Space of modular forms of level 100 and weight 3

• Label: 100.3
• Level: 100
• Weight: 3
• Dimension: 302
• Nonzero newspaces: 6
• Newform subspaces: 14
• Sturm bound: 1800
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1800\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(100))\).

	Total	New	Old
Modular forms	670	344	326
Cusp forms	530	302	228
Eisenstein series	140	42	98

Trace form

302 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 10 * q^5 + 14 * q^6 + 28 * q^7 + 6 * q^8 - 4 * q^9 - 16 * q^10 - 40 * q^11 - 90 * q^12 - 24 * q^13 - 122 * q^14 - 2 * q^15 - 114 * q^16 + 94 * q^17 - 54 * q^18 + 100 * q^19 + 34 * q^20 + 64 * q^21 + 150 * q^22 + 112 * q^23 + 268 * q^24 - 92 * q^25 + 188 * q^26 - 154 * q^27 + 70 * q^28 - 184 * q^29 - 50 * q^30 - 84 * q^31 - 266 * q^32 - 400 * q^33 - 322 * q^34 - 208 * q^35 - 330 * q^36 - 244 * q^37 - 500 * q^38 - 400 * q^39 - 436 * q^40 - 92 * q^41 - 470 * q^42 - 180 * q^43 - 200 * q^44 - 120 * q^45 + 74 * q^46 + 76 * q^47 - 140 * q^48 + 296 * q^49 - 6 * q^50 + 112 * q^51 + 148 * q^52 + 540 * q^53 + 416 * q^54 + 300 * q^55 + 114 * q^56 + 652 * q^57 + 692 * q^58 + 550 * q^59 + 1050 * q^60 + 184 * q^61 + 800 * q^62 + 914 * q^63 + 568 * q^64 + 260 * q^65 + 110 * q^66 + 308 * q^67 + 262 * q^68 - 614 * q^69 + 70 * q^70 - 272 * q^71 + 224 * q^72 - 704 * q^73 + 388 * q^74 - 18 * q^75 + 100 * q^76 - 460 * q^77 + 240 * q^78 - 200 * q^79 + 134 * q^80 - 232 * q^81 + 438 * q^82 - 698 * q^83 + 1126 * q^84 - 1208 * q^85 + 314 * q^86 - 1098 * q^87 + 990 * q^88 - 1064 * q^89 + 1454 * q^90 - 156 * q^91 + 930 * q^92 - 74 * q^93 + 998 * q^94 - 224 * q^95 + 794 * q^96 - 64 * q^97 - 114 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.3.b	\(\chi_{100}(51, \cdot)\)	100.3.b.a	1	1
		100.3.b.b	1
		100.3.b.c	2
		100.3.b.d	4
		100.3.b.e	4
		100.3.b.f	4
100.3.d	\(\chi_{100}(99, \cdot)\)	100.3.d.a	8	1
		100.3.d.b	8
100.3.f	\(\chi_{100}(57, \cdot)\)	100.3.f.a	2	2
		100.3.f.b	4
100.3.h	\(\chi_{100}(19, \cdot)\)	100.3.h.a	8	4
		100.3.h.b	104
100.3.j	\(\chi_{100}(11, \cdot)\)	100.3.j.a	112	4
100.3.k	\(\chi_{100}(13, \cdot)\)	100.3.k.a	40	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

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