Space of modular forms of level 99 and weight 2

• Label: 99.2
• Level: 99
• Weight: 2
• Dimension: 240
• Nonzero newspaces: 8
• Newform subspaces: 19
• Sturm bound: 1440
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(1440\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(99))\).

	Total	New	Old
Modular forms	440	320	120
Cusp forms	281	240	41
Eisenstein series	159	80	79

Trace form

240 * q - 15 * q^2 - 20 * q^3 - 15 * q^4 - 15 * q^5 - 20 * q^6 - 20 * q^7 - 25 * q^8 - 20 * q^9 - 60 * q^10 - 20 * q^11 - 40 * q^12 - 20 * q^13 - 30 * q^14 - 20 * q^15 - 45 * q^16 - 30 * q^17 - 20 * q^18 - 60 * q^19 - 10 * q^20 - 20 * q^21 - 45 * q^22 - 25 * q^23 + 10 * q^24 - 5 * q^25 + 20 * q^26 + 10 * q^27 + 20 * q^28 + 20 * q^29 + 40 * q^30 + 5 * q^31 + 95 * q^32 + 30 * q^33 + 10 * q^34 + 40 * q^35 + 50 * q^36 - 35 * q^37 + 50 * q^38 + 10 * q^39 + 20 * q^40 + 40 * q^42 - 20 * q^43 - 25 * q^44 - 30 * q^45 - 110 * q^46 - 50 * q^47 + 20 * q^48 - 70 * q^49 + 5 * q^50 - 10 * q^51 - 20 * q^52 + 10 * q^53 + 60 * q^54 - 25 * q^55 + 60 * q^56 + 60 * q^57 + 60 * q^58 + 75 * q^59 + 120 * q^60 + 20 * q^61 + 180 * q^62 + 60 * q^63 + 105 * q^64 + 90 * q^65 + 110 * q^66 + 65 * q^67 + 160 * q^68 + 60 * q^69 + 90 * q^70 + 75 * q^71 + 130 * q^72 - 30 * q^73 + 150 * q^74 + 50 * q^75 + 10 * q^76 + 60 * q^77 + 60 * q^78 - 20 * q^79 - 120 * q^80 - 20 * q^81 - 10 * q^82 - 110 * q^83 - 110 * q^84 - 80 * q^85 - 160 * q^86 - 120 * q^87 - 95 * q^88 - 145 * q^89 - 220 * q^90 - 40 * q^91 - 220 * q^92 - 120 * q^93 - 90 * q^94 - 210 * q^95 - 310 * q^96 - 75 * q^97 - 275 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
99.2.a	\(\chi_{99}(1, \cdot)\)	99.2.a.a	1	1
		99.2.a.b	1
		99.2.a.c	1
		99.2.a.d	1
99.2.d	\(\chi_{99}(98, \cdot)\)	99.2.d.a	4	1
99.2.e	\(\chi_{99}(34, \cdot)\)	99.2.e.a	2	2
		99.2.e.b	2
		99.2.e.c	2
		99.2.e.d	6
		99.2.e.e	8
99.2.f	\(\chi_{99}(37, \cdot)\)	99.2.f.a	4	4
		99.2.f.b	4
		99.2.f.c	8
99.2.g	\(\chi_{99}(32, \cdot)\)	99.2.g.a	4	2
		99.2.g.b	16
99.2.j	\(\chi_{99}(8, \cdot)\)	99.2.j.a	16	4
99.2.m	\(\chi_{99}(4, \cdot)\)	99.2.m.a	8	8
		99.2.m.b	72
99.2.p	\(\chi_{99}(2, \cdot)\)	99.2.p.a	80	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(99)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)