Space of modular forms of level 99 and weight 4

• Label: 99.4
• Level: 99
• Weight: 4
• Dimension: 800
• Nonzero newspaces: 8
• Newform subspaces: 23
• Sturm bound: 2880
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 23 \)
Sturm bound:			\(2880\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(99))\).

	Total	New	Old
Modular forms	1160	880	280
Cusp forms	1000	800	200
Eisenstein series	160	80	80

Trace form

800 * q - 9 * q^2 - 14 * q^3 + 11 * q^4 + 15 * q^5 - 38 * q^6 - 51 * q^7 - 107 * q^8 - 110 * q^9 + 26 * q^10 + 101 * q^11 + 272 * q^12 + 123 * q^13 - 90 * q^14 - 74 * q^15 - 537 * q^16 - 561 * q^17 - 452 * q^18 + 376 * q^19 + 556 * q^20 - 62 * q^21 + 582 * q^22 + 1096 * q^23 + 1378 * q^24 + 893 * q^25 + 1666 * q^26 + 784 * q^27 - 1994 * q^28 - 1367 * q^29 - 2156 * q^30 - 2135 * q^31 - 5096 * q^32 - 1818 * q^33 - 2176 * q^34 - 2557 * q^35 - 970 * q^36 - 405 * q^37 - 992 * q^38 - 1238 * q^39 + 3438 * q^40 + 3159 * q^41 + 3352 * q^42 + 3616 * q^43 + 5332 * q^44 + 2550 * q^45 + 1906 * q^46 + 1373 * q^47 + 662 * q^48 - 165 * q^49 + 1717 * q^50 + 836 * q^51 + 5540 * q^52 + 5069 * q^53 + 2910 * q^54 + 701 * q^55 + 3672 * q^56 + 2982 * q^57 - 370 * q^58 - 324 * q^59 - 4848 * q^60 - 2781 * q^61 - 13776 * q^62 - 5946 * q^63 - 10373 * q^64 - 9150 * q^65 - 7480 * q^66 - 5524 * q^67 - 12454 * q^68 - 6042 * q^69 - 10034 * q^70 - 10617 * q^71 - 5252 * q^72 - 3875 * q^73 + 2112 * q^74 + 2456 * q^75 + 5218 * q^76 + 8310 * q^77 + 11040 * q^78 + 5431 * q^79 + 14226 * q^80 - 206 * q^81 + 16715 * q^82 + 2696 * q^83 - 15794 * q^84 + 7373 * q^85 - 2939 * q^86 - 3114 * q^87 + 6846 * q^88 + 3904 * q^89 + 6692 * q^90 + 2259 * q^91 + 3784 * q^92 + 7206 * q^93 - 2340 * q^94 + 8241 * q^95 + 27530 * q^96 + 1132 * q^97 + 12362 * q^98 + 15363 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)

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
99.4.a	\(\chi_{99}(1, \cdot)\)	99.4.a.a	1	1
		99.4.a.b	1
		99.4.a.c	2
		99.4.a.d	2
		99.4.a.e	2
		99.4.a.f	2
		99.4.a.g	2
99.4.d	\(\chi_{99}(98, \cdot)\)	99.4.d.a	2	1
		99.4.d.b	2
		99.4.d.c	8
99.4.e	\(\chi_{99}(34, \cdot)\)	99.4.e.a	2	2
		99.4.e.b	24
		99.4.e.c	34
99.4.f	\(\chi_{99}(37, \cdot)\)	99.4.f.a	4	4
		99.4.f.b	8
		99.4.f.c	8
		99.4.f.d	12
		99.4.f.e	24
99.4.g	\(\chi_{99}(32, \cdot)\)	99.4.g.a	4	2
		99.4.g.b	64
99.4.j	\(\chi_{99}(8, \cdot)\)	99.4.j.a	48	4
99.4.m	\(\chi_{99}(4, \cdot)\)	99.4.m.a	272	8
99.4.p	\(\chi_{99}(2, \cdot)\)	99.4.p.a	272	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces

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