Space of modular forms of level 1600 and weight 4

• Label: 1600.4
• Level: 1600
• Weight: 4
• Dimension: 118997
• Nonzero newspaces: 28
• Sturm bound: 614400
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(614400\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1600))\).

	Total	New	Old
Modular forms	232416	119899	112517
Cusp forms	228384	118997	109387
Eisenstein series	4032	902	3130

Trace form

118997 * q - 104 * q^2 - 78 * q^3 - 104 * q^4 - 128 * q^5 - 168 * q^6 - 80 * q^7 - 104 * q^8 - 157 * q^9 - 128 * q^10 - 146 * q^11 - 104 * q^12 - 32 * q^13 - 104 * q^14 - 96 * q^15 - 168 * q^16 - 78 * q^17 - 104 * q^18 - 54 * q^19 - 128 * q^20 - 180 * q^21 + 368 * q^22 - 80 * q^23 + 896 * q^24 - 160 * q^25 - 368 * q^26 - 264 * q^27 - 864 * q^28 - 504 * q^29 - 128 * q^30 - 488 * q^31 - 1344 * q^32 - 1060 * q^33 - 1104 * q^34 - 96 * q^35 - 1048 * q^36 - 624 * q^37 + 336 * q^38 - 64 * q^39 - 128 * q^40 + 814 * q^41 + 3056 * q^42 + 758 * q^43 + 896 * q^44 - 128 * q^45 - 168 * q^46 + 864 * q^47 - 104 * q^48 + 881 * q^49 - 128 * q^50 + 4228 * q^51 - 3416 * q^52 + 304 * q^53 - 1832 * q^54 - 96 * q^55 + 224 * q^56 - 776 * q^57 + 2272 * q^58 - 4538 * q^59 - 128 * q^60 - 1248 * q^61 + 2888 * q^62 - 2268 * q^63 + 5944 * q^64 + 3840 * q^65 + 5368 * q^66 + 1290 * q^67 + 1960 * q^68 + 5212 * q^69 - 128 * q^70 - 1472 * q^71 - 752 * q^72 - 3842 * q^73 - 2736 * q^74 - 6704 * q^75 - 6280 * q^76 - 10996 * q^77 - 2096 * q^78 - 2656 * q^79 - 128 * q^80 - 13187 * q^81 + 6856 * q^82 - 8238 * q^83 + 4040 * q^84 - 4832 * q^85 - 688 * q^86 - 5232 * q^87 - 3224 * q^88 - 2290 * q^89 - 128 * q^90 + 3324 * q^91 - 12720 * q^92 + 11296 * q^93 - 9032 * q^94 + 7632 * q^95 - 13088 * q^96 + 5098 * q^97 - 12208 * q^98 + 6842 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1600))\)

