Space of modular forms of level 8044, weight 2, and trivial character

• Label: 8044.2.a
• Level: $8044$
• Weight: $2$
• Character orbit: 8044.a
• Rep. character: $\chi_{8044}(1,\cdot)$
• Character field: $\Q$
• Dimension: $167$
• Newform subspaces: $2$
• Sturm bound: $2012$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8044 = 2^{2} \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8044.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(2012\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8044))\).

	Total	New	Old
Modular forms	1009	167	842
Cusp forms	1004	167	837
Eisenstein series	5	0	5

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

\(2\)	\(2011\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(87\)
\(-\)	\(-\)	$+$	\(80\)
Plus space		\(+\)	\(80\)
Minus space		\(-\)	\(87\)

Trace form

\( 167 q - 4 q^{5} - 4 q^{7} + 161 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8044))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	2011
8044.2.a.a	$8044$	$2$	8044.a	1.a	$1$	$80$	$80$	$64.232$		None	✓	$1$	$1$	\(0\)	\(-13\)	\(-2\)	\(-12\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
8044.2.a.b	$8044$	$2$	8044.a	1.a	$1$	$87$	$87$	$64.232$		None	✓	$1$	$0$	\(0\)	\(13\)	\(-2\)	\(8\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8044))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8044)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2011))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4022))\)\(^{\oplus 2}\)