Space of modular forms of level 322, weight 4, and Character 322.c

• Label: 322.4.c
• Level: $322$
• Weight: $4$
• Character orbit: 322.c
• Rep. character: $\chi_{322}(321,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(322, [\chi])\).

	Total	New	Old
Modular forms	148	48	100
Cusp forms	140	48	92
Eisenstein series	8	0	8

Trace form

48 * q + 192 * q^4 - 376 * q^9 + 768 * q^16 + 240 * q^18 - 280 * q^23 + 1848 * q^25 + 200 * q^29 + 928 * q^35 - 1504 * q^36 - 1328 * q^39 + 992 * q^46 - 152 * q^49 - 976 * q^50 - 624 * q^58 + 3072 * q^64 - 752 * q^70 - 1056 * q^71 + 960 * q^72 + 5192 * q^77 - 2624 * q^78 + 7144 * q^81 + 4536 * q^85 - 1120 * q^92 - 792 * q^93 + 208 * q^95 - 5312 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(322, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
322.4.c.a	$322$	$4$	322.c	161.c	$2$	$24$	$24$	$18.999$		None		✓			322.4.c.a	$4$	$0$	\(-48\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
322.4.c.b	$322$	$4$	322.c	161.c	$2$	$24$	$24$	$18.999$		None		✓			322.4.c.b	$4$	$0$	\(48\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(322, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(322, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)