Space of modular forms of level 100 and weight 4

• Label: 100.4
• Level: 100
• Weight: 4
• Dimension: 463
• Nonzero newspaces: 6
• Newform subspaces: 16
• Sturm bound: 2400
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(2400\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(100))\).

	Total	New	Old
Modular forms	970	503	467
Cusp forms	830	463	367
Eisenstein series	140	40	100

Trace form

463 * q - 6 * q^2 - 8 * q^3 - 10 * q^4 - 35 * q^5 - 34 * q^6 + 32 * q^7 + 78 * q^8 + 198 * q^9 + 64 * q^10 + 40 * q^11 + 150 * q^12 - 276 * q^13 - 10 * q^14 - 172 * q^15 - 386 * q^16 - 108 * q^17 - 622 * q^18 + 128 * q^19 - 326 * q^20 + 316 * q^21 - 730 * q^22 + 344 * q^23 + 623 * q^25 + 892 * q^26 + 844 * q^27 + 1750 * q^28 + 408 * q^29 + 1230 * q^30 + 184 * q^31 + 1254 * q^32 - 660 * q^33 - 10 * q^34 - 628 * q^35 - 1290 * q^36 - 645 * q^37 - 720 * q^38 - 72 * q^39 + 204 * q^40 - 1588 * q^41 - 1630 * q^42 - 80 * q^43 - 1340 * q^44 - 2185 * q^45 + 626 * q^46 - 2056 * q^47 - 680 * q^48 - 3099 * q^49 - 2206 * q^50 - 532 * q^51 - 832 * q^52 + 707 * q^53 - 3780 * q^54 - 740 * q^55 - 4534 * q^56 + 2108 * q^57 - 3824 * q^58 + 596 * q^59 + 2810 * q^60 + 2516 * q^61 + 460 * q^62 + 2068 * q^63 + 4820 * q^64 + 2395 * q^65 + 5070 * q^66 + 2792 * q^67 + 4846 * q^68 + 4804 * q^69 + 3030 * q^70 + 512 * q^71 + 4064 * q^72 - 2036 * q^73 + 3692 * q^75 - 2140 * q^76 - 2740 * q^77 - 7180 * q^78 + 1424 * q^79 - 2106 * q^80 - 2758 * q^81 - 9362 * q^82 + 1704 * q^83 - 11290 * q^84 + 3277 * q^85 + 106 * q^86 - 332 * q^87 + 830 * q^88 + 2797 * q^89 + 3494 * q^90 - 464 * q^91 + 7970 * q^92 - 4388 * q^93 + 11030 * q^94 - 2204 * q^95 + 6506 * q^96 - 6960 * q^97 + 12998 * q^98 - 3340 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.4.a	\(\chi_{100}(1, \cdot)\)	100.4.a.a	1	1
		100.4.a.b	1
		100.4.a.c	1
		100.4.a.d	2
100.4.c	\(\chi_{100}(49, \cdot)\)	100.4.c.a	2	1
		100.4.c.b	2
100.4.e	\(\chi_{100}(7, \cdot)\)	100.4.e.a	2	2
		100.4.e.b	2
		100.4.e.c	2
		100.4.e.d	8
		100.4.e.e	12
		100.4.e.f	24
100.4.g	\(\chi_{100}(21, \cdot)\)	100.4.g.a	28	4
100.4.i	\(\chi_{100}(9, \cdot)\)	100.4.i.a	32	4
100.4.l	\(\chi_{100}(3, \cdot)\)	100.4.l.a	8	8
		100.4.l.b	336

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

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