Space of modular forms of level 333, weight 2, and Character 333.z

• Label: 333.2.z
• Level: $333$
• Weight: $2$
• Character orbit: 333.z
• Rep. character: $\chi_{333}(14,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $76$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.z (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(76\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(333, [\chi])\).

	Total	New	Old
Modular forms	160	160	0
Cusp forms	144	144	0
Eisenstein series	16	16	0

Trace form

144 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 + 2 * q^7 + 12 * q^8 - 6 * q^9 - 16 * q^10 + 38 * q^12 - 6 * q^14 - 28 * q^15 - 124 * q^16 - 10 * q^19 + 24 * q^20 + 12 * q^21 + 6 * q^22 - 24 * q^23 - 24 * q^24 - 18 * q^27 + 12 * q^28 - 24 * q^29 - 66 * q^30 - 12 * q^31 + 18 * q^32 + 10 * q^33 + 2 * q^34 + 30 * q^35 + 24 * q^36 + 2 * q^37 - 12 * q^38 + 10 * q^39 + 36 * q^41 + 54 * q^42 + 14 * q^43 + 24 * q^44 - 58 * q^45 - 4 * q^46 - 24 * q^47 - 54 * q^48 - 44 * q^49 - 36 * q^50 + 12 * q^51 + 26 * q^52 + 2 * q^54 + 6 * q^55 - 78 * q^56 + 4 * q^57 - 6 * q^58 - 6 * q^59 - 42 * q^60 + 12 * q^61 + 36 * q^62 - 20 * q^63 - 12 * q^65 + 40 * q^66 + 66 * q^68 - 62 * q^69 + 16 * q^70 - 48 * q^71 + 158 * q^72 + 30 * q^74 - 50 * q^75 + 6 * q^76 - 12 * q^77 + 60 * q^78 + 2 * q^79 - 126 * q^80 + 34 * q^81 - 36 * q^82 - 82 * q^84 - 6 * q^86 - 18 * q^87 + 6 * q^88 - 36 * q^89 - 104 * q^90 - 58 * q^91 + 192 * q^92 - 80 * q^93 - 10 * q^94 + 18 * q^95 - 138 * q^96 - 36 * q^97 + 54 * q^98 + 96 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(333, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
333.2.z.a	$333$	$2$	333.z	333.z	$12$	$144$	$36$	$2.659$		None		✓	✓	✓	333.2.z.a	$2$	$0$	\(-6\)	\(-6\)	\(-6\)	\(2\)		$\mathrm{SU}(2)[C_{12}]$