Space of modular forms of level 403, weight 3, and Character 403.bo

• Label: 403.3.bo
• Level: $403$
• Weight: $3$
• Character orbit: 403.bo
• Rep. character: $\chi_{403}(53,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $512$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	403.bo (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(403, [\chi])\).

	Total	New	Old
Modular forms	608	512	96
Cusp forms	576	512	64
Eisenstein series	32	0	32

Trace form

\( 512 q - 248 q^{4} + 6 q^{5} + 36 q^{6} + 48 q^{7} - 12 q^{8} - 212 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(403, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
403.3.bo.a	$403$	$3$	403.bo	31.h	$30$	$512$	$64$	$10.981$		None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(48\)		$\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{3}^{\mathrm{old}}(403, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(403, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)