$1344$	$2$	1344.bk	56.p	$6$	$4$	$2$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1344.2.bk.e	$1344$	$2$	1344.bk	56.p	$6$	$4$	$2$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(2+\cdots)q^{7}+\cdots\)
1344.2.bk.f	$1344$	$2$	1344.bk	56.p	$6$	$4$	$2$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(2+\cdots)q^{7}+\cdots\)
1344.2.bk.g	$1344$	$2$	1344.bk	56.p	$6$	$4$	$2$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{3}+(2-\zeta_{12}^{2})q^{5}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+\cdots\)
1344.2.bk.h	$1344$	$2$	1344.bk	56.p	$6$	$4$	$2$	$10.732$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{3}+(4-2\zeta_{12}^{2})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
1344.2.bk.i	$1344$	$2$	1344.bk	56.p	$6$	$8$	$4$	$10.732$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{3}+(-2-\beta _{1}-\beta _{3})q^{5}+\beta _{5}q^{7}+\cdots\)
1344.2.bk.j	$1344$	$2$	1344.bk	56.p	$6$	$8$	$4$	$10.732$	8.0.2702336256.1	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1344.2.bk.k	$1344$	$2$	1344.bk	56.p	$6$	$8$	$4$	$10.732$	8.0.2702336256.1	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{3}+(1+\beta _{2}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1344.2.bk.l	$1344$	$2$	1344.bk	56.p	$6$	$8$	$4$	$10.732$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{3}+(2+\beta _{1}+\beta _{3})q^{5}-\beta _{5}q^{7}+\cdots\)

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

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