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

• Label: 1344.3.m
• Level: $1344$
• Weight: $3$
• Character orbit: 1344.m
• Rep. character: $\chi_{1344}(127,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $768$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1344.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(768\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

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

Trace form

\( 48 q - 144 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.3.m.a	$1344$	$3$	1344.m	4.b	$2$	$4$	$4$	$36.621$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					336.3.m.c	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}-3q^{9}+\cdots\)
1344.3.m.b	$1344$	$3$	1344.m	4.b	$2$	$4$	$4$	$36.621$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					336.3.m.b	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+2q^{5}-\beta _{3}q^{7}-3q^{9}+(-4\beta _{2}+\cdots)q^{11}+\cdots\)
1344.3.m.c	$1344$	$3$	1344.m	4.b	$2$	$4$	$4$	$36.621$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					336.3.m.a	$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(5-\beta _{1})q^{5}-\beta _{3}q^{7}-3q^{9}+\cdots\)
1344.3.m.d	$1344$	$3$	1344.m	4.b	$2$	$8$	$8$	$36.621$	8.0.49787136.1	None					672.3.m.a	$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+(-2+\beta _{4})q^{5}+\beta _{6}q^{7}-3q^{9}+\cdots\)
1344.3.m.e	$1344$	$3$	1344.m	4.b	$2$	$12$	$12$	$36.621$	12.0.\(\cdots\).1	None					84.3.g.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{28}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+(-1-\beta _{8})q^{5}+\beta _{1}q^{7}-3q^{9}+\cdots\)
1344.3.m.f	$1344$	$3$	1344.m	4.b	$2$	$16$	$16$	$36.621$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		672.3.m.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{36}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{4}q^{7}-3q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(1344, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)