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

• Label: 322.2.k
• Level: $322$
• Weight: $2$
• Character orbit: 322.k
• Rep. character: $\chi_{322}(83,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $160$
• 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.k (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{22})\)
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	520	160	360
Cusp forms	440	160	280
Eisenstein series	80	0	80

Trace form

\( 160 q - 16 q^{4} + 8 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
322.2.k.a	$322$	$2$	322.k	161.k	$22$	$80$	$8$	$2.571$		None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(-11\)		$\mathrm{SU}(2)[C_{22}]$
322.2.k.b	$322$	$2$	322.k	161.k	$22$	$80$	$8$	$2.571$		None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(11\)		$\mathrm{SU}(2)[C_{22}]$

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

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