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

• Label: 29.2.e
• Level: $29$
• Weight: $2$
• Character orbit: 29.e
• Rep. character: $\chi_{29}(4,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
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	24	24	0
Cusp forms	12	12	0
Eisenstein series	12	12	0

Trace form

12 * q - 7 * q^2 - 7 * q^3 - q^4 - q^5 - 3 * q^6 - 11 * q^7 + 14 * q^8 - 3 * q^9 - 7 * q^10 + 7 * q^11 + 9 * q^13 - 7 * q^14 + 7 * q^15 + 9 * q^16 + 42 * q^18 - 7 * q^19 - 11 * q^20 - 7 * q^21 - 4 * q^22 - 5 * q^23 - 25 * q^24 + 13 * q^25 - 21 * q^26 - 7 * q^27 + 12 * q^28 - 15 * q^29 + 2 * q^30 - 21 * q^31 - 17 * q^33 - 13 * q^34 + 19 * q^35 - 40 * q^36 + 7 * q^37 + 28 * q^38 + 21 * q^39 + 35 * q^40 + 50 * q^42 + 7 * q^43 + 42 * q^44 + 16 * q^45 - 7 * q^47 - 14 * q^48 + 13 * q^49 - 28 * q^50 + 20 * q^51 - 6 * q^52 - 10 * q^53 - 38 * q^54 - 35 * q^55 - 21 * q^56 - 14 * q^57 - 57 * q^58 + 44 * q^59 - 28 * q^60 - 7 * q^61 + 37 * q^62 - 13 * q^63 - 26 * q^64 - 6 * q^65 + 21 * q^66 - 37 * q^67 + 14 * q^68 + 21 * q^69 - 21 * q^71 + 35 * q^72 + 14 * q^73 + 7 * q^76 - 7 * q^77 + 17 * q^78 + 49 * q^79 - 6 * q^80 + q^81 + 22 * q^82 + 5 * q^83 + 21 * q^84 + 14 * q^85 - 44 * q^86 + 15 * q^87 - 66 * q^88 + 7 * q^89 + 28 * q^90 - 3 * q^91 - 6 * q^92 + 19 * q^93 + 66 * q^94 - 7 * q^95 + 30 * q^96 + 14 * q^97 - 42 * q^98

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.e.a	$29$	$2$	29.e	29.e	$14$	$12$	$2$	$0.232$	12.0.\(\cdots\).1	None		✓	✓	✓	29.2.e.a	$2$	$0$	\(-7\)	\(-7\)	\(-1\)	\(-11\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)