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

• Label: 99.2.f
• Level: $99$
• Weight: $2$
• Character orbit: 99.f
• Rep. character: $\chi_{99}(37,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
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	64	24	40
Cusp forms	32	16	16
Eisenstein series	32	8	24

Trace form

16 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 8 * q^7 - 8 * q^8 - 24 * q^10 + 2 * q^11 - 8 * q^13 - 2 * q^14 + 12 * q^16 - 14 * q^17 - 8 * q^19 - 6 * q^20 + 24 * q^22 + 12 * q^23 + 8 * q^25 - 10 * q^26 + 24 * q^28 + 4 * q^29 + 8 * q^31 + 48 * q^32 - 8 * q^34 - 12 * q^37 + 10 * q^38 - 12 * q^40 - 20 * q^41 - 16 * q^43 - 34 * q^44 - 32 * q^46 - 14 * q^47 - 40 * q^49 - 18 * q^50 + 16 * q^52 - 10 * q^53 + 8 * q^55 - 12 * q^56 + 4 * q^58 + 26 * q^59 + 24 * q^61 + 28 * q^62 + 52 * q^64 + 28 * q^65 + 28 * q^68 + 20 * q^70 + 12 * q^71 + 44 * q^73 + 30 * q^74 + 8 * q^76 + 2 * q^77 + 24 * q^79 - 22 * q^80 - 4 * q^82 - 34 * q^83 + 44 * q^85 - 8 * q^86 - 76 * q^88 + 4 * q^89 + 8 * q^91 - 10 * q^92 - 8 * q^94 - 30 * q^95 - 84 * q^97 - 40 * q^98

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.f.a	$99$	$2$	99.f	11.c	$5$	$4$	$1$	$0.791$	\(\Q(\zeta_{10})\)	None					33.2.e.b	$2$	$0$	\(1\)	\(0\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
99.2.f.b	$99$	$2$	99.f	11.c	$5$	$4$	$1$	$0.791$	\(\Q(\zeta_{10})\)	None					33.2.e.a	$2$	$0$	\(3\)	\(0\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10})q^{4}+(1-2\zeta_{10}+\cdots)q^{5}+\cdots\)
99.2.f.c	$99$	$2$	99.f	11.c	$5$	$8$	$2$	$0.791$	8.0.484000000.9	None		✓	✓		99.2.f.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{1}q^{2}+(1+2\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(99, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)