Space of modular forms of level 403, weight 2, and Character 403.ba

• Label: 403.2.ba
• Level: $403$
• Weight: $2$
• Character orbit: 403.ba
• Rep. character: $\chi_{403}(6,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $140$
• Newform subspaces: $1$
• Sturm bound: $74$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.ba (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 403 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(74\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).

	Total	New	Old
Modular forms	156	156	0
Cusp forms	140	140	0
Eisenstein series	16	16	0

Trace form

\( 140 q - 8 q^{2} - 12 q^{4} - 2 q^{5} + 6 q^{6} + 12 q^{7} - 10 q^{8} - 124 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
403.2.ba.a	$403$	$2$	403.ba	403.aa	$12$	$140$	$35$	$3.218$		None		$2$	$0$	\(-8\)	\(0\)	\(-2\)	\(12\)		$\mathrm{SU}(2)[C_{12}]$