Space of modular forms of level 4019, weight 2, and trivial character

• Label: 4019.2.a
• Level: $4019$
• Weight: $2$
• Character orbit: 4019.a
• Rep. character: $\chi_{4019}(1,\cdot)$
• Character field: $\Q$
• Dimension: $335$
• Newform subspaces: $2$
• Sturm bound: $670$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(670\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4019))\).

	Total	New	Old
Modular forms	336	336	0
Cusp forms	335	335	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.

\(4019\)	Dim
\(+\)	\(149\)
\(-\)	\(186\)

Trace form

\( 335 q - 2 q^{2} - 2 q^{3} + 336 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 331 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4019))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		4019
4019.2.a.a	$4019$	$2$	4019.a	1.a	$1$	$149$	$149$	$32.092$		None	✓	$1$	$1$	\(-8\)	\(-12\)	\(-36\)	\(-32\)		$+$	$+$		$\mathrm{SU}(2)$
4019.2.a.b	$4019$	$2$	4019.a	1.a	$1$	$186$	$186$	$32.092$		None	✓	$1$	$0$	\(6\)	\(10\)	\(38\)	\(32\)		$-$	$-$		$\mathrm{SU}(2)$