Space of modular forms of level 3600 and weight 2

• Label: 3600.2
• Level: 3600
• Weight: 2
• Dimension: 141014
• Nonzero newspaces: 56
• Sturm bound: 1382400
• Trace bound: 45

Defining parameters

Level:	\( N \)	=	\( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(1382400\)
Trace bound:			\(45\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3600))\).

	Total	New	Old
Modular forms	351872	142675	209197
Cusp forms	339329	141014	198315
Eisenstein series	12543	1661	10882

Trace form

141014 * q - 78 * q^2 - 78 * q^3 - 76 * q^4 - 120 * q^5 - 168 * q^6 - 53 * q^7 - 72 * q^8 - 22 * q^9 - 288 * q^10 - 81 * q^11 - 104 * q^12 - 81 * q^13 - 96 * q^14 - 96 * q^15 - 148 * q^16 - 168 * q^17 - 124 * q^18 - 152 * q^19 - 96 * q^20 - 223 * q^21 - 124 * q^22 - 55 * q^23 - 136 * q^24 - 16 * q^25 - 304 * q^26 - 96 * q^27 - 336 * q^28 - 147 * q^29 - 128 * q^30 - 123 * q^31 - 188 * q^32 - 255 * q^33 - 216 * q^34 - 84 * q^35 - 172 * q^36 - 364 * q^37 - 144 * q^38 - 135 * q^39 - 176 * q^40 - 109 * q^41 - 64 * q^42 - 149 * q^43 - 104 * q^44 - 180 * q^45 - 444 * q^46 - 225 * q^47 - 52 * q^48 - 308 * q^49 - 136 * q^50 - 374 * q^51 - 80 * q^52 - 266 * q^53 - 60 * q^54 - 298 * q^55 - 24 * q^56 - 132 * q^57 - 40 * q^58 - 287 * q^59 - 128 * q^60 - 277 * q^61 + 24 * q^62 - 219 * q^63 - 256 * q^64 - 316 * q^65 - 48 * q^66 - 311 * q^67 + 120 * q^68 - 151 * q^69 - 24 * q^70 - 330 * q^71 + 8 * q^72 - 162 * q^73 + 156 * q^74 - 120 * q^75 - 152 * q^76 - 185 * q^77 + 68 * q^78 - 201 * q^79 - 16 * q^80 - 302 * q^81 - 96 * q^82 - 191 * q^83 + 40 * q^84 - 224 * q^85 + 148 * q^86 + 15 * q^87 + 172 * q^88 - 28 * q^89 - 128 * q^90 - 384 * q^91 + 356 * q^92 - 195 * q^93 + 132 * q^94 - 198 * q^95 - 100 * q^96 - 291 * q^97 + 398 * q^98 + 9 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3600))\)

