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

• Label: 322.2.c
• Level: $322$
• Weight: $2$
• Character orbit: 322.c
• Rep. character: $\chi_{322}(321,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	52	16	36
Cusp forms	44	16	28
Eisenstein series	8	0	8

Trace form

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

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.c.a	$322$	$2$	322.c	161.c	$2$	$4$	$4$	$2.571$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots\)
322.2.c.b	$322$	$2$	322.c	161.c	$2$	$4$	$4$	$2.571$	\(\Q(\sqrt{-2}, \sqrt{-7})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
322.2.c.c	$322$	$2$	322.c	161.c	$2$	$4$	$4$	$2.571$	4.0.2312.1	None		$2$	$0$	\(4\)	\(0\)	\(-8\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}-2q^{5}-\beta _{2}q^{6}+\cdots\)
322.2.c.d	$322$	$2$	322.c	161.c	$2$	$4$	$4$	$2.571$	4.0.2312.1	None		$2$	$0$	\(4\)	\(0\)	\(8\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}+2q^{5}-\beta _{2}q^{6}+\cdots\)

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

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