Space of modular forms of level 2031, weight 4, and trivial character

• Label: 2031.4.a
• Level: $2031$
• Weight: $4$
• Character orbit: 2031.a
• Rep. character: $\chi_{2031}(1,\cdot)$
• Character field: $\Q$
• Dimension: $338$
• Newform subspaces: $4$
• Sturm bound: $904$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2031 = 3 \cdot 677 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2031.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(904\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2031))\).

	Total	New	Old
Modular forms	680	338	342
Cusp forms	676	338	338
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(677\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(187\)	\(94\)	\(93\)		\(186\)	\(94\)	\(92\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(153\)	\(75\)	\(78\)		\(152\)	\(75\)	\(77\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(168\)	\(75\)	\(93\)		\(167\)	\(75\)	\(92\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(172\)	\(94\)	\(78\)		\(171\)	\(94\)	\(77\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(359\)	\(188\)	\(171\)		\(357\)	\(188\)	\(169\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(321\)	\(150\)	\(171\)		\(319\)	\(150\)	\(169\)		\(2\)	\(0\)	\(2\)

Trace form

338 * q + 4 * q^2 + 1332 * q^4 + 16 * q^5 - 12 * q^7 + 48 * q^8 + 3042 * q^9 + 84 * q^10 - 56 * q^11 + 44 * q^13 - 272 * q^14 + 5236 * q^16 - 96 * q^17 + 36 * q^18 + 136 * q^19 - 92 * q^20 - 84 * q^21 - 464 * q^22 - 152 * q^23 + 8354 * q^25 - 560 * q^28 + 352 * q^29 + 48 * q^30 + 404 * q^31 + 28 * q^32 + 96 * q^33 + 288 * q^34 - 464 * q^35 + 11988 * q^36 - 420 * q^37 + 40 * q^38 + 748 * q^40 - 320 * q^41 + 168 * q^42 + 64 * q^43 + 660 * q^44 + 144 * q^45 + 832 * q^46 - 696 * q^47 - 624 * q^48 + 16902 * q^49 - 700 * q^50 - 664 * q^52 - 1760 * q^53 - 1904 * q^55 - 1980 * q^56 + 84 * q^57 - 1444 * q^58 - 520 * q^59 + 1224 * q^60 - 1528 * q^61 + 2856 * q^62 - 108 * q^63 + 21616 * q^64 + 1368 * q^65 - 592 * q^67 + 960 * q^68 + 5752 * q^70 + 1208 * q^71 + 432 * q^72 - 548 * q^73 + 4964 * q^74 + 48 * q^75 + 6888 * q^76 + 1904 * q^77 + 780 * q^78 - 1288 * q^79 - 2100 * q^80 + 27378 * q^81 + 1584 * q^82 - 1040 * q^83 - 2808 * q^84 + 3896 * q^85 + 2716 * q^86 + 384 * q^87 - 996 * q^88 + 1776 * q^89 + 756 * q^90 + 3176 * q^91 + 3168 * q^92 - 1332 * q^93 - 1584 * q^94 - 1648 * q^95 + 300 * q^96 - 116 * q^97 + 540 * q^98 - 504 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2031))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	677
2031.4.a.a	$2031$	$4$	2031.a	1.a	$1$	$75$	$75$	$119.833$		None	✓	✓	✓	✓	2031.4.a.a	$1$	$1$	\(-17\)	\(225\)	\(-76\)	\(-59\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2031.4.a.b	$2031$	$4$	2031.a	1.a	$1$	$75$	$75$	$119.833$		None	✓	✓	✓	✓	2031.4.a.b	$1$	$1$	\(5\)	\(-225\)	\(-16\)	\(-45\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2031.4.a.c	$2031$	$4$	2031.a	1.a	$1$	$94$	$94$	$119.833$		None	✓	✓	✓	✓	2031.4.a.c	$1$	$0$	\(-3\)	\(-282\)	\(24\)	\(53\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
2031.4.a.d	$2031$	$4$	2031.a	1.a	$1$	$94$	$94$	$119.833$		None	✓	✓	✓	✓	2031.4.a.d	$1$	$0$	\(19\)	\(282\)	\(84\)	\(39\)		$-$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2031))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2031)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(677))\)\(^{\oplus 2}\)