Space of modular forms of level 322, weight 2, and Character 322.o

• Label: 322.2.o
• Level: $322$
• Weight: $2$
• Character orbit: 322.o
• Rep. character: $\chi_{322}(5,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $320$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.o (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(322, [\chi])\).

	Total	New	Old
Modular forms	1040	320	720
Cusp forms	880	320	560
Eisenstein series	160	0	160

Trace form

\( 320 q + 16 q^{4} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(322, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
322.2.o.a	$322$	$2$	322.o	161.o	$66$	$160$	$8$	$2.571$		None		✓			322.2.o.a	$4$	$0$	\(-8\)	\(6\)	\(0\)	\(-11\)		$\mathrm{SU}(2)[C_{66}]$
322.2.o.b	$322$	$2$	322.o	161.o	$66$	$160$	$8$	$2.571$		None		✓			322.2.o.b	$4$	$0$	\(8\)	\(-6\)	\(0\)	\(11\)		$\mathrm{SU}(2)[C_{66}]$

Decomposition of \(S_{2}^{\mathrm{old}}(322, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(322, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)