Space of modular forms of level 224, weight 4, and Character 224.bd

• Label: 224.4.bd
• Level: $224$
• Weight: $4$
• Character orbit: 224.bd
• Rep. character: $\chi_{224}(37,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $752$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 224 \)
Character field:			\(\Q(\zeta_{24})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(128\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(224, [\chi])\).

	Total	New	Old
Modular forms	784	784	0
Cusp forms	752	752	0
Eisenstein series	32	32	0

Trace form

\( 752 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(224, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
224.4.bd.a	$224$	$4$	224.bd	224.ad	$24$	$752$	$94$	$13.216$		None		$4$	$0$	\(-4\)	\(-4\)	\(-4\)	\(-8\)		$\mathrm{SU}(2)[C_{24}]$