Space of modular forms of level 6031, weight 2, and trivial character

• Label: 6031.2.a
• Level: $6031$
• Weight: $2$
• Character orbit: 6031.a
• Rep. character: $\chi_{6031}(1,\cdot)$
• Character field: $\Q$
• Dimension: $487$
• Newform subspaces: $5$
• Sturm bound: $1038$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1038\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6031))\).

	Total	New	Old
Modular forms	520	487	33
Cusp forms	517	487	30
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.

\(37\)	\(163\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(110\)
\(+\)	\(-\)	$-$	\(133\)
\(-\)	\(+\)	$-$	\(135\)
\(-\)	\(-\)	$+$	\(109\)
Plus space		\(+\)	\(219\)
Minus space		\(-\)	\(268\)

Trace form

\( 487 q + 3 q^{2} + 4 q^{3} + 485 q^{4} + 6 q^{5} + 15 q^{8} + 491 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6031))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		37	163
6031.2.a.a	$6031$	$2$	6031.a	1.a	$1$	$1$	$1$	$48.158$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{4}+4q^{5}+q^{7}+6q^{9}+\cdots\)
6031.2.a.b	$6031$	$2$	6031.a	1.a	$1$	$109$	$109$	$48.158$		None	✓	$1$	$1$	\(-11\)	\(-14\)	\(-28\)	\(-16\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6031.2.a.c	$6031$	$2$	6031.a	1.a	$1$	$110$	$110$	$48.158$		None	✓	$1$	$1$	\(-9\)	\(0\)	\(-26\)	\(-4\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6031.2.a.d	$6031$	$2$	6031.a	1.a	$1$	$133$	$133$	$48.158$		None	✓	$1$	$0$	\(14\)	\(8\)	\(34\)	\(8\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6031.2.a.e	$6031$	$2$	6031.a	1.a	$1$	$134$	$134$	$48.158$		None	✓	$1$	$0$	\(9\)	\(7\)	\(22\)	\(11\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6031))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(163))\)\(^{\oplus 2}\)