Space of modular forms of level 4022, weight 2, and trivial character

• Label: 4022.2.a
• Level: $4022$
• Weight: $2$
• Character orbit: 4022.a
• Rep. character: $\chi_{4022}(1,\cdot)$
• Character field: $\Q$
• Dimension: $168$
• Newform subspaces: $6$
• Sturm bound: $1006$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1006\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4022))\).

	Total	New	Old
Modular forms	505	168	337
Cusp forms	502	168	334
Eisenstein series	3	0	3

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
\(+\)	\(+\)	$+$	\(37\)
\(+\)	\(-\)	$-$	\(47\)
\(-\)	\(+\)	$-$	\(50\)
\(-\)	\(-\)	$+$	\(34\)
Plus space		\(+\)	\(71\)
Minus space		\(-\)	\(97\)

Trace form

\( 168 q + 4 q^{3} + 168 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 174 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4022))\) 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
4022.2.a.a	$4022$	$2$	4022.a	1.a	$1$	$1$	$1$	$32.116$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
4022.2.a.b	$4022$	$2$	4022.a	1.a	$1$	$3$	$3$	$32.116$	3.3.169.1	None	✓	$1$	$1$	\(3\)	\(-3\)	\(1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
4022.2.a.c	$4022$	$2$	4022.a	1.a	$1$	$31$	$31$	$32.116$		None	✓	$1$	$1$	\(31\)	\(-14\)	\(-13\)	\(-29\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4022.2.a.d	$4022$	$2$	4022.a	1.a	$1$	$37$	$37$	$32.116$		None	✓	$1$	$1$	\(-37\)	\(-5\)	\(-13\)	\(-22\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
4022.2.a.e	$4022$	$2$	4022.a	1.a	$1$	$46$	$46$	$32.116$		None	✓	$1$	$0$	\(-46\)	\(8\)	\(14\)	\(28\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
4022.2.a.f	$4022$	$2$	4022.a	1.a	$1$	$50$	$50$	$32.116$		None	✓	$1$	$0$	\(50\)	\(18\)	\(11\)	\(30\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4022))\) into lower level spaces

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