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

• Label: 228.2.k
• Level: $228$
• Weight: $2$
• Character orbit: 228.k
• Rep. character: $\chi_{228}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• 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.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(23\)

Dimensions

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

	Total	New	Old
Modular forms	88	40	48
Cusp forms	72	40	32
Eisenstein series	16	0	16

Trace form

40 * q + 2 * q^4 - 2 * q^6 - 20 * q^9 + 12 * q^10 + 12 * q^13 + 18 * q^14 + 2 * q^16 - 28 * q^20 + 12 * q^21 + 4 * q^24 - 20 * q^25 + 14 * q^28 - 60 * q^32 - 36 * q^34 + 2 * q^36 + 14 * q^38 - 72 * q^40 + 24 * q^41 + 18 * q^44 - 24 * q^48 - 48 * q^49 + 6 * q^52 - 24 * q^53 - 2 * q^54 + 12 * q^57 + 32 * q^58 + 6 * q^60 + 20 * q^61 - 26 * q^62 - 28 * q^64 - 16 * q^66 + 80 * q^68 + 72 * q^70 + 18 * q^72 - 12 * q^73 + 48 * q^74 - 66 * q^76 - 64 * q^77 + 66 * q^78 + 62 * q^80 - 20 * q^81 - 36 * q^82 + 16 * q^85 - 18 * q^86 - 48 * q^89 - 12 * q^90 + 18 * q^92 + 12 * q^93 + 4 * q^96 - 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.k.a	$228$	$2$	228.k	76.f	$6$	$20$	$10$	$1.821$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			228.2.k.a	$2$	$0$	\(-1\)	\(-10\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}-\beta _{12}q^{3}+\beta _{9}q^{4}+(\beta _{6}-\beta _{17}+\cdots)q^{5}+\cdots\)
228.2.k.b	$228$	$2$	228.k	76.f	$6$	$20$	$10$	$1.821$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			228.2.k.a	$2$	$0$	\(1\)	\(10\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{8}-\beta _{16})q^{2}-\beta _{11}q^{3}+\beta _{17}q^{4}+\cdots\)

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

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