Space of modular forms of level 503, weight 2, and Character 503.c

• Label: 503.2.c
• Level: $503$
• Weight: $2$
• Character orbit: 503.c
• Rep. character: $\chi_{503}(2,\cdot)$
• Character field: $\Q(\zeta_{251})$
• Dimension: $10250$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.c (of order \(251\) and degree \(250\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 503 \)
Character field:			\(\Q(\zeta_{251})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(503, [\chi])\).

	Total	New	Old
Modular forms	10750	10750	0
Cusp forms	10250	10250	0
Eisenstein series	500	500	0

Trace form

\( 10250 q - 249 q^{2} - 249 q^{3} - 285 q^{4} - 245 q^{5} - 237 q^{6} - 247 q^{7} - 239 q^{8} - 280 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(503, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
503.2.c.a	$503$	$2$	503.c	503.c	$251$	$10250$	$41$	$4.016$		None		$2$	$0$	\(-249\)	\(-249\)	\(-245\)	\(-247\)		$\mathrm{SU}(2)[C_{251}]$