Space of modular forms of level 230, weight 4, and Character 230.j

• Label: 230.4.j
• Level: $230$
• Weight: $4$
• Character orbit: 230.j
• Rep. character: $\chi_{230}(9,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $360$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(230, [\chi])\).

	Total	New	Old
Modular forms	1120	360	760
Cusp forms	1040	360	680
Eisenstein series	80	0	80

Trace form

\( 360 q + 144 q^{4} + 32 q^{5} + 8 q^{6} + 224 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(230, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
230.4.j.a	$230$	$4$	230.j	115.j	$22$	$360$	$36$	$13.570$		None		$4$	$0$	\(0\)	\(0\)	\(32\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{4}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)