Space of modular forms of level 8039, weight 2, and trivial character

• Label: 8039.2.a
• Level: $8039$
• Weight: $2$
• Character orbit: 8039.a
• Rep. character: $\chi_{8039}(1,\cdot)$
• Character field: $\Q$
• Dimension: $670$
• Newform subspaces: $2$
• Sturm bound: $1340$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1340\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8039))\).

	Total	New	Old
Modular forms	671	671	0
Cusp forms	670	670	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.

\(8039\)	Dim
\(+\)	\(279\)
\(-\)	\(391\)

Trace form

\( 670 q + q^{2} + 673 q^{4} + 2 q^{5} + 6 q^{7} - 3 q^{8} + 676 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8039))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		8039
8039.2.a.a	$8039$	$2$	8039.a	1.a	$1$	$279$	$279$	$64.192$		None	✓	$1$	$1$	\(-13\)	\(-12\)	\(-20\)	\(-57\)		$+$	$+$		$\mathrm{SU}(2)$
8039.2.a.b	$8039$	$2$	8039.a	1.a	$1$	$391$	$391$	$64.192$		None	✓	$1$	$0$	\(14\)	\(12\)	\(22\)	\(63\)		$-$	$-$		$\mathrm{SU}(2)$