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
1600.4.a	\(\chi_{1600}(1, \cdot)\)	1600.4.a.a	1	1
		1600.4.a.b	1
		1600.4.a.c	1
		1600.4.a.d	1
		1600.4.a.e	1
		1600.4.a.f	1
		1600.4.a.g	1
		1600.4.a.h	1
		1600.4.a.i	1
		1600.4.a.j	1
		1600.4.a.k	1
		1600.4.a.l	1
		1600.4.a.m	1
		1600.4.a.n	1
		1600.4.a.o	1
		1600.4.a.p	1
		1600.4.a.q	1
		1600.4.a.r	1
		1600.4.a.s	1
		1600.4.a.t	1
		1600.4.a.u	1
		1600.4.a.v	1
		1600.4.a.w	1
		1600.4.a.x	1
		1600.4.a.y	1
		1600.4.a.z	1
		1600.4.a.ba	1
		1600.4.a.bb	1
		1600.4.a.bc	1
		1600.4.a.bd	1
		1600.4.a.be	1
		1600.4.a.bf	1
		1600.4.a.bg	1
		1600.4.a.bh	1
		1600.4.a.bi	1
		1600.4.a.bj	1
		1600.4.a.bk	1
		1600.4.a.bl	1
		1600.4.a.bm	1
		1600.4.a.bn	1
		1600.4.a.bo	1
		1600.4.a.bp	1
		1600.4.a.bq	1
		1600.4.a.br	1
		1600.4.a.bs	1
		1600.4.a.bt	1
		1600.4.a.bu	1
		1600.4.a.bv	1
		1600.4.a.bw	1
		1600.4.a.bx	1
		1600.4.a.by	1
		1600.4.a.bz	1
		1600.4.a.ca	1
		1600.4.a.cb	2
		1600.4.a.cc	2
		1600.4.a.cd	2
		1600.4.a.ce	2
		1600.4.a.cf	2
		1600.4.a.cg	2
		1600.4.a.ch	2
		1600.4.a.ci	2
		1600.4.a.cj	2
		1600.4.a.ck	2
		1600.4.a.cl	2
1600.4.a.cm	2
1600.4.a.cn	2
1600.4.a.co	2
1600.4.a.cp	2
1600.4.a.cq	3
1600.4.a.cr	3
1600.4.a.cs	3
1600.4.a.ct	3
1600.4.a.cu	4
1600.4.a.cv	4
1600.4.a.cw	4
1600.4.a.cx	4
1600.4.c	\(\chi_{1600}(449, \cdot)\)	n/a	106	1
1600.4.d	\(\chi_{1600}(801, \cdot)\)	n/a	114	1
1600.4.f	\(\chi_{1600}(1249, \cdot)\)	n/a	108	1
1600.4.j	\(\chi_{1600}(143, \cdot)\)	n/a	212	2
1600.4.l	\(\chi_{1600}(401, \cdot)\)	n/a	222	2
1600.4.n	\(\chi_{1600}(1343, \cdot)\)	n/a	212	2
1600.4.o	\(\chi_{1600}(543, \cdot)\)	n/a	216	2
1600.4.q	\(\chi_{1600}(49, \cdot)\)	n/a	212	2
1600.4.s	\(\chi_{1600}(207, \cdot)\)	n/a	212	2
1600.4.u	\(\chi_{1600}(321, \cdot)\)	n/a	712	4
1600.4.v	\(\chi_{1600}(407, \cdot)\)	None	0	4
1600.4.y	\(\chi_{1600}(201, \cdot)\)	None	0	4
1600.4.ba	\(\chi_{1600}(249, \cdot)\)	None	0	4
1600.4.bb	\(\chi_{1600}(7, \cdot)\)	None	0	4
1600.4.be	\(\chi_{1600}(289, \cdot)\)	n/a	720	4
1600.4.bg	\(\chi_{1600}(129, \cdot)\)	n/a	712	4
1600.4.bj	\(\chi_{1600}(161, \cdot)\)	n/a	720	4
1600.4.bl	\(\chi_{1600}(43, \cdot)\)	n/a	3440	8
1600.4.bm	\(\chi_{1600}(101, \cdot)\)	n/a	3624	8
1600.4.bn	\(\chi_{1600}(149, \cdot)\)	n/a	3440	8
1600.4.br	\(\chi_{1600}(107, \cdot)\)	n/a	3440	8
1600.4.bt	\(\chi_{1600}(303, \cdot)\)	n/a	1424	8
1600.4.bu	\(\chi_{1600}(81, \cdot)\)	n/a	1424	8
1600.4.bx	\(\chi_{1600}(223, \cdot)\)	n/a	1440	8
1600.4.by	\(\chi_{1600}(63, \cdot)\)	n/a	1424	8
1600.4.cb	\(\chi_{1600}(209, \cdot)\)	n/a	1424	8
1600.4.cc	\(\chi_{1600}(47, \cdot)\)	n/a	1424	8
1600.4.cf	\(\chi_{1600}(87, \cdot)\)	None	0	16
1600.4.cg	\(\chi_{1600}(9, \cdot)\)	None	0	16
1600.4.ci	\(\chi_{1600}(41, \cdot)\)	None	0	16
1600.4.cl	\(\chi_{1600}(23, \cdot)\)	None	0	16
1600.4.cm	\(\chi_{1600}(3, \cdot)\)	n/a	22976	32
1600.4.cq	\(\chi_{1600}(29, \cdot)\)	n/a	22976	32
1600.4.cr	\(\chi_{1600}(21, \cdot)\)	n/a	22976	32
1600.4.cs	\(\chi_{1600}(67, \cdot)\)	n/a	22976	32

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1600))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1600)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 21}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)