Space of modular forms of level 222, weight 2, and Character 222.q

• Label: 222.2.q
• Level: $222$
• Weight: $2$
• Character orbit: 222.q
• Rep. character: $\chi_{222}(5,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $76$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	222.q (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(76\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(222, [\chi])\).

	Total	New	Old
Modular forms	504	144	360
Cusp forms	408	144	264
Eisenstein series	96	0	96

Trace form

144 * q + 12 * q^9 - 12 * q^12 + 12 * q^15 - 36 * q^21 + 24 * q^28 - 168 * q^31 - 72 * q^34 - 24 * q^37 - 48 * q^40 + 12 * q^42 - 48 * q^43 - 48 * q^46 - 24 * q^49 + 36 * q^54 - 36 * q^57 - 24 * q^58 - 36 * q^63 + 24 * q^67 - 132 * q^69 + 24 * q^70 + 72 * q^75 - 48 * q^78 - 24 * q^79 - 156 * q^81 - 24 * q^82 - 72 * q^87 + 24 * q^88 - 120 * q^91 + 60 * q^93 + 144 * q^94 + 120 * q^97 + 156 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(222, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
222.2.q.a	$222$	$2$	222.q	111.q	$36$	$144$	$12$	$1.773$		None		✓	✓	✓	222.2.q.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

Decomposition of \(S_{2}^{\mathrm{old}}(222, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(222, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)