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

• Label: 228.2.m
• Level: $228$
• Weight: $2$
• Character orbit: 228.m
• Rep. character: $\chi_{228}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 228 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	88	88	0
Cusp forms	72	72	0
Eisenstein series	16	16	0

Trace form

72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

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.m.a	$228$	$2$	228.m	228.m	$6$	$72$	$36$	$1.821$		None		✓	✓	✓	228.2.m.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$