Space of modular forms of level 323, weight 2, and Character 323.o

• Label: 323.2.o
• Level: $323$
• Weight: $2$
• Character orbit: 323.o
• Rep. character: $\chi_{323}(30,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $112$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 323 = 17 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	323.o (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 323 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(323, [\chi])\).

	Total	New	Old
Modular forms	128	128	0
Cusp forms	112	112	0
Eisenstein series	16	16	0

Trace form

112 * q + 48 * q^4 - 12 * q^6 - 4 * q^7 - 6 * q^10 - 8 * q^11 + 8 * q^12 - 20 * q^13 + 10 * q^14 - 32 * q^16 - 8 * q^17 - 56 * q^18 + 16 * q^20 + 4 * q^21 + 12 * q^22 - 8 * q^23 + 34 * q^24 - 12 * q^27 - 30 * q^28 + 6 * q^29 - 32 * q^30 - 24 * q^31 + 20 * q^33 - 30 * q^34 - 16 * q^35 - 20 * q^37 - 12 * q^38 - 4 * q^39 - 26 * q^40 - 4 * q^41 - 38 * q^44 - 48 * q^45 + 36 * q^47 + 36 * q^48 - 128 * q^50 + 28 * q^51 + 92 * q^52 + 14 * q^54 + 20 * q^55 + 152 * q^56 - 12 * q^57 + 32 * q^58 + 28 * q^61 - 42 * q^62 - 6 * q^63 - 120 * q^64 + 68 * q^65 - 36 * q^67 - 20 * q^68 + 24 * q^69 - 20 * q^71 - 40 * q^72 - 10 * q^73 - 38 * q^74 + 32 * q^75 - 28 * q^78 - 38 * q^79 + 44 * q^80 - 16 * q^81 - 34 * q^82 - 112 * q^84 + 72 * q^85 + 48 * q^86 + 40 * q^88 - 84 * q^89 - 86 * q^90 - 24 * q^91 - 30 * q^92 + 58 * q^95 + 200 * q^96 - 14 * q^97 + 108 * q^98 + 66 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(323, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
323.2.o.a	$323$	$2$	323.o	323.o	$12$	$112$	$28$	$2.579$		None		✓	✓	✓	323.2.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$