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

\( 40 q + 2 q^{4} - 2 q^{6} - 20 q^{9} + O(q^{10}) \)

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	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		$2$	$0$	\(-1\)	\(-10\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}-\beta _{12}q^{3}+\beta _{9}q^{4}+(\beta _{6}-\beta _{17}+\cdots)q^{5}+\cdots\)
228.2.k.b	$228$	$2$	228.k	76.f	$6$	$20$	$10$	$1.821$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(1\)	\(10\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{8}-\beta _{16})q^{2}-\beta _{11}q^{3}+\beta _{17}q^{4}+\cdots\)

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

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