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

• Label: 228.2.i
• Level: $228$
• Weight: $2$
• Character orbit: 228.i
• Rep. character: $\chi_{228}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	92	8	84
Cusp forms	68	8	60
Eisenstein series	24	0	24

Trace form

\( 8 q - 2 q^{5} + 4 q^{7} - 4 q^{9} + O(q^{10}) \)

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.i.a	$228$	$2$	228.i	19.c	$3$	$4$	$2$	$1.821$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
228.2.i.b	$228$	$2$	228.i	19.c	$3$	$4$	$2$	$1.821$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(2\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(228, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)