Space of modular forms of level 228, weight 5, and Character 228.h

• Label: 228.5.h
• Level: $228$
• Weight: $5$
• Character orbit: 228.h
• Rep. character: $\chi_{228}(37,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $200$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	228.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(200\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(228, [\chi])\).

	Total	New	Old
Modular forms	166	14	152
Cusp forms	154	14	140
Eisenstein series	12	0	12

Trace form

\( 14 q + 18 q^{5} - 86 q^{7} - 378 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(228, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
228.5.h.a	$228$	$5$	228.h	19.b	$2$	$14$	$14$	$23.568$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(18\)	\(-86\)	$2^{14}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(1+\beta _{1})q^{5}+(-6+\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(228, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)