Space of modular forms of level 4000 and weight 2

• Label: 4000.2
• Level: 4000
• Weight: 2
• Dimension: 247552
• Nonzero newspaces: 30
• Sturm bound: 1920000
• Trace bound: 37

Defining parameters

Level:	\( N \)	=	\( 4000 = 2^{5} \cdot 5^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(1920000\)
Trace bound:			\(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4000))\).

	Total	New	Old
Modular forms	485760	250112	235648
Cusp forms	474241	247552	226689
Eisenstein series	11519	2560	8959

Trace form

247552 * q - 256 * q^2 - 192 * q^3 - 256 * q^4 - 320 * q^5 - 464 * q^6 - 192 * q^7 - 256 * q^8 - 384 * q^9 - 320 * q^10 - 348 * q^11 - 256 * q^12 - 256 * q^13 - 256 * q^14 - 240 * q^15 - 464 * q^16 - 128 * q^17 - 256 * q^18 - 196 * q^19 - 320 * q^20 - 464 * q^21 - 256 * q^22 - 192 * q^23 - 256 * q^24 - 480 * q^25 - 624 * q^26 - 204 * q^27 - 256 * q^28 - 264 * q^29 - 320 * q^30 - 364 * q^31 - 256 * q^32 - 672 * q^33 - 256 * q^34 - 240 * q^35 - 464 * q^36 - 296 * q^37 - 256 * q^38 - 220 * q^39 - 320 * q^40 - 728 * q^41 - 256 * q^42 - 224 * q^43 - 256 * q^44 - 320 * q^45 - 464 * q^46 - 216 * q^47 - 256 * q^48 - 160 * q^49 - 320 * q^50 - 484 * q^51 - 256 * q^52 - 264 * q^53 - 256 * q^54 - 240 * q^55 - 464 * q^56 - 360 * q^57 - 256 * q^58 - 196 * q^59 - 320 * q^60 - 464 * q^61 - 256 * q^62 - 176 * q^63 - 208 * q^64 - 800 * q^65 - 336 * q^66 - 168 * q^67 - 144 * q^68 - 160 * q^69 - 320 * q^70 - 316 * q^71 - 16 * q^72 - 320 * q^73 - 80 * q^74 - 240 * q^75 - 496 * q^76 - 160 * q^77 + 48 * q^78 - 132 * q^79 - 320 * q^80 - 104 * q^81 - 96 * q^82 - 152 * q^83 + 48 * q^84 - 320 * q^85 - 336 * q^86 - 148 * q^87 - 80 * q^88 - 320 * q^89 - 320 * q^90 - 316 * q^91 - 112 * q^92 - 160 * q^93 - 144 * q^94 - 240 * q^95 - 336 * q^96 - 608 * q^97 - 208 * q^98 - 156 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4000))\)

