Space of modular forms of level 230, weight 5, and Character 230.c

• Label: 230.5.c
• Level: $230$
• Weight: $5$
• Character orbit: 230.c
• Rep. character: $\chi_{230}(229,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(230, [\chi])\).

	Total	New	Old
Modular forms	148	48	100
Cusp forms	140	48	92
Eisenstein series	8	0	8

Trace form

\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(230, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
230.5.c.a	$230$	$5$	230.c	115.c	$2$	$48$	$48$	$23.775$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(230, [\chi]) \cong \)