Space of modular forms of level 2007, weight 2, and Character 2007.c

• Label: 2007.2.c
• Level: $2007$
• Weight: $2$
• Character orbit: 2007.c
• Rep. character: $\chi_{2007}(2006,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $2$
• Sturm bound: $448$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2007 = 3^{2} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2007.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 669 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2007, [\chi])\).

	Total	New	Old
Modular forms	228	76	152
Cusp forms	220	76	144
Eisenstein series	8	0	8

Trace form

\( 76 q - 80 q^{4} - 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2007, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2007.2.c.a	$2007$	$2$	2007.c	669.c	$2$	$28$	$28$	$16.026$		\(\Q(\sqrt{-223}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{2}]$
2007.2.c.b	$2007$	$2$	2007.c	669.c	$2$	$48$	$48$	$16.026$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2007, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2007, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(669, [\chi])\)\(^{\oplus 2}\)