Space of modular forms of level 5029, weight 2, and trivial character

• Label: 5029.2.a
• Level: $5029$
• Weight: $2$
• Character orbit: 5029.a
• Rep. character: $\chi_{5029}(1,\cdot)$
• Character field: $\Q$
• Dimension: $405$
• Newform subspaces: $4$
• Sturm bound: $864$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 5029 = 47 \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5029.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(864\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5029))\).

	Total	New	Old
Modular forms	434	405	29
Cusp forms	431	405	26
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.

\(47\)	\(107\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(99\)	\(97\)	\(2\)		\(99\)	\(97\)	\(2\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(118\)	\(110\)	\(8\)		\(117\)	\(110\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(112\)	\(105\)	\(7\)		\(111\)	\(105\)	\(6\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(105\)	\(93\)	\(12\)		\(104\)	\(93\)	\(11\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(204\)	\(190\)	\(14\)		\(203\)	\(190\)	\(13\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(230\)	\(215\)	\(15\)		\(228\)	\(215\)	\(13\)		\(2\)	\(0\)	\(2\)

Trace form

405 * q + q^2 + 405 * q^4 - 2 * q^5 + 12 * q^6 - 4 * q^7 + 9 * q^8 + 409 * q^9 + 6 * q^10 + 12 * q^11 + 6 * q^12 - 22 * q^13 + 6 * q^14 + 8 * q^15 + 417 * q^16 + 2 * q^17 + 3 * q^18 + 2 * q^20 - 4 * q^21 + 16 * q^22 - 4 * q^23 + 50 * q^24 + 399 * q^25 + 10 * q^26 + 12 * q^27 - 16 * q^28 + 14 * q^29 - 16 * q^30 - 21 * q^32 + 36 * q^33 - 6 * q^34 + 32 * q^35 + 381 * q^36 - 26 * q^37 - 4 * q^38 - 38 * q^40 - 18 * q^41 - 42 * q^42 - 20 * q^43 + 84 * q^44 + 22 * q^45 - 24 * q^46 - 9 * q^47 - 28 * q^48 + 401 * q^49 - 29 * q^50 + 8 * q^51 - 74 * q^52 + 10 * q^53 + 30 * q^54 + 72 * q^55 - 20 * q^56 - 32 * q^57 - 18 * q^58 + 28 * q^59 - 76 * q^60 - 30 * q^61 - 64 * q^62 - 16 * q^63 + 465 * q^64 - 80 * q^65 - 96 * q^66 + 12 * q^67 - 40 * q^68 + 20 * q^69 - 12 * q^70 + 60 * q^71 - 55 * q^72 - 42 * q^73 - 38 * q^74 + 36 * q^75 - 24 * q^76 + 16 * q^77 - 20 * q^78 - 42 * q^80 + 397 * q^81 - 54 * q^82 - 68 * q^83 - 66 * q^84 + 8 * q^85 - 104 * q^86 + 32 * q^87 + 24 * q^88 - 10 * q^89 + 10 * q^90 - 20 * q^91 - 52 * q^92 + 3 * q^94 + 4 * q^95 - 96 * q^96 - 34 * q^97 - 23 * q^98 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5029))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		47	107
5029.2.a.a	$5029$	$2$	5029.a	1.a	$1$	$93$	$93$	$40.157$		None	✓	✓	✓	✓	5029.2.a.a	$1$	$1$	\(-8\)	\(-17\)	\(-24\)	\(-9\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
5029.2.a.b	$5029$	$2$	5029.a	1.a	$1$	$97$	$97$	$40.157$		None	✓	✓	✓	✓	5029.2.a.b	$1$	$1$	\(-11\)	\(-17\)	\(-16\)	\(-17\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
5029.2.a.c	$5029$	$2$	5029.a	1.a	$1$	$105$	$105$	$40.157$		None	✓	✓	✓	✓	5029.2.a.c	$1$	$0$	\(10\)	\(15\)	\(26\)	\(11\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
5029.2.a.d	$5029$	$2$	5029.a	1.a	$1$	$110$	$110$	$40.157$		None	✓	✓	✓	✓	5029.2.a.d	$1$	$0$	\(10\)	\(19\)	\(12\)	\(11\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5029))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5029)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(107))\)\(^{\oplus 2}\)