Space of modular forms of level 1248, weight 2, and Character 1248.j

• Label: 1248.2.j
• Level: $1248$
• Weight: $2$
• Character orbit: 1248.j
• Rep. character: $\chi_{1248}(911,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $448$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(448\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).

	Total	New	Old
Modular forms	240	48	192
Cusp forms	208	48	160
Eisenstein series	32	0	32

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1248.2.j.a	$1248$	$2$	1248.j	24.f	$2$	$48$	$48$	$9.965$		None			✓	✓	312.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 3}\)