Space of modular forms of level 29, weight 3, and Character 29.f

• Label: 29.3.f
• Level: $29$
• Weight: $3$
• Character orbit: 29.f
• Rep. character: $\chi_{29}(2,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $7$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	29.f (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(7\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(29, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	48	48	0
Eisenstein series	24	24	0

Trace form

48 * q - 16 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 28 * q^8 - 14 * q^9 - 20 * q^10 - 8 * q^11 - 68 * q^12 - 14 * q^13 + 26 * q^14 - 4 * q^15 + 18 * q^16 - 26 * q^17 - 34 * q^18 + 2 * q^19 + 46 * q^20 + 218 * q^21 + 154 * q^22 + 56 * q^23 + 154 * q^24 - 34 * q^25 + 110 * q^26 + 126 * q^27 - 170 * q^29 + 24 * q^30 - 88 * q^31 - 132 * q^32 - 224 * q^33 - 224 * q^34 - 210 * q^35 - 434 * q^36 - 56 * q^37 - 294 * q^38 - 232 * q^39 - 492 * q^40 - 34 * q^41 - 14 * q^42 + 176 * q^43 + 126 * q^44 + 114 * q^45 + 744 * q^46 + 208 * q^47 + 640 * q^48 + 506 * q^49 + 732 * q^50 + 322 * q^51 + 690 * q^52 - 14 * q^53 - 36 * q^54 + 284 * q^55 + 332 * q^56 - 508 * q^58 - 44 * q^59 - 316 * q^60 - 30 * q^61 - 504 * q^62 - 686 * q^63 - 896 * q^64 - 554 * q^65 - 608 * q^66 - 574 * q^67 - 796 * q^68 - 806 * q^69 - 1066 * q^70 + 224 * q^71 + 748 * q^72 - 22 * q^73 + 820 * q^74 + 768 * q^75 + 514 * q^76 + 436 * q^77 + 282 * q^78 + 564 * q^79 + 1162 * q^80 + 670 * q^81 - 18 * q^82 - 126 * q^83 + 572 * q^84 + 38 * q^85 - 118 * q^87 - 384 * q^88 - 160 * q^89 - 828 * q^90 - 434 * q^91 - 1022 * q^92 - 406 * q^93 - 2 * q^94 - 642 * q^95 - 1176 * q^96 + 604 * q^97 - 102 * q^98 + 316 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(29, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
29.3.f.a	$29$	$3$	29.f	29.f	$28$	$48$	$4$	$0.790$		None		✓	✓	✓	29.3.f.a	$2$	$0$	\(-16\)	\(-12\)	\(-14\)	\(-10\)		$\mathrm{SU}(2)[C_{28}]$