Space of modular forms of level 29, weight 2, and trivial character

• Label: 29.2.a
• Level: $29$
• Weight: $2$
• Character orbit: 29.a
• Rep. character: $\chi_{29}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(29))\).

	Total	New	Old
Modular forms	3	3	0
Cusp forms	2	2	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.

\(29\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(-\)		\(3\)	\(3\)	\(0\)		\(2\)	\(2\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 6 * q^6 - 6 * q^8 + 2 * q^10 + 2 * q^11 + 10 * q^12 - 2 * q^13 + 8 * q^14 - 2 * q^15 + 6 * q^16 - 4 * q^17 - 8 * q^18 + 12 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 4 * q^23 - 10 * q^24 - 8 * q^25 + 10 * q^26 + 2 * q^27 - 16 * q^28 + 2 * q^29 + 6 * q^30 + 6 * q^31 + 6 * q^32 - 2 * q^33 - 4 * q^34 + 16 * q^36 - 8 * q^37 - 12 * q^38 - 10 * q^39 + 6 * q^40 + 8 * q^41 + 16 * q^42 + 10 * q^43 - 6 * q^44 - 12 * q^46 + 2 * q^47 + 6 * q^48 + 2 * q^49 + 8 * q^50 + 4 * q^51 - 18 * q^52 + 2 * q^53 + 2 * q^54 - 2 * q^55 + 8 * q^56 + 12 * q^57 - 2 * q^58 + 4 * q^59 - 10 * q^60 - 4 * q^61 - 26 * q^62 - 16 * q^63 - 14 * q^64 + 2 * q^65 + 2 * q^66 + 12 * q^68 + 12 * q^69 - 8 * q^70 - 12 * q^71 - 8 * q^72 + 8 * q^73 + 8 * q^74 - 8 * q^75 + 12 * q^76 + 8 * q^77 + 22 * q^78 - 2 * q^79 - 6 * q^80 - 2 * q^81 + 16 * q^82 + 4 * q^83 - 24 * q^84 + 4 * q^85 - 6 * q^86 + 2 * q^87 - 2 * q^88 - 8 * q^89 + 8 * q^90 + 16 * q^91 + 28 * q^92 + 26 * q^93 + 10 * q^94 - 12 * q^95 + 2 * q^96 - 8 * q^97 - 2 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		29
29.2.a.a	$29$	$2$	29.a	1.a	$1$	$2$	$2$	$0.232$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	29.2.a.a	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)