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

• Label: 99.4.e
• Level: $99$
• Weight: $4$
• Character orbit: 99.e
• Rep. character: $\chi_{99}(34,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	76	60	16
Cusp forms	68	60	8
Eisenstein series	8	0	8

Trace form

60 * q + 2 * q^3 - 120 * q^4 + 24 * q^5 + 14 * q^6 + 12 * q^7 - 12 * q^8 - 44 * q^9 + 44 * q^11 + 298 * q^12 - 24 * q^13 + 150 * q^14 - 28 * q^15 - 480 * q^16 + 96 * q^17 - 716 * q^18 + 120 * q^19 + 150 * q^20 + 80 * q^21 + 264 * q^23 + 102 * q^24 - 822 * q^25 + 696 * q^26 + 572 * q^27 - 384 * q^28 + 84 * q^29 - 574 * q^30 + 102 * q^31 - 1392 * q^32 + 176 * q^33 + 396 * q^34 + 1080 * q^35 + 194 * q^36 + 264 * q^37 - 1038 * q^38 - 64 * q^39 + 180 * q^40 + 156 * q^41 + 2078 * q^42 - 168 * q^43 - 880 * q^44 + 430 * q^45 + 1080 * q^46 + 816 * q^47 + 1258 * q^48 - 2106 * q^49 - 1554 * q^50 + 740 * q^51 - 1302 * q^52 - 228 * q^53 - 124 * q^54 - 396 * q^55 + 1500 * q^56 + 1200 * q^57 - 594 * q^58 + 2250 * q^59 - 1874 * q^60 + 876 * q^61 - 3300 * q^62 - 632 * q^63 + 5748 * q^64 - 1800 * q^65 - 550 * q^66 + 894 * q^67 + 126 * q^68 + 1510 * q^69 + 360 * q^70 - 4884 * q^71 - 4764 * q^72 - 672 * q^73 + 1134 * q^74 - 1670 * q^75 - 2076 * q^76 + 616 * q^77 + 5870 * q^78 - 420 * q^79 + 2100 * q^80 + 1444 * q^81 - 5148 * q^82 + 684 * q^83 - 8822 * q^84 + 1656 * q^85 - 576 * q^86 - 1464 * q^87 - 2784 * q^89 + 8968 * q^90 + 3480 * q^91 + 3546 * q^92 + 1640 * q^93 + 2574 * q^94 - 2628 * q^95 - 1040 * q^96 + 840 * q^97 + 6444 * q^98 - 110 * 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.e.a	$99$	$4$	99.e	9.c	$3$	$2$	$1$	$5.841$	\(\Q(\sqrt{-3}) \)	None		✓			99.4.e.a	$2$	$0$	\(4\)	\(-9\)	\(19\)	\(26\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\zeta_{6})q^{2}+(-6+3\zeta_{6})q^{3}-8\zeta_{6}q^{4}+\cdots\)
99.4.e.b	$99$	$4$	99.e	9.c	$3$	$24$	$12$	$5.841$		None		✓			99.4.e.b	$2$	$0$	\(-4\)	\(6\)	\(2\)	\(8\)		$\mathrm{SU}(2)[C_{3}]$
99.4.e.c	$99$	$4$	99.e	9.c	$3$	$34$	$17$	$5.841$		None		✓	✓		99.4.e.c	$2$	$0$	\(0\)	\(5\)	\(3\)	\(-22\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(99, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)