Space of modular forms of level 1800 and weight 3

• Label: 1800.3
• Level: 1800
• Weight: 3
• Dimension: 70553
• Nonzero newspaces: 36
• Sturm bound: 518400
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(518400\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1800))\).

	Total	New	Old
Modular forms	175488	71291	104197
Cusp forms	170112	70553	99559
Eisenstein series	5376	738	4638

Trace form

70553 * q - 40 * q^2 - 54 * q^3 - 34 * q^4 - 4 * q^5 - 76 * q^6 - 30 * q^7 - 10 * q^8 - 90 * q^9 - 144 * q^10 - 10 * q^11 - 62 * q^12 + 60 * q^13 + 6 * q^14 - 64 * q^15 - 86 * q^16 - 46 * q^17 - 144 * q^18 - 98 * q^19 - 68 * q^20 + 92 * q^21 - 194 * q^22 + 78 * q^23 - 72 * q^24 - 18 * q^25 - 320 * q^26 - 132 * q^27 - 284 * q^28 - 108 * q^29 - 64 * q^30 - 14 * q^31 - 230 * q^32 - 310 * q^33 - 254 * q^34 - 168 * q^35 - 78 * q^36 - 228 * q^37 - 298 * q^38 - 362 * q^39 - 8 * q^40 - 284 * q^41 + 2 * q^42 - 298 * q^43 - 10 * q^44 - 396 * q^46 - 918 * q^47 - 948 * q^48 - 879 * q^49 - 908 * q^50 - 718 * q^51 - 926 * q^52 - 624 * q^53 - 800 * q^54 - 780 * q^55 - 444 * q^56 - 578 * q^57 - 30 * q^58 - 522 * q^59 + 56 * q^60 - 268 * q^61 + 1224 * q^62 + 38 * q^63 + 536 * q^64 + 378 * q^65 + 1660 * q^66 + 382 * q^67 + 2136 * q^68 + 376 * q^69 + 948 * q^70 + 1188 * q^71 + 1954 * q^72 + 1178 * q^73 + 2050 * q^74 - 352 * q^75 + 686 * q^76 - 408 * q^77 + 146 * q^78 + 510 * q^79 + 292 * q^80 - 786 * q^81 - 644 * q^82 - 688 * q^83 - 744 * q^84 - 628 * q^85 - 922 * q^86 - 374 * q^87 - 1454 * q^88 - 1072 * q^89 - 64 * q^90 - 576 * q^91 - 654 * q^92 + 416 * q^93 - 984 * q^94 - 100 * q^95 - 968 * q^96 - 1704 * q^97 + 350 * q^98 - 254 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1800))\)

