Space of modular forms of level 230, weight 3, and Character 230.f

• Label: 230.3.f
• Level: $230$
• Weight: $3$
• Character orbit: 230.f
• Rep. character: $\chi_{230}(47,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $44$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(230, [\chi])\).

	Total	New	Old
Modular forms	152	44	108
Cusp forms	136	44	92
Eisenstein series	16	0	16

Trace form

\( 44 q + 4 q^{2} + 8 q^{5} + 16 q^{7} - 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(230, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
230.3.f.a	$230$	$3$	230.f	5.c	$4$	$20$	$10$	$6.267$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-20\)	\(0\)	\(4\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{8})q^{2}+\beta _{1}q^{3}+2\beta _{8}q^{4}+\cdots\)
230.3.f.b	$230$	$3$	230.f	5.c	$4$	$24$	$12$	$6.267$		None		$2$	$0$	\(24\)	\(0\)	\(4\)	\(8\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)