Space of modular forms of level 3000 and weight 2

• Label: 3000.2
• Level: 3000
• Weight: 2
• Dimension: 92800
• Nonzero newspaces: 27
• Sturm bound: 960000
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 3000 = 2^{3} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 27 \)
Sturm bound:			\(960000\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3000))\).

	Total	New	Old
Modular forms	244320	93824	150496
Cusp forms	235681	92800	142881
Eisenstein series	8639	1024	7615

Trace form

92800 * q - 64 * q^3 - 128 * q^4 - 116 * q^6 - 120 * q^7 - 126 * q^9 - 160 * q^10 + 8 * q^11 - 76 * q^12 + 4 * q^13 - 24 * q^14 - 80 * q^15 - 264 * q^16 - 4 * q^17 - 92 * q^18 - 160 * q^19 - 16 * q^21 - 168 * q^22 - 24 * q^23 - 92 * q^24 - 320 * q^25 - 32 * q^26 - 88 * q^27 - 120 * q^28 - 12 * q^29 - 80 * q^30 - 264 * q^31 + 40 * q^32 - 152 * q^33 - 64 * q^34 - 108 * q^36 - 48 * q^37 + 56 * q^38 - 172 * q^39 - 160 * q^40 - 84 * q^41 - 20 * q^42 - 336 * q^43 + 56 * q^44 - 80 * q^45 - 168 * q^46 - 192 * q^47 - 4 * q^48 - 442 * q^49 - 244 * q^51 - 96 * q^52 - 168 * q^53 - 12 * q^54 - 240 * q^55 - 264 * q^57 - 128 * q^58 - 128 * q^59 - 80 * q^60 - 36 * q^61 - 68 * q^63 - 104 * q^64 - 10 * q^65 - 28 * q^66 - 48 * q^67 + 56 * q^68 + 16 * q^69 - 160 * q^70 + 80 * q^71 + 36 * q^72 - 316 * q^73 + 88 * q^74 - 80 * q^75 - 56 * q^76 + 28 * q^78 - 32 * q^79 - 286 * q^81 + 256 * q^82 + 312 * q^83 + 316 * q^84 + 150 * q^85 + 448 * q^86 + 204 * q^87 + 824 * q^88 - 32 * q^89 + 40 * q^90 + 200 * q^91 + 792 * q^92 + 192 * q^93 + 1080 * q^94 + 240 * q^95 + 228 * q^96 - 68 * q^97 + 1032 * q^98 + 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3000))\)

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
3000.2.a	\(\chi_{3000}(1, \cdot)\)	3000.2.a.a	2	1
		3000.2.a.b	2
		3000.2.a.c	2
		3000.2.a.d	2
		3000.2.a.e	2
		3000.2.a.f	2
		3000.2.a.g	2
		3000.2.a.h	2
		3000.2.a.i	4
		3000.2.a.j	4
		3000.2.a.k	4
		3000.2.a.l	4
		3000.2.a.m	4
		3000.2.a.n	4
		3000.2.a.o	4
		3000.2.a.p	4
3000.2.b	\(\chi_{3000}(251, \cdot)\)	n/a	384	1
3000.2.d	\(\chi_{3000}(2749, \cdot)\)	n/a	192	1
3000.2.f	\(\chi_{3000}(1249, \cdot)\)	3000.2.f.a	4	1
		3000.2.f.b	4
		3000.2.f.c	4
		3000.2.f.d	4
		3000.2.f.e	8
		3000.2.f.f	8
		3000.2.f.g	8
		3000.2.f.h	8
3000.2.h	\(\chi_{3000}(1751, \cdot)\)	None	0	1
3000.2.k	\(\chi_{3000}(1501, \cdot)\)	n/a	192	1
3000.2.m	\(\chi_{3000}(1499, \cdot)\)	n/a	384	1
3000.2.o	\(\chi_{3000}(2999, \cdot)\)	None	0	1
3000.2.r	\(\chi_{3000}(1193, \cdot)\)	n/a	192	2
3000.2.s	\(\chi_{3000}(943, \cdot)\)	None	0	2
3000.2.v	\(\chi_{3000}(307, \cdot)\)	n/a	384	2
3000.2.w	\(\chi_{3000}(557, \cdot)\)	n/a	768	2
3000.2.y	\(\chi_{3000}(601, \cdot)\)	n/a	176	4
3000.2.ba	\(\chi_{3000}(551, \cdot)\)	None	0	4
3000.2.bc	\(\chi_{3000}(49, \cdot)\)	n/a	184	4
3000.2.be	\(\chi_{3000}(349, \cdot)\)	n/a	720	4
3000.2.bg	\(\chi_{3000}(851, \cdot)\)	n/a	1392	4
3000.2.bi	\(\chi_{3000}(599, \cdot)\)	None	0	4
3000.2.bk	\(\chi_{3000}(299, \cdot)\)	n/a	1392	4
3000.2.bm	\(\chi_{3000}(301, \cdot)\)	n/a	720	4
3000.2.bp	\(\chi_{3000}(293, \cdot)\)	n/a	2784	8
3000.2.bq	\(\chi_{3000}(43, \cdot)\)	n/a	1440	8
3000.2.bt	\(\chi_{3000}(7, \cdot)\)	None	0	8
3000.2.bu	\(\chi_{3000}(257, \cdot)\)	n/a	720	8
3000.2.bw	\(\chi_{3000}(121, \cdot)\)	n/a	1520	20
3000.2.bz	\(\chi_{3000}(119, \cdot)\)	None	0	20
3000.2.cb	\(\chi_{3000}(59, \cdot)\)	n/a	11920	20
3000.2.cc	\(\chi_{3000}(61, \cdot)\)	n/a	6000	20
3000.2.cf	\(\chi_{3000}(11, \cdot)\)	n/a	11920	20
3000.2.cg	\(\chi_{3000}(109, \cdot)\)	n/a	6000	20
3000.2.ci	\(\chi_{3000}(169, \cdot)\)	n/a	1480	20
3000.2.cl	\(\chi_{3000}(71, \cdot)\)	None	0	20
3000.2.cn	\(\chi_{3000}(53, \cdot)\)	n/a	23840	40
3000.2.co	\(\chi_{3000}(103, \cdot)\)	None	0	40
3000.2.cq	\(\chi_{3000}(17, \cdot)\)	n/a	6000	40
3000.2.ct	\(\chi_{3000}(67, \cdot)\)	n/a	12000	40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3000))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3000)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(750))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1000))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1500))\)\(^{\oplus 2}\)