Space of modular forms of level 2011, weight 2, and trivial character

• Label: 2011.2.a
• Level: $2011$
• Weight: $2$
• Character orbit: 2011.a
• Rep. character: $\chi_{2011}(1,\cdot)$
• Character field: $\Q$
• Dimension: $167$
• Newform subspaces: $2$
• Sturm bound: $335$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(335\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2011))\).

	Total	New	Old
Modular forms	168	168	0
Cusp forms	167	167	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.

\(2011\)	Dim
\(+\)	\(77\)
\(-\)	\(90\)

Trace form

\( 167 q - 2 q^{2} - 4 q^{3} + 162 q^{4} - 4 q^{7} + 161 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2011))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2011
2011.2.a.a	$2011$	$2$	2011.a	1.a	$1$	$77$	$77$	$16.058$		None	✓	$1$	$1$	\(-13\)	\(-13\)	\(-47\)	\(-8\)		$+$	$+$		$\mathrm{SU}(2)$
2011.2.a.b	$2011$	$2$	2011.a	1.a	$1$	$90$	$90$	$16.058$		None	✓	$1$	$0$	\(11\)	\(9\)	\(47\)	\(4\)		$-$	$-$		$\mathrm{SU}(2)$