Space of modular forms of level 228, weight 2, and Character 228.w

• Label: 228.2.w
• Level: $228$
• Weight: $2$
• Character orbit: 228.w
• Rep. character: $\chi_{228}(67,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.w (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(228, [\chi])\).

	Total	New	Old
Modular forms	264	120	144
Cusp forms	216	120	96
Eisenstein series	48	0	48

Trace form

120 * q - 6 * q^4 + 6 * q^6 - 12 * q^10 - 12 * q^13 - 18 * q^14 - 6 * q^16 + 60 * q^20 - 12 * q^21 - 36 * q^28 - 30 * q^32 - 54 * q^34 - 6 * q^36 - 132 * q^38 - 54 * q^40 - 24 * q^41 - 60 * q^44 - 90 * q^46 + 24 * q^48 + 60 * q^49 - 54 * q^50 - 6 * q^52 + 24 * q^53 + 6 * q^54 - 72 * q^58 + 12 * q^60 + 132 * q^62 + 42 * q^64 - 72 * q^65 + 48 * q^66 + 78 * q^68 - 144 * q^69 + 36 * q^70 + 36 * q^72 + 36 * q^73 + 96 * q^74 + 120 * q^76 - 144 * q^77 + 24 * q^78 - 6 * q^80 + 66 * q^82 + 108 * q^84 - 120 * q^85 + 144 * q^86 + 72 * q^88 - 24 * q^89 + 30 * q^90 - 24 * q^93 + 24 * q^97 + 12 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(228, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
228.2.w.a	$228$	$2$	228.w	76.k	$18$	$60$	$10$	$1.821$		None		✓			228.2.w.a	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
228.2.w.b	$228$	$2$	228.w	76.k	$18$	$60$	$10$	$1.821$		None		✓			228.2.w.a	$2$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(228, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)