Space of modular forms of level 100 and weight 9

• Label: 100.9
• Level: 100
• Weight: 9
• Dimension: 1271
• Nonzero newspaces: 6
• Newform subspaces: 18
• Sturm bound: 5400
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(5400\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(100))\).

	Total	New	Old
Modular forms	2470	1313	1157
Cusp forms	2330	1271	1059
Eisenstein series	140	42	98

Trace form

1271 * q - 10 * q^2 + 140 * q^3 + 142 * q^4 - 910 * q^5 + 2030 * q^6 + 4060 * q^7 - 6010 * q^8 - 289 * q^9 + 24464 * q^10 + 840 * q^11 - 21690 * q^12 - 134910 * q^13 - 172826 * q^14 + 48478 * q^15 + 178062 * q^16 - 761480 * q^17 + 713670 * q^18 + 718900 * q^19 - 150126 * q^20 - 223376 * q^21 - 607050 * q^22 + 456240 * q^23 + 3652684 * q^24 + 643198 * q^25 - 1498636 * q^26 - 855730 * q^27 - 4673690 * q^28 - 3896706 * q^29 + 4819630 * q^30 + 3166524 * q^31 + 4154870 * q^32 + 7122080 * q^33 - 8846410 * q^34 - 3418728 * q^35 - 237498 * q^36 - 19733110 * q^37 + 17530100 * q^38 + 22510400 * q^39 + 1827404 * q^40 + 12698618 * q^41 - 56675270 * q^42 + 6309420 * q^43 - 9331720 * q^44 + 18719490 * q^45 + 23228090 * q^46 - 11954100 * q^47 + 76716340 * q^48 + 10309931 * q^49 - 60618206 * q^50 + 42485848 * q^51 - 107605580 * q^52 + 27444970 * q^53 - 5800552 * q^54 - 11288940 * q^55 + 46362290 * q^56 - 84097460 * q^57 + 76910900 * q^58 + 119809950 * q^59 + 8549610 * q^60 + 153479902 * q^61 - 173314600 * q^62 + 57553850 * q^63 - 71479688 * q^64 + 177500570 * q^65 + 21737870 * q^66 - 159630460 * q^67 + 41026790 * q^68 - 375700262 * q^69 + 19541830 * q^70 + 77172432 * q^71 + 79509200 * q^72 + 201619090 * q^73 - 14573060 * q^74 + 54011742 * q^75 + 134583460 * q^76 + 209455780 * q^77 + 167171040 * q^78 + 138506200 * q^79 + 13898694 * q^80 - 510388657 * q^81 - 25724370 * q^82 - 166486050 * q^83 - 821131802 * q^84 - 53211548 * q^85 - 233824150 * q^86 - 583747650 * q^87 + 615876510 * q^88 + 47700444 * q^89 + 1122304694 * q^90 + 347762196 * q^91 + 260716130 * q^92 - 32801930 * q^93 - 929235706 * q^94 + 256003896 * q^95 + 73649210 * q^96 + 1256639690 * q^97 + 8834530 * q^98

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(100))\)

We only show spaces with odd 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
100.9.b	\(\chi_{100}(51, \cdot)\)	100.9.b.a	1	1
		100.9.b.b	2
		100.9.b.c	2
		100.9.b.d	16
		100.9.b.e	16
		100.9.b.f	16
		100.9.b.g	20
100.9.d	\(\chi_{100}(99, \cdot)\)	100.9.d.a	2	1
		100.9.d.b	4
		100.9.d.c	32
		100.9.d.d	32
100.9.f	\(\chi_{100}(57, \cdot)\)	100.9.f.a	4	2
		100.9.f.b	8
		100.9.f.c	12
100.9.h	\(\chi_{100}(19, \cdot)\)	100.9.h.a	472	4
100.9.j	\(\chi_{100}(11, \cdot)\)	100.9.j.a	8	4
		100.9.j.b	464
100.9.k	\(\chi_{100}(13, \cdot)\)	100.9.k.a	160	8

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(100)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 1}\)