Space of modular forms of level 6019, weight 2, and trivial character

• Label: 6019.2.a
• Level: $6019$
• Weight: $2$
• Character orbit: 6019.a
• Rep. character: $\chi_{6019}(1,\cdot)$
• Character field: $\Q$
• Dimension: $463$
• Newform subspaces: $5$
• Sturm bound: $1082$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1082\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6019))\).

	Total	New	Old
Modular forms	542	463	79
Cusp forms	539	463	76
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.

\(13\)	\(463\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(108\)
\(+\)	\(-\)	$-$	\(123\)
\(-\)	\(+\)	$-$	\(130\)
\(-\)	\(-\)	$+$	\(102\)
Plus space		\(+\)	\(210\)
Minus space		\(-\)	\(253\)

Trace form

\( 463 q + q^{2} + 461 q^{4} + 6 q^{5} + 8 q^{7} - 3 q^{8} + 463 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		13	463
6019.2.a.a	$6019$	$2$	6019.a	1.a	$1$	$1$	$1$	$48.062$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}-3q^{7}-3q^{9}-q^{11}+\cdots\)
6019.2.a.b	$6019$	$2$	6019.a	1.a	$1$	$101$	$101$	$48.062$		None	✓	$1$	$1$	\(-8\)	\(-13\)	\(-43\)	\(-1\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6019.2.a.c	$6019$	$2$	6019.a	1.a	$1$	$108$	$108$	$48.062$		None	✓	$1$	$1$	\(-11\)	\(1\)	\(-40\)	\(-8\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6019.2.a.d	$6019$	$2$	6019.a	1.a	$1$	$123$	$123$	$48.062$		None	✓	$1$	$0$	\(10\)	\(1\)	\(46\)	\(12\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6019.2.a.e	$6019$	$2$	6019.a	1.a	$1$	$130$	$130$	$48.062$		None	✓	$1$	$0$	\(10\)	\(11\)	\(40\)	\(8\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6019))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6019)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(463))\)\(^{\oplus 2}\)