Space of modular forms of level 1007, weight 2, and Character 1007.b

• Label: 1007.2.b
• Level: $1007$
• Weight: $2$
• Character orbit: 1007.b
• Rep. character: $\chi_{1007}(476,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1007 = 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1007.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1007, [\chi])\).

	Total	New	Old
Modular forms	92	80	12
Cusp forms	88	80	8
Eisenstein series	4	0	4

Trace form

\( 80 q - 74 q^{4} + 4 q^{6} + 12 q^{7} - 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1007, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1007.2.b.a	$1007$	$2$	1007.b	53.b	$2$	$80$	$80$	$8.041$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1007, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1007, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 2}\)