Space of modular forms of level 99, weight 4, and Character 99.p

• Label: 99.4.p
• Level: $99$
• Weight: $4$
• Character orbit: 99.p
• Rep. character: $\chi_{99}(2,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $272$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.p (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(99, [\chi])\).

	Total	New	Old
Modular forms	304	304	0
Cusp forms	272	272	0
Eisenstein series	32	32	0

Trace form

272 * q - 15 * q^2 - 6 * q^3 + 125 * q^4 + 3 * q^5 - 60 * q^6 - 5 * q^7 - 88 * q^9 + 51 * q^11 - 6 * q^12 - 5 * q^13 - 9 * q^14 + 60 * q^15 + 461 * q^16 + 450 * q^18 + 430 * q^19 - 129 * q^20 - 2 * q^22 + 228 * q^23 + 550 * q^24 - 725 * q^25 - 924 * q^27 - 20 * q^28 - 915 * q^29 - 520 * q^30 + 15 * q^31 - 1973 * q^33 - 172 * q^34 - 182 * q^36 + 60 * q^37 + 1341 * q^38 - 1700 * q^39 + 315 * q^40 - 15 * q^41 + 1507 * q^42 + 2322 * q^45 - 100 * q^46 - 1173 * q^47 + 316 * q^48 - 1081 * q^49 + 1860 * q^50 + 195 * q^51 - 5 * q^52 + 846 * q^55 - 1962 * q^56 + 4440 * q^57 + 721 * q^58 - 3456 * q^59 + 1261 * q^60 - 5 * q^61 - 3960 * q^63 - 2780 * q^64 - 6903 * q^66 + 1990 * q^67 - 11520 * q^68 - 89 * q^69 + 1614 * q^70 + 1625 * q^72 - 20 * q^73 - 15 * q^74 + 2469 * q^75 + 10860 * q^77 - 1912 * q^78 - 5 * q^79 - 484 * q^81 + 3088 * q^82 - 6405 * q^83 - 6375 * q^84 - 5 * q^85 - 4863 * q^86 + 4780 * q^88 + 5600 * q^90 - 152 * q^91 + 19443 * q^92 + 482 * q^93 - 5 * q^94 + 10305 * q^95 + 14855 * q^96 + 654 * q^97 + 7439 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(99, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.4.p.a	$99$	$4$	99.p	99.p	$30$	$272$	$34$	$5.841$		None		✓	✓	✓	99.4.p.a	$4$	$0$	\(-15\)	\(-6\)	\(3\)	\(-5\)		$\mathrm{SU}(2)[C_{30}]$