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

• Label: 403.3.j
• Level: $403$
• Weight: $3$
• Character orbit: 403.j
• Rep. character: $\chi_{403}(125,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $140$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	403.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
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	156	140	16
Cusp forms	148	140	8
Eisenstein series	8	0	8

Trace form

\( 140 q + 4 q^{2} - 20 q^{5} - 24 q^{8} + 420 q^{9} + O(q^{10}) \)

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.j.a	$403$	$3$	403.j	13.d	$4$	$140$	$70$	$10.981$		None		$2$	$0$	\(4\)	\(0\)	\(-20\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{3}^{\mathrm{old}}(403, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)