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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(117\)	\(110\)	\(7\)		\(117\)	\(110\)	\(7\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(142\)	\(133\)	\(9\)		\(141\)	\(133\)	\(8\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(143\)	\(135\)	\(8\)		\(142\)	\(135\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(118\)	\(109\)	\(9\)		\(117\)	\(109\)	\(8\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(235\)	\(219\)	\(16\)		\(234\)	\(219\)	\(15\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(285\)	\(268\)	\(17\)		\(283\)	\(268\)	\(15\)		\(2\)	\(0\)	\(2\)

Trace form

487 * q + 3 * q^2 + 4 * q^3 + 485 * q^4 + 6 * q^5 + 15 * q^8 + 491 * q^9 - 14 * q^10 + 12 * q^12 + 2 * q^13 - 24 * q^15 + 461 * q^16 + 14 * q^17 + 23 * q^18 - 4 * q^19 + 26 * q^20 + 24 * q^21 - 16 * q^22 - 12 * q^23 + 477 * q^25 + 18 * q^26 + 40 * q^27 - 8 * q^28 + 14 * q^29 - 16 * q^30 - 4 * q^31 + 23 * q^32 - 4 * q^33 - 42 * q^34 + 4 * q^35 + 433 * q^36 + q^37 + 12 * q^38 - 36 * q^39 - 46 * q^40 + 36 * q^41 - 60 * q^42 - 14 * q^43 - 24 * q^44 + 38 * q^45 + 32 * q^46 - 6 * q^47 - 8 * q^48 + 511 * q^49 + q^50 - 36 * q^51 - 26 * q^52 - 4 * q^53 + 28 * q^54 - 56 * q^55 - 28 * q^56 - 32 * q^57 + 18 * q^58 - 16 * q^59 - 32 * q^60 - 8 * q^62 - 28 * q^63 + 445 * q^64 - 60 * q^65 + 72 * q^66 + 8 * q^67 + 110 * q^68 - 16 * q^69 - 20 * q^70 - 26 * q^71 + 63 * q^72 - 6 * q^73 - 7 * q^74 + 4 * q^75 + 36 * q^76 + 36 * q^77 + 36 * q^78 - 24 * q^79 + 78 * q^80 + 511 * q^81 + 6 * q^82 + 30 * q^83 + 12 * q^84 + 4 * q^85 - 68 * q^86 - 12 * q^87 - 48 * q^88 + 18 * q^89 + 14 * q^90 - 8 * q^91 - 68 * q^92 + 40 * q^93 - 96 * q^94 + 56 * q^95 - 60 * q^96 - 60 * q^97 + 43 * q^98 + 12 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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	✓	✓			6031.2.a.a	$1$	$0$	\(0\)	\(3\)	\(4\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{4}+4q^{5}+q^{7}+6q^{9}+\cdots\)
6031.2.a.b	$6031$	$2$	6031.a	1.a	$1$	$109$	$109$	$48.158$		None	✓	✓	✓	✓	6031.2.a.b	$1$	$1$	\(-11\)	\(-14\)	\(-28\)	\(-16\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6031.2.a.c	$6031$	$2$	6031.a	1.a	$1$	$110$	$110$	$48.158$		None	✓	✓	✓	✓	6031.2.a.c	$1$	$1$	\(-9\)	\(0\)	\(-26\)	\(-4\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6031.2.a.d	$6031$	$2$	6031.a	1.a	$1$	$133$	$133$	$48.158$		None	✓	✓	✓	✓	6031.2.a.d	$1$	$0$	\(14\)	\(8\)	\(34\)	\(8\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6031.2.a.e	$6031$	$2$	6031.a	1.a	$1$	$134$	$134$	$48.158$		None	✓	✓	✓		6031.2.a.e	$1$	$0$	\(9\)	\(7\)	\(22\)	\(11\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

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

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