Space of modular forms of level 221, weight 2, and Character 221.z

• Label: 221.2.z
• Level: $221$
• Weight: $2$
• Character orbit: 221.z
• Rep. character: $\chi_{221}(44,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $152$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.z (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 221 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(221, [\chi])\).

	Total	New	Old
Modular forms	184	184	0
Cusp forms	152	152	0
Eisenstein series	32	32	0

Trace form

\( 152 q - 8 q^{2} - 16 q^{3} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(221, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
221.2.z.a	$221$	$2$	221.z	221.z	$16$	$152$	$19$	$1.765$		None		$2$	$0$	\(-8\)	\(-16\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$