Space of modular forms of level 6037, weight 2, and trivial character

• Label: 6037.2.a
• Level: $6037$
• Weight: $2$
• Character orbit: 6037.a
• Rep. character: $\chi_{6037}(1,\cdot)$
• Character field: $\Q$
• Dimension: $502$
• Newform subspaces: $2$
• Sturm bound: $1006$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1006\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6037))\).

	Total	New	Old
Modular forms	503	503	0
Cusp forms	502	502	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.

\(6037\)	Dim
\(+\)	\(243\)
\(-\)	\(259\)

Trace form

\( 502 q - 2 q^{3} + 502 q^{4} - 2 q^{5} + 6 q^{6} + 6 q^{8} + 500 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6037))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		6037
6037.2.a.a	$6037$	$2$	6037.a	1.a	$1$	$243$	$243$	$48.206$		None	✓	$1$	$1$	\(-47\)	\(-31\)	\(-40\)	\(-42\)		$+$	$+$		$\mathrm{SU}(2)$
6037.2.a.b	$6037$	$2$	6037.a	1.a	$1$	$259$	$259$	$48.206$		None	✓	$1$	$0$	\(47\)	\(29\)	\(38\)	\(42\)		$-$	$-$		$\mathrm{SU}(2)$