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

• Label: 228.2.p
• Level: $228$
• Weight: $2$
• Character orbit: 228.p
• Rep. character: $\chi_{228}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $80$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(80\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	92	12	80
Cusp forms	68	12	56
Eisenstein series	24	0	24

Trace form

\( 12 q - 3 q^{3} - 4 q^{7} + q^{9} + O(q^{10}) \)

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.p.a	$228$	$2$	228.p	57.f	$6$	$2$	$1$	$1.821$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(-3\)	\(0\)	\(-10\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1-\zeta_{6})q^{3}-5q^{7}+3\zeta_{6}q^{9}+(-6+\cdots)q^{13}+\cdots\)
228.2.p.b	$228$	$2$	228.p	57.f	$6$	$2$	$1$	$1.821$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(2\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+\zeta_{6})q^{3}+q^{7}+3\zeta_{6}q^{9}+(2-\zeta_{6})q^{13}+\cdots\)
228.2.p.c	$228$	$2$	228.p	57.f	$6$	$4$	$2$	$1.821$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-2\)	\(9\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
228.2.p.d	$228$	$2$	228.p	57.f	$6$	$4$	$2$	$1.821$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-1\)	\(-9\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(-3+2\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

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