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

• Label: 501.2.e
• Level: $501$
• Weight: $2$
• Character orbit: 501.e
• Rep. character: $\chi_{501}(4,\cdot)$
• Character field: $\Q(\zeta_{83})$
• Dimension: $2296$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 501 = 3 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	501.e (of order \(83\) and degree \(82\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 167 \)
Character field:			\(\Q(\zeta_{83})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	4756	2296	2460
Cusp forms	4428	2296	2132
Eisenstein series	328	0	328

Trace form

\( 2296 q - 32 q^{4} - 4 q^{6} - 28 q^{9} + O(q^{10}) \)

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.e.a	$501$	$2$	501.e	167.c	$83$	$1148$	$14$	$4.001$		None		$2$	$0$	\(-2\)	\(-14\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{83}]$
501.2.e.b	$501$	$2$	501.e	167.c	$83$	$1148$	$14$	$4.001$		None		$2$	$0$	\(2\)	\(14\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{83}]$

Decomposition of \(S_{2}^{\mathrm{old}}(501, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(501, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 2}\)