Space of modular forms of level 4034, weight 2, and trivial character

• Label: 4034.2.a
• Level: $4034$
• Weight: $2$
• Character orbit: 4034.a
• Rep. character: $\chi_{4034}(1,\cdot)$
• Character field: $\Q$
• Dimension: $169$
• Newform subspaces: $4$
• Sturm bound: $1009$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1009\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4034))\).

	Total	New	Old
Modular forms	506	169	337
Cusp forms	503	169	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.

\(2\)	\(2017\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(35\)
\(+\)	\(-\)	$-$	\(49\)
\(-\)	\(+\)	$-$	\(52\)
\(-\)	\(-\)	$+$	\(33\)
Plus space		\(+\)	\(68\)
Minus space		\(-\)	\(101\)

Trace form

\( 169 q + q^{2} + 4 q^{3} + 169 q^{4} + 4 q^{7} + q^{8} + 169 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4034))\) 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	2017
4034.2.a.a	$4034$	$2$	4034.a	1.a	$1$	$33$	$33$	$32.212$		None	✓	$1$	$1$	\(33\)	\(-14\)	\(-22\)	\(-12\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4034.2.a.b	$4034$	$2$	4034.a	1.a	$1$	$35$	$35$	$32.212$		None	✓	$1$	$1$	\(-35\)	\(-6\)	\(6\)	\(-14\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
4034.2.a.c	$4034$	$2$	4034.a	1.a	$1$	$49$	$49$	$32.212$		None	✓	$1$	$0$	\(-49\)	\(8\)	\(-8\)	\(18\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
4034.2.a.d	$4034$	$2$	4034.a	1.a	$1$	$52$	$52$	$32.212$		None	✓	$1$	$0$	\(52\)	\(16\)	\(24\)	\(12\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4034))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4034)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2017))\)\(^{\oplus 2}\)