Space of modular forms of level 6029, weight 2, and trivial character

• Label: 6029.2.a
• Level: $6029$
• Weight: $2$
• Character orbit: 6029.a
• Rep. character: $\chi_{6029}(1,\cdot)$
• Character field: $\Q$
• Dimension: $502$
• Newform subspaces: $2$
• Sturm bound: $1005$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1005\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6029))\).

	Total	New	Old
Modular forms	503	503	0
Cusp forms	502	502	0
Eisenstein series	1	1	0

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

\(6029\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(234\)	\(234\)	\(0\)		\(234\)	\(234\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(269\)	\(269\)	\(0\)		\(268\)	\(268\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

502 * q - 2 * q^2 + 502 * q^4 - 6 * q^5 - 6 * q^6 - 2 * q^7 - 6 * q^8 + 498 * q^9 + 2 * q^10 - 6 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 + 498 * q^16 + 6 * q^18 + 10 * q^19 - 22 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 - 18 * q^24 + 484 * q^25 - 20 * q^26 - 30 * q^28 - 22 * q^29 + 10 * q^30 + 6 * q^31 - 14 * q^32 + 6 * q^33 - 20 * q^34 - 14 * q^35 + 472 * q^36 + 2 * q^38 - 8 * q^39 + 10 * q^40 + 2 * q^41 + 16 * q^42 - 2 * q^43 - 30 * q^44 - 42 * q^45 - 12 * q^46 + 14 * q^47 - 24 * q^48 + 504 * q^49 - 12 * q^50 + 28 * q^51 - 24 * q^52 - 30 * q^53 - 28 * q^54 - 40 * q^55 - 46 * q^56 + 30 * q^57 - 32 * q^58 - 2 * q^59 - 30 * q^60 + 4 * q^61 - 20 * q^62 + 6 * q^63 + 476 * q^64 - 2 * q^65 - 104 * q^66 - 18 * q^67 - 44 * q^68 - 14 * q^69 - 12 * q^70 - 4 * q^71 - 12 * q^72 + 6 * q^73 - 52 * q^74 - 6 * q^75 + 36 * q^76 - 24 * q^77 - 88 * q^78 - 26 * q^79 - 72 * q^80 + 478 * q^81 + 38 * q^82 - 26 * q^83 - 12 * q^84 - 32 * q^85 + 28 * q^86 + 2 * q^87 - 16 * q^88 - 14 * q^89 - 2 * q^90 - 12 * q^91 - 6 * q^92 + 6 * q^93 + 32 * q^94 - 16 * q^95 - 28 * q^96 - 18 * q^97 - 32 * q^98 - 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6029))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		6029
6029.2.a.a	$6029$	$2$	6029.a	1.a	$1$	$234$	$234$	$48.142$		None	✓	✓	✓	✓	6029.2.a.a	$1$	$1$	\(-10\)	\(-43\)	\(-24\)	\(-61\)		$+$	$+$		$\mathrm{SU}(2)$
6029.2.a.b	$6029$	$2$	6029.a	1.a	$1$	$268$	$268$	$48.142$		None	✓	✓	✓	✓	6029.2.a.b	$1$	$0$	\(8\)	\(43\)	\(18\)	\(59\)		$-$	$-$		$\mathrm{SU}(2)$