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

• Label: 230.4.b
• Level: $230$
• Weight: $4$
• Character orbit: 230.b
• Rep. character: $\chi_{230}(139,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	112	32	80
Cusp forms	104	32	72
Eisenstein series	8	0	8

Trace form

\( 32 q - 128 q^{4} - 12 q^{5} - 24 q^{6} - 316 q^{9} + O(q^{10}) \)

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.b.a	$230$	$4$	230.b	5.b	$2$	$14$	$14$	$13.570$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{8}q^{2}+(\beta _{1}-\beta _{8})q^{3}-4q^{4}+(-\beta _{7}+\cdots)q^{5}+\cdots\)
230.4.b.b	$230$	$4$	230.b	5.b	$2$	$18$	$18$	$13.570$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{5}q^{2}+\beta _{1}q^{3}-4q^{4}+(-\beta _{5}-\beta _{12}+\cdots)q^{5}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)