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 + 16 * q^16 + 44 * q^18 - 132 * q^21 - 48 * q^23 - 12 * q^24 + 40 * q^25 + 12 * q^26 - 44 * q^28 - 44 * q^30 + 12 * q^31 - 26 * q^35 + 40 * q^36 + 44 * q^37 - 20 * q^39 - 88 * q^43 + 12 * q^46 - 24 * q^47 + 10 * q^49 + 44 * q^51 - 72 * q^54 - 22 * q^56 - 88 * q^57 - 28 * q^58 - 72 * q^59 - 110 * q^63 - 32 * q^64 - 154 * q^65 - 44 * q^70 + 64 * q^71 - 44 * q^72 + 96 * q^75 - 102 * q^77 + 48 * q^78 - 88 * q^79 + 12 * q^81 - 48 * q^82 - 22 * q^84 - 60 * q^85 - 22 * q^86 - 294 * q^87 + 8 * q^92 + 64 * q^93 + 36 * q^94 - 22 * q^95 + 12 * q^96 - 12 * q^98 - 88 * q^99

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

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