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

• Label: 29.2.d
• Level: $29$
• Weight: $2$
• Character orbit: 29.d
• Rep. character: $\chi_{29}(7,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29.d (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
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	18	18	0
Cusp forms	6	6	0
Eisenstein series	12	12	0

Trace form

6 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + q^5 - 3 * q^6 + q^7 - 7 * q^8 + 6 * q^9 + 9 * q^10 - 11 * q^11 + 4 * q^12 - 5 * q^13 + 9 * q^14 + 5 * q^15 + 4 * q^16 + 8 * q^17 - 9 * q^18 + q^19 + 2 * q^20 + 5 * q^21 + 6 * q^22 - 7 * q^23 + 7 * q^24 - 24 * q^25 + 4 * q^26 - 11 * q^27 - 12 * q^28 + 6 * q^29 - 18 * q^30 + 5 * q^31 - 13 * q^32 + q^33 + 2 * q^34 - q^35 + 5 * q^36 + 11 * q^37 + 2 * q^38 + 3 * q^39 + 14 * q^40 + 20 * q^41 - 4 * q^42 + 13 * q^43 + 20 * q^44 + q^45 + 11 * q^47 + 6 * q^48 - 22 * q^49 + q^50 - 2 * q^51 - 10 * q^52 + 3 * q^53 + 6 * q^54 - 17 * q^55 - 7 * q^56 - 2 * q^57 - 16 * q^58 - 56 * q^59 - 4 * q^60 + 3 * q^61 + 3 * q^62 + 15 * q^63 + q^64 + 5 * q^65 - 5 * q^66 + 19 * q^67 - 12 * q^68 - 7 * q^69 - 2 * q^70 + 21 * q^71 - 25 * q^73 - 6 * q^74 + 48 * q^75 - 5 * q^76 + 11 * q^77 + 13 * q^78 - 9 * q^79 - 18 * q^80 + 18 * q^81 - 2 * q^82 + 17 * q^83 + 3 * q^84 - 8 * q^85 - 16 * q^86 - 5 * q^87 + 42 * q^88 + 7 * q^89 + 2 * q^90 + 5 * q^91 - 17 * q^93 + 8 * q^94 + 13 * q^95 - 2 * q^96 + q^97 + 19 * q^98 - 32 * q^99

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.d.a	$29$	$2$	29.d	29.d	$7$	$6$	$1$	$0.232$	\(\Q(\zeta_{14})\)	None		✓	✓	✓	29.2.d.a	$2$	$0$	\(-2\)	\(-5\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)