Space of modular forms of level 2002, weight 2, and Character 2002.c

• Label: 2002.2.c
• Level: $2002$
• Weight: $2$
• Character orbit: 2002.c
• Rep. character: $\chi_{2002}(1847,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $672$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2002.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(672\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2002, [\chi])\).

	Total	New	Old
Modular forms	344	96	248
Cusp forms	328	96	232
Eisenstein series	16	0	16

Trace form

\( 96 q - 96 q^{4} - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2002, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2002.2.c.a	$2002$	$2$	2002.c	77.b	$2$	$48$	$48$	$15.986$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$
2002.2.c.b	$2002$	$2$	2002.c	77.b	$2$	$48$	$48$	$15.986$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2002, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2002, [\chi]) \cong \)