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

• Label: 403.3.b
• Level: $403$
• Weight: $3$
• Character orbit: 403.b
• Rep. character: $\chi_{403}(402,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $3$
• Sturm bound: $112$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	403.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 403 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(112\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	78	78	0
Cusp forms	74	74	0
Eisenstein series	4	4	0

Trace form

\( 74 q - 156 q^{4} - 226 q^{9} + O(q^{10}) \)

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.b.a	$403$	$3$	403.b	403.b	$2$	$1$	$1$	$10.981$	\(\Q\)	\(\Q(\sqrt{-403}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+9q^{9}-9q^{11}+13q^{13}+2^{4}q^{16}+\cdots\)
403.3.b.b	$403$	$3$	403.b	403.b	$2$	$1$	$1$	$10.981$	\(\Q\)	\(\Q(\sqrt{-403}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+9q^{9}+9q^{11}-13q^{13}+2^{4}q^{16}+\cdots\)
403.3.b.c	$403$	$3$	403.b	403.b	$2$	$72$	$72$	$10.981$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$