Space of modular forms of level 8009, weight 2, and trivial character

• Label: 8009.2.a
• Level: $8009$
• Weight: $2$
• Character orbit: 8009.a
• Rep. character: $\chi_{8009}(1,\cdot)$
• Character field: $\Q$
• Dimension: $667$
• Newform subspaces: $2$
• Sturm bound: $1335$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8009 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8009.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1335\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8009))\).

	Total	New	Old
Modular forms	668	668	0
Cusp forms	667	667	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.

\(8009\)	Dim
\(+\)	\(306\)
\(-\)	\(361\)

Trace form

\( 667 q - 3 q^{2} - 2 q^{3} + 667 q^{4} - 4 q^{5} + 4 q^{7} - 3 q^{8} + 657 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8009))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		8009
8009.2.a.a	$8009$	$2$	8009.a	1.a	$1$	$306$	$306$	$63.952$		None	✓	$1$	$1$	\(-13\)	\(-25\)	\(-25\)	\(-102\)		$+$	$+$		$\mathrm{SU}(2)$
8009.2.a.b	$8009$	$2$	8009.a	1.a	$1$	$361$	$361$	$63.952$		None	✓	$1$	$0$	\(10\)	\(23\)	\(21\)	\(106\)		$-$	$-$		$\mathrm{SU}(2)$