Space of modular forms of level 2008, weight 4, and trivial character

• Label: 2008.4.a
• Level: $2008$
• Weight: $4$
• Character orbit: 2008.a
• Rep. character: $\chi_{2008}(1,\cdot)$
• Character field: $\Q$
• Dimension: $187$
• Newform subspaces: $4$
• Sturm bound: $1008$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2008 = 2^{3} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2008.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1008\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2008))\).

	Total	New	Old
Modular forms	760	187	573
Cusp forms	752	187	565
Eisenstein series	8	0	8

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

\(2\)	\(251\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(43\)
\(+\)	\(-\)	$-$	\(50\)
\(-\)	\(+\)	$-$	\(40\)
\(-\)	\(-\)	$+$	\(54\)
Plus space		\(+\)	\(97\)
Minus space		\(-\)	\(90\)

Trace form

\( 187 q + 6 q^{3} + 4 q^{5} - 36 q^{7} + 1693 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2008))\) 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	251
2008.4.a.a	$2008$	$4$	2008.a	1.a	$1$	$40$	$40$	$118.476$		None	✓	$1$	$1$	\(0\)	\(-4\)	\(-32\)	\(-10\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2008.4.a.b	$2008$	$4$	2008.a	1.a	$1$	$43$	$43$	$118.476$		None	✓	$1$	$0$	\(0\)	\(16\)	\(34\)	\(41\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
2008.4.a.c	$2008$	$4$	2008.a	1.a	$1$	$50$	$50$	$118.476$		None	✓	$1$	$1$	\(0\)	\(-11\)	\(-31\)	\(-71\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2008.4.a.d	$2008$	$4$	2008.a	1.a	$1$	$54$	$54$	$118.476$		None	✓	$1$	$0$	\(0\)	\(5\)	\(33\)	\(4\)		$-$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2008))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2008)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 2}\)