Space of modular forms of level 501, weight 2, and Character 501.c

• Label: 501.2.c
• Level: $501$
• Weight: $2$
• Character orbit: 501.c
• Rep. character: $\chi_{501}(500,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 501 = 3 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	501.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 501 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(501, [\chi])\).

	Total	New	Old
Modular forms	58	58	0
Cusp forms	54	54	0
Eisenstein series	4	4	0

Trace form

\( 54 q - 2 q^{3} - 60 q^{4} + 4 q^{6} - 4 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(501, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
501.2.c.a	$501$	$2$	501.c	501.c	$2$	$22$	$22$	$4.001$		\(\Q(\sqrt{-167}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{2}]$
501.2.c.b	$501$	$2$	501.c	501.c	$2$	$32$	$32$	$4.001$		None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{2}]$