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

• Label: 99.2.m
• Level: $99$
• Weight: $2$
• Character orbit: 99.m
• Rep. character: $\chi_{99}(4,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.m (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	112	112	0
Cusp forms	80	80	0
Eisenstein series	32	32	0

Trace form

80 * q - 5 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 - 7 * q^6 - 3 * q^7 - 8 * q^8 - 25 * q^9 - 40 * q^10 - q^11 + 2 * q^12 - 3 * q^13 - 11 * q^14 - 8 * q^15 + 5 * q^16 - 8 * q^17 - 24 * q^18 + 6 * q^19 - 21 * q^20 - 16 * q^21 - 5 * q^22 + 6 * q^23 - 3 * q^24 + 2 * q^25 - 28 * q^26 + 27 * q^27 - 36 * q^28 - 32 * q^29 + 12 * q^30 + 48 * q^32 + 28 * q^33 + 2 * q^34 + 30 * q^35 + 39 * q^36 - 18 * q^37 - 5 * q^38 - 35 * q^39 - 13 * q^40 + 13 * q^41 + 49 * q^42 - 2 * q^43 - 10 * q^44 + 16 * q^45 - 11 * q^47 - 50 * q^48 - 5 * q^49 - 24 * q^50 + 69 * q^51 - 15 * q^52 + 32 * q^53 + 88 * q^54 - 14 * q^55 + 102 * q^56 - 18 * q^57 + 7 * q^58 - 13 * q^59 - 63 * q^60 - 3 * q^61 + 190 * q^62 - 7 * q^63 - 8 * q^64 + 52 * q^65 + 105 * q^66 - 14 * q^67 - 32 * q^68 + 24 * q^69 - 52 * q^70 - 6 * q^71 + 41 * q^72 - 48 * q^73 + 81 * q^74 + 28 * q^75 + 10 * q^76 - 37 * q^77 - 40 * q^78 - 3 * q^79 - 4 * q^80 + 23 * q^81 - 2 * q^82 - 10 * q^83 + 3 * q^84 + 19 * q^85 - 56 * q^86 - 120 * q^87 + 55 * q^88 - 128 * q^89 - 22 * q^90 - 4 * q^91 + 29 * q^92 - 44 * q^93 - 35 * q^94 - 81 * q^95 - 97 * q^96 - 27 * q^97 - 256 * q^98 - 185 * 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.m.a	$99$	$2$	99.m	99.m	$15$	$8$	$1$	$0.791$	\(\Q(\zeta_{15})\)	None		✓			99.2.m.a	$4$	$0$	\(-4\)	\(3\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(1-2\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
99.2.m.b	$99$	$2$	99.m	99.m	$15$	$72$	$9$	$0.791$		None		✓	✓		99.2.m.b	$4$	$0$	\(-1\)	\(-12\)	\(-8\)	\(-2\)		$\mathrm{SU}(2)[C_{15}]$