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
1800.3.c	\(\chi_{1800}(449, \cdot)\)	1800.3.c.a	4	1
		1800.3.c.b	8
		1800.3.c.c	8
		1800.3.c.d	8
		1800.3.c.e	8
1800.3.e	\(\chi_{1800}(1351, \cdot)\)	None	0	1
1800.3.g	\(\chi_{1800}(451, \cdot)\)	n/a	187	1
1800.3.i	\(\chi_{1800}(1349, \cdot)\)	n/a	144	1
1800.3.j	\(\chi_{1800}(199, \cdot)\)	None	0	1
1800.3.l	\(\chi_{1800}(1601, \cdot)\)	1800.3.l.a	2	1
		1800.3.l.b	4
		1800.3.l.c	4
		1800.3.l.d	4
		1800.3.l.e	4
		1800.3.l.f	4
		1800.3.l.g	4
		1800.3.l.h	6
		1800.3.l.i	6
1800.3.n	\(\chi_{1800}(701, \cdot)\)	n/a	152	1
1800.3.p	\(\chi_{1800}(1099, \cdot)\)	n/a	178	1
1800.3.r	\(\chi_{1800}(107, \cdot)\)	n/a	288	2
1800.3.u	\(\chi_{1800}(757, \cdot)\)	n/a	356	2
1800.3.v	\(\chi_{1800}(793, \cdot)\)	1800.3.v.a	2	2
		1800.3.v.b	2
		1800.3.v.c	2
		1800.3.v.d	2
		1800.3.v.e	2
		1800.3.v.f	2
		1800.3.v.g	2
		1800.3.v.h	4
		1800.3.v.i	4
		1800.3.v.j	4
		1800.3.v.k	4
		1800.3.v.l	4
		1800.3.v.m	4
		1800.3.v.n	4
		1800.3.v.o	4
		1800.3.v.p	4
		1800.3.v.q	4
		1800.3.v.r	6
		1800.3.v.s	6
		1800.3.v.t	8
		1800.3.v.u	8
		1800.3.v.v	8
1800.3.y	\(\chi_{1800}(143, \cdot)\)	None	0	2
1800.3.ba	\(\chi_{1800}(499, \cdot)\)	n/a	856	2
1800.3.bb	\(\chi_{1800}(101, \cdot)\)	n/a	900	2
1800.3.bd	\(\chi_{1800}(401, \cdot)\)	n/a	228	2
1800.3.bf	\(\chi_{1800}(799, \cdot)\)	None	0	2
1800.3.bi	\(\chi_{1800}(149, \cdot)\)	n/a	856	2
1800.3.bk	\(\chi_{1800}(1051, \cdot)\)	n/a	900	2
1800.3.bm	\(\chi_{1800}(151, \cdot)\)	None	0	2
1800.3.bo	\(\chi_{1800}(1049, \cdot)\)	n/a	216	2
1800.3.bp	\(\chi_{1800}(269, \cdot)\)	n/a	960	4
1800.3.br	\(\chi_{1800}(91, \cdot)\)	n/a	1192	4
1800.3.bt	\(\chi_{1800}(271, \cdot)\)	None	0	4
1800.3.bv	\(\chi_{1800}(89, \cdot)\)	n/a	240	4
1800.3.bx	\(\chi_{1800}(19, \cdot)\)	n/a	1192	4
1800.3.bz	\(\chi_{1800}(341, \cdot)\)	n/a	960	4
1800.3.cb	\(\chi_{1800}(161, \cdot)\)	n/a	240	4
1800.3.cd	\(\chi_{1800}(559, \cdot)\)	None	0	4
1800.3.cf	\(\chi_{1800}(193, \cdot)\)	n/a	432	4
1800.3.cg	\(\chi_{1800}(407, \cdot)\)	None	0	4
1800.3.cj	\(\chi_{1800}(443, \cdot)\)	n/a	1712	4
1800.3.ck	\(\chi_{1800}(157, \cdot)\)	n/a	1712	4
1800.3.cn	\(\chi_{1800}(287, \cdot)\)	None	0	8
1800.3.cq	\(\chi_{1800}(73, \cdot)\)	n/a	600	8
1800.3.cr	\(\chi_{1800}(37, \cdot)\)	n/a	2384	8
1800.3.cu	\(\chi_{1800}(323, \cdot)\)	n/a	1920	8
1800.3.cw	\(\chi_{1800}(79, \cdot)\)	None	0	8
1800.3.cy	\(\chi_{1800}(41, \cdot)\)	n/a	1440	8
1800.3.da	\(\chi_{1800}(221, \cdot)\)	n/a	5728	8
1800.3.db	\(\chi_{1800}(139, \cdot)\)	n/a	5728	8
1800.3.dc	\(\chi_{1800}(209, \cdot)\)	n/a	1440	8
1800.3.de	\(\chi_{1800}(31, \cdot)\)	None	0	8
1800.3.dg	\(\chi_{1800}(211, \cdot)\)	n/a	5728	8
1800.3.di	\(\chi_{1800}(29, \cdot)\)	n/a	5728	8
1800.3.dl	\(\chi_{1800}(13, \cdot)\)	n/a	11456	16
1800.3.dm	\(\chi_{1800}(83, \cdot)\)	n/a	11456	16
1800.3.dp	\(\chi_{1800}(23, \cdot)\)	None	0	16
1800.3.dq	\(\chi_{1800}(97, \cdot)\)	n/a	2880	16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1800))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1800)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 27}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)