Space of modular forms of level 99 and weight 8

• Label: 99.8
• Level: 99
• Weight: 8
• Dimension: 1920
• Nonzero newspaces: 8
• Newform subspaces: 21
• Sturm bound: 5760
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 21 \)
Sturm bound:			\(5760\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(99))\).

	Total	New	Old
Modular forms	2600	2000	600
Cusp forms	2440	1920	520
Eisenstein series	160	80	80

Trace form

1920 * q + 15 * q^2 - 68 * q^3 - 117 * q^4 + 1125 * q^5 + 2446 * q^6 - 1744 * q^7 - 18979 * q^8 - 2000 * q^9 + 27806 * q^10 + 10792 * q^11 - 16144 * q^12 - 25648 * q^13 - 13014 * q^14 + 2356 * q^15 + 45791 * q^16 - 24126 * q^17 - 85772 * q^18 - 169608 * q^19 + 154196 * q^20 + 374428 * q^21 + 506664 * q^22 + 412835 * q^23 - 1091438 * q^24 - 973547 * q^25 - 1192150 * q^26 - 17054 * q^27 + 1785662 * q^28 + 1684916 * q^29 + 1760044 * q^30 - 162283 * q^31 - 2355064 * q^32 - 1329852 * q^33 - 1549156 * q^34 - 3191372 * q^35 - 2499322 * q^36 + 1309265 * q^37 + 7507160 * q^38 + 5233882 * q^39 + 1891278 * q^40 + 209148 * q^41 - 5703992 * q^42 - 2896468 * q^43 + 493592 * q^44 - 1747110 * q^45 + 483242 * q^46 + 1900450 * q^47 + 15032870 * q^48 - 1507444 * q^49 - 192403 * q^50 + 1544414 * q^51 - 5348940 * q^52 - 16131002 * q^53 - 29389638 * q^54 - 1029369 * q^55 + 17674392 * q^56 + 18720240 * q^57 + 30187558 * q^58 + 26643267 * q^59 + 20554512 * q^60 + 3396960 * q^61 - 17303940 * q^62 - 8303772 * q^63 - 38872829 * q^64 - 28335030 * q^65 - 39774352 * q^66 - 40620179 * q^67 - 29108462 * q^68 + 9550404 * q^69 + 14778966 * q^70 + 31597179 * q^71 + 79897180 * q^72 + 72470010 * q^73 + 79551864 * q^74 - 24130534 * q^75 + 21506 * q^76 - 44374392 * q^77 - 35055816 * q^78 - 81494648 * q^79 - 69251214 * q^80 + 2057200 * q^81 + 8819637 * q^82 + 53125150 * q^83 + 92060350 * q^84 + 15059048 * q^85 - 33165073 * q^86 - 44513136 * q^87 + 110808214 * q^88 - 3311857 * q^89 - 132747628 * q^90 + 35202868 * q^91 - 141443656 * q^92 - 76461744 * q^93 - 88013268 * q^94 - 24803814 * q^95 + 221604362 * q^96 - 7415949 * q^97 + 239728024 * q^98 + 195300576 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(99))\)

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
99.8.a	\(\chi_{99}(1, \cdot)\)	99.8.a.a	1	1
		99.8.a.b	2
		99.8.a.c	2
		99.8.a.d	2
		99.8.a.e	3
		99.8.a.f	4
		99.8.a.g	4
		99.8.a.h	5
		99.8.a.i	5
99.8.d	\(\chi_{99}(98, \cdot)\)	99.8.d.a	28	1
99.8.e	\(\chi_{99}(34, \cdot)\)	99.8.e.a	66	2
		99.8.e.b	74
99.8.f	\(\chi_{99}(37, \cdot)\)	99.8.f.a	24	4
		99.8.f.b	28
		99.8.f.c	28
		99.8.f.d	56
99.8.g	\(\chi_{99}(32, \cdot)\)	99.8.g.a	4	2
		99.8.g.b	160
99.8.j	\(\chi_{99}(8, \cdot)\)	99.8.j.a	112	4
99.8.m	\(\chi_{99}(4, \cdot)\)	99.8.m.a	656	8
99.8.p	\(\chi_{99}(2, \cdot)\)	99.8.p.a	656	8

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(99)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 1}\)