Space of modular forms of level 1344, weight 3, and Character 1344.d

• Label: 1344.3.d
• Level: $1344$
• Weight: $3$
• Character orbit: 1344.d
• Rep. character: $\chi_{1344}(449,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $12$
• Sturm bound: $768$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1344.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(768\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1344, [\chi])\).

	Total	New	Old
Modular forms	536	96	440
Cusp forms	488	96	392
Eisenstein series	48	0	48

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1344, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.3.d.a	$1344$	$3$	1344.d	3.b	$2$	$4$	$4$	$36.621$	4.0.116032.1	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)
1344.3.d.b	$1344$	$3$	1344.d	3.b	$2$	$4$	$4$	$36.621$	4.0.65856.1	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(1-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
1344.3.d.c	$1344$	$3$	1344.d	3.b	$2$	$4$	$4$	$36.621$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
1344.3.d.d	$1344$	$3$	1344.d	3.b	$2$	$4$	$4$	$36.621$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots\)
1344.3.d.e	$1344$	$3$	1344.d	3.b	$2$	$4$	$4$	$36.621$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
1344.3.d.f	$1344$	$3$	1344.d	3.b	$2$	$4$	$4$	$36.621$	4.0.65856.1	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(1-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
1344.3.d.g	$1344$	$3$	1344.d	3.b	$2$	$4$	$4$	$36.621$	4.0.116032.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\beta _{1})q^{3}+(2-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)
1344.3.d.h	$1344$	$3$	1344.d	3.b	$2$	$8$	$8$	$36.621$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta _{5}q^{3}+(\beta _{2}+4\beta _{3}+\beta _{7})q^{5}+\beta _{6}q^{7}+\cdots\)
1344.3.d.i	$1344$	$3$	1344.d	3.b	$2$	$12$	$12$	$36.621$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(\beta _{3}+\beta _{11})q^{5}-\beta _{1}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
1344.3.d.j	$1344$	$3$	1344.d	3.b	$2$	$12$	$12$	$36.621$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{5}-\beta _{7}+\beta _{11})q^{5}-\beta _{1}q^{7}+\cdots\)
1344.3.d.k	$1344$	$3$	1344.d	3.b	$2$	$12$	$12$	$36.621$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{3}+\beta _{11})q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
1344.3.d.l	$1344$	$3$	1344.d	3.b	$2$	$24$	$24$	$36.621$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)