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

• Label: 403.2.f
• Level: $403$
• Weight: $2$
• Character orbit: 403.f
• Rep. character: $\chi_{403}(94,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $74$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(74\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	80	72	8
Cusp forms	72	72	0
Eisenstein series	8	0	8

Trace form

\( 72 q - 2 q^{2} - 38 q^{4} - 8 q^{5} + 12 q^{8} - 36 q^{9} + O(q^{10}) \)

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.f.a	$403$	$2$	403.f	13.c	$3$	$2$	$1$	$3.218$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(0\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-3q^{5}-2\zeta_{6}q^{7}+\cdots\)
403.2.f.b	$403$	$2$	403.f	13.c	$3$	$34$	$17$	$3.218$		None		$2$	$0$	\(4\)	\(0\)	\(-14\)	\(6\)		$\mathrm{SU}(2)[C_{3}]$
403.2.f.c	$403$	$2$	403.f	13.c	$3$	$36$	$18$	$3.218$		None		$2$	$0$	\(-5\)	\(0\)	\(12\)	\(-4\)		$\mathrm{SU}(2)[C_{3}]$