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
4000.2.a	\(\chi_{4000}(1, \cdot)\)	4000.2.a.a	4	1
		4000.2.a.b	4
		4000.2.a.c	4
		4000.2.a.d	4
		4000.2.a.e	4
		4000.2.a.f	4
		4000.2.a.g	4
		4000.2.a.h	4
		4000.2.a.i	4
		4000.2.a.j	4
		4000.2.a.k	6
		4000.2.a.l	6
		4000.2.a.m	6
		4000.2.a.n	6
		4000.2.a.o	8
		4000.2.a.p	8
		4000.2.a.q	8
		4000.2.a.r	8
4000.2.c	\(\chi_{4000}(1249, \cdot)\)	4000.2.c.a	8	1
		4000.2.c.b	8
		4000.2.c.c	8
		4000.2.c.d	8
		4000.2.c.e	8
		4000.2.c.f	12
		4000.2.c.g	12
		4000.2.c.h	16
		4000.2.c.i	16
4000.2.d	\(\chi_{4000}(2001, \cdot)\)	4000.2.d.a	4	1
		4000.2.d.b	4
		4000.2.d.c	40
		4000.2.d.d	48
4000.2.f	\(\chi_{4000}(3249, \cdot)\)	4000.2.f.a	4	1
		4000.2.f.b	4
		4000.2.f.c	20
		4000.2.f.d	20
		4000.2.f.e	48
4000.2.j	\(\chi_{4000}(2807, \cdot)\)	None	0	2
4000.2.l	\(\chi_{4000}(1001, \cdot)\)	None	0	2
4000.2.n	\(\chi_{4000}(2943, \cdot)\)	n/a	192	2
4000.2.o	\(\chi_{4000}(943, \cdot)\)	n/a	192	2
4000.2.q	\(\chi_{4000}(249, \cdot)\)	None	0	2
4000.2.s	\(\chi_{4000}(807, \cdot)\)	None	0	2
4000.2.u	\(\chi_{4000}(801, \cdot)\)	n/a	360	4
4000.2.v	\(\chi_{4000}(307, \cdot)\)	n/a	1536	4
4000.2.y	\(\chi_{4000}(501, \cdot)\)	n/a	1536	4
4000.2.ba	\(\chi_{4000}(749, \cdot)\)	n/a	1536	4
4000.2.bb	\(\chi_{4000}(1307, \cdot)\)	n/a	1536	4
4000.2.be	\(\chi_{4000}(49, \cdot)\)	n/a	336	4
4000.2.bg	\(\chi_{4000}(449, \cdot)\)	n/a	360	4
4000.2.bj	\(\chi_{4000}(401, \cdot)\)	n/a	336	4
4000.2.bl	\(\chi_{4000}(7, \cdot)\)	None	0	8
4000.2.bm	\(\chi_{4000}(201, \cdot)\)	None	0	8
4000.2.bp	\(\chi_{4000}(143, \cdot)\)	n/a	672	8
4000.2.bq	\(\chi_{4000}(543, \cdot)\)	n/a	720	8
4000.2.bt	\(\chi_{4000}(649, \cdot)\)	None	0	8
4000.2.bu	\(\chi_{4000}(407, \cdot)\)	None	0	8
4000.2.bw	\(\chi_{4000}(161, \cdot)\)	n/a	3000	20
4000.2.by	\(\chi_{4000}(43, \cdot)\)	n/a	5664	16
4000.2.bz	\(\chi_{4000}(149, \cdot)\)	n/a	5664	16
4000.2.cb	\(\chi_{4000}(101, \cdot)\)	n/a	5664	16
4000.2.ce	\(\chi_{4000}(107, \cdot)\)	n/a	5664	16
4000.2.ch	\(\chi_{4000}(81, \cdot)\)	n/a	2960	20
4000.2.cj	\(\chi_{4000}(209, \cdot)\)	n/a	2960	20
4000.2.ck	\(\chi_{4000}(129, \cdot)\)	n/a	3000	20
4000.2.cn	\(\chi_{4000}(9, \cdot)\)	None	0	40
4000.2.co	\(\chi_{4000}(87, \cdot)\)	None	0	40
4000.2.cr	\(\chi_{4000}(47, \cdot)\)	n/a	5920	40
4000.2.cs	\(\chi_{4000}(63, \cdot)\)	n/a	6000	40
4000.2.cv	\(\chi_{4000}(23, \cdot)\)	None	0	40
4000.2.cw	\(\chi_{4000}(41, \cdot)\)	None	0	40
4000.2.cy	\(\chi_{4000}(3, \cdot)\)	n/a	47840	80
4000.2.da	\(\chi_{4000}(29, \cdot)\)	n/a	47840	80
4000.2.dd	\(\chi_{4000}(21, \cdot)\)	n/a	47840	80
4000.2.df	\(\chi_{4000}(67, \cdot)\)	n/a	47840	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4000))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4000)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1000))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2000))\)\(^{\oplus 2}\)