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

• Label: 1344.2.bl
• Level: $1344$
• Weight: $2$
• Character orbit: 1344.bl
• Rep. character: $\chi_{1344}(703,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $12$
• Sturm bound: $512$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(512\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(11\)

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.bl.a	$1344$	$2$	1344.bl	28.f	$6$	$2$	$1$	$10.732$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-1\)	\(-6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1344.2.bl.b	$1344$	$2$	1344.bl	28.f	$6$	$2$	$1$	$10.732$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
1344.2.bl.c	$1344$	$2$	1344.bl	28.f	$6$	$2$	$1$	$10.732$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
1344.2.bl.d	$1344$	$2$	1344.bl	28.f	$6$	$2$	$1$	$10.732$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-1\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1344.2.bl.e	$1344$	$2$	1344.bl	28.f	$6$	$2$	$1$	$10.732$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
1344.2.bl.f	$1344$	$2$	1344.bl	28.f	$6$	$2$	$1$	$10.732$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1344.2.bl.g	$1344$	$2$	1344.bl	28.f	$6$	$2$	$1$	$10.732$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
1344.2.bl.h	$1344$	$2$	1344.bl	28.f	$6$	$2$	$1$	$10.732$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
1344.2.bl.i	$1344$	$2$	1344.bl	28.f	$6$	$8$	$4$	$10.732$	8.0.562828176.1	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-2\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1})q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1344.2.bl.j	$1344$	$2$	1344.bl	28.f	$6$	$8$	$4$	$10.732$	8.0.562828176.1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(2\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1})q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1344.2.bl.k	$1344$	$2$	1344.bl	28.f	$6$	$16$	$8$	$10.732$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(4\)	$2^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1})q^{3}-\beta _{7}q^{5}+(\beta _{1}+\beta _{6}+\cdots)q^{7}+\cdots\)
1344.2.bl.l	$1344$	$2$	1344.bl	28.f	$6$	$16$	$8$	$10.732$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(-4\)	$2^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1})q^{3}-\beta _{7}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)