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

• Label: 224.4.x
• Level: $224$
• Weight: $4$
• Character orbit: 224.x
• Rep. character: $\chi_{224}(27,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $376$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	224.x (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 224 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	392	392	0
Cusp forms	376	376	0
Eisenstein series	16	16	0

Trace form

\( 376 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \)

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.x.a	$224$	$4$	224.x	224.x	$8$	$8$	$2$	$13.216$	8.0.157351936.1	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{8}]$	\(q+(-\beta _{2}-3\beta _{4})q^{2}+(-7\beta _{3}+5\beta _{5}+\cdots)q^{4}+\cdots\)
224.4.x.b	$224$	$4$	224.x	224.x	$8$	$368$	$92$	$13.216$		None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$