Space of modular forms of level 6038, weight 2, and trivial character

• Label: 6038.2.a
• Level: $6038$
• Weight: $2$
• Character orbit: 6038.a
• Rep. character: $\chi_{6038}(1,\cdot)$
• Character field: $\Q$
• Dimension: $252$
• Newform subspaces: $5$
• Sturm bound: $1510$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1510\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6038))\).

	Total	New	Old
Modular forms	757	252	505
Cusp forms	754	252	502
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.

\(2\)	\(3019\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(57\)
\(+\)	\(-\)	$-$	\(69\)
\(-\)	\(+\)	$-$	\(72\)
\(-\)	\(-\)	$+$	\(54\)
Plus space		\(+\)	\(111\)
Minus space		\(-\)	\(141\)

Trace form

\( 252 q + 4 q^{3} + 252 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 258 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6038))\) 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	3019
6038.2.a.a	$6038$	$2$	6038.a	1.a	$1$	$2$	$2$	$48.214$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$2$	\(2\)	\(-3\)	\(-5\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+\beta )q^{5}+\cdots\)
6038.2.a.b	$6038$	$2$	6038.a	1.a	$1$	$54$	$54$	$48.214$		None	✓	$1$	$1$	\(54\)	\(-21\)	\(-14\)	\(-44\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6038.2.a.c	$6038$	$2$	6038.a	1.a	$1$	$57$	$57$	$48.214$		None	✓	$1$	$1$	\(-57\)	\(-5\)	\(-15\)	\(-28\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6038.2.a.d	$6038$	$2$	6038.a	1.a	$1$	$69$	$69$	$48.214$		None	✓	$1$	$0$	\(-69\)	\(8\)	\(18\)	\(32\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6038.2.a.e	$6038$	$2$	6038.a	1.a	$1$	$70$	$70$	$48.214$		None	✓	$1$	$0$	\(70\)	\(25\)	\(18\)	\(50\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6038))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(3019))\)\(^{\oplus 2}\)