Space of modular forms of level 4001, weight 2, and trivial character

• Label: 4001.2.a
• Level: $4001$
• Weight: $2$
• Character orbit: 4001.a
• Rep. character: $\chi_{4001}(1,\cdot)$
• Character field: $\Q$
• Dimension: $333$
• Newform subspaces: $2$
• Sturm bound: $667$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(667\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4001))\).

	Total	New	Old
Modular forms	334	334	0
Cusp forms	333	333	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.

\(4001\)	Dim
\(+\)	\(149\)
\(-\)	\(184\)

Trace form

\( 333 q - 3 q^{2} + 333 q^{4} - 4 q^{5} + 2 q^{7} - 9 q^{8} + 325 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4001))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		4001
4001.2.a.a	$4001$	$2$	4001.a	1.a	$1$	$149$	$149$	$31.948$		None	✓	✓	✓	✓	4001.2.a.a	$1$	$1$	\(-6\)	\(-28\)	\(-19\)	\(-47\)		$+$	$+$		$\mathrm{SU}(2)$
4001.2.a.b	$4001$	$2$	4001.a	1.a	$1$	$184$	$184$	$31.948$		None	✓	✓	✓	✓	4001.2.a.b	$1$	$0$	\(3\)	\(28\)	\(15\)	\(49\)		$-$	$-$		$\mathrm{SU}(2)$