Space of modular forms of level 99, weight 2, and Character 99.e

• Label: 99.2.e
• Level: $99$
• Weight: $2$
• Character orbit: 99.e
• Rep. character: $\chi_{99}(34,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(99, [\chi])\).

	Total	New	Old
Modular forms	28	20	8
Cusp forms	20	20	0
Eisenstein series	8	0	8

Trace form

20 * q - q^3 - 10 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 12 * q^8 - 5 * q^9 - 4 * q^11 - 2 * q^12 - 2 * q^13 + 6 * q^14 + 8 * q^15 - 10 * q^16 - 12 * q^17 + 4 * q^18 + 4 * q^19 + 6 * q^20 - 4 * q^21 - 6 * q^23 + 18 * q^24 - 7 * q^25 + 48 * q^26 - 22 * q^27 + 16 * q^28 + 12 * q^29 - 22 * q^30 - 5 * q^31 + 12 * q^32 + 2 * q^33 - 12 * q^34 + 26 * q^36 - 2 * q^37 - 30 * q^38 - 40 * q^39 - 12 * q^40 + 12 * q^41 + 26 * q^42 - 8 * q^43 + 20 * q^44 + 19 * q^45 + 6 * q^47 - 50 * q^48 - 6 * q^50 - 34 * q^51 + 10 * q^52 - 12 * q^53 - 28 * q^54 - 6 * q^55 - 12 * q^56 + 18 * q^57 + 18 * q^58 - 27 * q^59 + 88 * q^60 - 2 * q^61 - 60 * q^62 + 52 * q^63 + 8 * q^64 + 18 * q^65 - 10 * q^66 - 11 * q^67 - 18 * q^68 - 29 * q^69 + 12 * q^70 + 66 * q^71 + 84 * q^72 + 28 * q^73 + 54 * q^74 + 37 * q^75 - 20 * q^76 - 8 * q^77 - 10 * q^78 - 2 * q^79 - 96 * q^80 + 7 * q^81 + 12 * q^82 + 22 * q^84 - 24 * q^85 + 36 * q^86 - 12 * q^89 - 128 * q^90 + 44 * q^91 - 54 * q^92 + 29 * q^93 + 30 * q^94 + 36 * q^95 - 68 * q^96 - 23 * q^97 + 36 * q^98 - 5 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(99, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.2.e.a	$99$	$2$	99.e	9.c	$3$	$2$	$1$	$0.791$	\(\Q(\sqrt{-3}) \)	None		✓			99.2.e.a	$2$	$0$	\(-1\)	\(-3\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
99.2.e.b	$99$	$2$	99.e	9.c	$3$	$2$	$1$	$0.791$	\(\Q(\sqrt{-3}) \)	None		✓			99.2.e.b	$2$	$0$	\(0\)	\(-3\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
99.2.e.c	$99$	$2$	99.e	9.c	$3$	$2$	$1$	$0.791$	\(\Q(\sqrt{-3}) \)	None		✓			99.2.e.c	$2$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
99.2.e.d	$99$	$2$	99.e	9.c	$3$	$6$	$3$	$0.791$	\(\Q(\zeta_{18})\)	None		✓			99.2.e.d	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{5}-\beta_{4}+\cdots+\beta_{2})q^{2}+\cdots+(\beta_{4}+\beta_{2})q^{3}+\cdots\)
99.2.e.e	$99$	$2$	99.e	9.c	$3$	$8$	$4$	$0.791$	8.0.508277025.1	None		✓	✓		99.2.e.e	$2$	$0$	\(-1\)	\(5\)	\(-4\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)