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

• Label: 1344.2.h
• Level: $1344$
• Weight: $2$
• Character orbit: 1344.h
• Rep. character: $\chi_{1344}(575,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $512$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(512\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

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

\( 48 q - 48 q^{25} + 16 q^{33} + 48 q^{45} - 48 q^{49} - 16 q^{57} + 32 q^{61} - 48 q^{69} - 16 q^{81} - 32 q^{85} - 96 q^{93}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1344.2.h.a	$1344$	$2$	1344.h	12.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{8})\)	None					672.2.h.a	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}+\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1344.2.h.b	$1344$	$2$	1344.h	12.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{8})\)	None					672.2.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{3}-\beta_1)q^{3}+\beta_{2} q^{5}-\beta_1 q^{7}+\cdots\)
1344.2.h.c	$1344$	$2$	1344.h	12.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{8})\)	None					336.2.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{3}-\beta_1)q^{3}+\beta_{2} q^{5}-\beta_1 q^{7}+\cdots\)
1344.2.h.d	$1344$	$2$	1344.h	12.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{8})\)	None					672.2.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{3}+\beta_1)q^{3}+3\beta_{2} q^{5}+\beta_1 q^{7}+\cdots\)
1344.2.h.e	$1344$	$2$	1344.h	12.b	$2$	$4$	$4$	$10.732$	\(\Q(\zeta_{8})\)	None					672.2.h.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1344.2.h.f	$1344$	$2$	1344.h	12.b	$2$	$8$	$8$	$10.732$	\(\Q(i, \sqrt{2}, \sqrt{5})\)	None					672.2.h.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{7})q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+\cdots\)
1344.2.h.g	$1344$	$2$	1344.h	12.b	$2$	$8$	$8$	$10.732$	8.0.56070144.2	None					336.2.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{3}+\beta _{5})q^{5}+\beta _{4}q^{7}+(2+\cdots)q^{9}+\cdots\)
1344.2.h.h	$1344$	$2$	1344.h	12.b	$2$	$12$	$12$	$10.732$	12.0.\(\cdots\).2	None			✓		84.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}-\beta _{11}q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)