Space of modular forms of level 4007, weight 2, and trivial character

• Label: 4007.2.a
• Level: $4007$
• Weight: $2$
• Character orbit: 4007.a
• Rep. character: $\chi_{4007}(1,\cdot)$
• Character field: $\Q$
• Dimension: $334$
• Newform subspaces: $2$
• Sturm bound: $668$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(668\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4007))\).

	Total	New	Old
Modular forms	335	335	0
Cusp forms	334	334	0
Eisenstein series	1	1	0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(4007\)	Dim
\(+\)	\(139\)
\(-\)	\(195\)

Trace form

\( 334 q + q^{2} + 333 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 332 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4007))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		4007
4007.2.a.a	$4007$	$2$	4007.a	1.a	$1$	$139$	$139$	$31.996$		None	✓	$1$	$1$	\(-13\)	\(-22\)	\(-16\)	\(-44\)		$+$	$+$		$\mathrm{SU}(2)$
4007.2.a.b	$4007$	$2$	4007.a	1.a	$1$	$195$	$195$	$31.996$		None	✓	$1$	$0$	\(14\)	\(22\)	\(14\)	\(48\)		$-$	$-$		$\mathrm{SU}(2)$