Space of modular forms of level 29, weight 2, and Character 29.b

• Label: 29.2.b
• Level: $29$
• Weight: $2$
• Character orbit: 29.b
• Rep. character: $\chi_{29}(28,\cdot)$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(29, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

2 * q - 6 * q^4 - 6 * q^5 + 10 * q^6 + 4 * q^7 - 4 * q^9 - 2 * q^13 - 2 * q^16 + 18 * q^20 - 10 * q^22 + 12 * q^23 - 10 * q^24 + 8 * q^25 - 12 * q^28 - 6 * q^29 - 30 * q^30 + 10 * q^33 + 20 * q^34 - 12 * q^35 + 12 * q^36 + 20 * q^42 + 12 * q^45 - 6 * q^49 - 20 * q^51 + 6 * q^52 - 18 * q^53 + 10 * q^54 - 20 * q^58 + 12 * q^59 - 30 * q^62 - 8 * q^63 + 26 * q^64 + 6 * q^65 + 16 * q^67 - 10 * q^78 + 6 * q^80 - 22 * q^81 + 20 * q^82 - 12 * q^83 + 30 * q^86 + 20 * q^87 + 10 * q^88 - 4 * q^91 - 36 * q^92 + 30 * q^93 - 10 * q^94 - 30 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(29, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
29.2.b.a	$29$	$2$	29.b	29.b	$2$	$2$	$2$	$0.232$	\(\Q(\sqrt{-5}) \)	None		✓	✓	✓	29.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)