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
3600.2.a	\(\chi_{3600}(1, \cdot)\)	3600.2.a.a	1	1
		3600.2.a.b	1
		3600.2.a.c	1
		3600.2.a.d	1
		3600.2.a.e	1
		3600.2.a.f	1
		3600.2.a.g	1
		3600.2.a.h	1
		3600.2.a.i	1
		3600.2.a.j	1
		3600.2.a.k	1
		3600.2.a.l	1
		3600.2.a.m	1
		3600.2.a.n	1
		3600.2.a.o	1
		3600.2.a.p	1
		3600.2.a.q	1
		3600.2.a.r	1
		3600.2.a.s	1
		3600.2.a.t	1
		3600.2.a.u	1
		3600.2.a.v	1
		3600.2.a.w	1
		3600.2.a.x	1
		3600.2.a.y	1
		3600.2.a.z	1
		3600.2.a.ba	1
		3600.2.a.bb	1
		3600.2.a.bc	1
		3600.2.a.bd	1
		3600.2.a.be	1
		3600.2.a.bf	1
		3600.2.a.bg	1
		3600.2.a.bh	1
		3600.2.a.bi	1
		3600.2.a.bj	1
		3600.2.a.bk	1
		3600.2.a.bl	1
		3600.2.a.bm	1
		3600.2.a.bn	1
		3600.2.a.bo	1
		3600.2.a.bp	1
		3600.2.a.bq	1
		3600.2.a.br	1
		3600.2.a.bs	2
3600.2.b	\(\chi_{3600}(2951, \cdot)\)	None	0	1
3600.2.d	\(\chi_{3600}(649, \cdot)\)	None	0	1
3600.2.f	\(\chi_{3600}(2449, \cdot)\)	3600.2.f.a	2	1
		3600.2.f.b	2
		3600.2.f.c	2
		3600.2.f.d	2
		3600.2.f.e	2
		3600.2.f.f	2
		3600.2.f.g	2
		3600.2.f.h	2
		3600.2.f.i	2
		3600.2.f.j	2
		3600.2.f.k	2
		3600.2.f.l	2
		3600.2.f.m	2
		3600.2.f.n	2
		3600.2.f.o	2
		3600.2.f.p	2
		3600.2.f.q	2
		3600.2.f.r	2
		3600.2.f.s	2
		3600.2.f.t	2
		3600.2.f.u	2
		3600.2.f.v	2
3600.2.h	\(\chi_{3600}(1151, \cdot)\)	3600.2.h.a	2	1
		3600.2.h.b	2
		3600.2.h.c	2
		3600.2.h.d	4
		3600.2.h.e	4
		3600.2.h.f	4
		3600.2.h.g	4
		3600.2.h.h	4
		3600.2.h.i	4
		3600.2.h.j	8
3600.2.k	\(\chi_{3600}(1801, \cdot)\)	None	0	1
3600.2.m	\(\chi_{3600}(1799, \cdot)\)	None	0	1
3600.2.o	\(\chi_{3600}(3599, \cdot)\)	3600.2.o.a	4	1
		3600.2.o.b	8
		3600.2.o.c	8
		3600.2.o.d	8
		3600.2.o.e	8
3600.2.q	\(\chi_{3600}(1201, \cdot)\)	n/a	222	2
3600.2.t	\(\chi_{3600}(901, \cdot)\)	n/a	374	2
3600.2.u	\(\chi_{3600}(899, \cdot)\)	n/a	288	2
3600.2.w	\(\chi_{3600}(593, \cdot)\)	3600.2.w.a	4	2
		3600.2.w.b	4
		3600.2.w.c	4
		3600.2.w.d	4
		3600.2.w.e	4
		3600.2.w.f	4
		3600.2.w.g	4
		3600.2.w.h	4
		3600.2.w.i	8
		3600.2.w.j	8
		3600.2.w.k	8
		3600.2.w.l	8
		3600.2.w.m	8
3600.2.x	\(\chi_{3600}(2143, \cdot)\)	3600.2.x.a	2	2
		3600.2.x.b	2
		3600.2.x.c	2
		3600.2.x.d	4
		3600.2.x.e	4
		3600.2.x.f	4
		3600.2.x.g	8
		3600.2.x.h	8
		3600.2.x.i	8
		3600.2.x.j	8
		3600.2.x.k	8
		3600.2.x.l	8
		3600.2.x.m	8
		3600.2.x.n	8
		3600.2.x.o	8
3600.2.z	\(\chi_{3600}(2107, \cdot)\)	n/a	356	2
3600.2.bc	\(\chi_{3600}(2357, \cdot)\)	n/a	288	2
3600.2.bd	\(\chi_{3600}(307, \cdot)\)	n/a	356	2
3600.2.bg	\(\chi_{3600}(557, \cdot)\)	n/a	288	2
3600.2.bi	\(\chi_{3600}(343, \cdot)\)	None	0	2
3600.2.bj	\(\chi_{3600}(2393, \cdot)\)	None	0	2
3600.2.bl	\(\chi_{3600}(251, \cdot)\)	n/a	304	2
3600.2.bm	\(\chi_{3600}(1549, \cdot)\)	n/a	356	2
3600.2.bp	\(\chi_{3600}(721, \cdot)\)	n/a	296	4
3600.2.bs	\(\chi_{3600}(1199, \cdot)\)	n/a	216	2
3600.2.bu	\(\chi_{3600}(599, \cdot)\)	None	0	2
3600.2.bw	\(\chi_{3600}(601, \cdot)\)	None	0	2
3600.2.bx	\(\chi_{3600}(2351, \cdot)\)	n/a	228	2
3600.2.bz	\(\chi_{3600}(49, \cdot)\)	n/a	212	2
3600.2.cb	\(\chi_{3600}(1849, \cdot)\)	None	0	2
3600.2.cd	\(\chi_{3600}(551, \cdot)\)	None	0	2
3600.2.cg	\(\chi_{3600}(431, \cdot)\)	n/a	240	4
3600.2.ci	\(\chi_{3600}(289, \cdot)\)	n/a	296	4
3600.2.ck	\(\chi_{3600}(1369, \cdot)\)	None	0	4
3600.2.cm	\(\chi_{3600}(71, \cdot)\)	None	0	4
3600.2.co	\(\chi_{3600}(719, \cdot)\)	n/a	240	4
3600.2.cq	\(\chi_{3600}(359, \cdot)\)	None	0	4
3600.2.cs	\(\chi_{3600}(361, \cdot)\)	None	0	4
3600.2.cu	\(\chi_{3600}(349, \cdot)\)	n/a	1712	4
3600.2.cv	\(\chi_{3600}(851, \cdot)\)	n/a	1800	4
3600.2.cy	\(\chi_{3600}(7, \cdot)\)	None	0	4
3600.2.db	\(\chi_{3600}(857, \cdot)\)	None	0	4
3600.2.dc	\(\chi_{3600}(293, \cdot)\)	n/a	1712	4
3600.2.df	\(\chi_{3600}(43, \cdot)\)	n/a	1712	4
3600.2.dg	\(\chi_{3600}(893, \cdot)\)	n/a	1712	4
3600.2.dj	\(\chi_{3600}(643, \cdot)\)	n/a	1712	4
3600.2.dk	\(\chi_{3600}(257, \cdot)\)	n/a	424	4
3600.2.dn	\(\chi_{3600}(607, \cdot)\)	n/a	432	4
3600.2.dq	\(\chi_{3600}(299, \cdot)\)	n/a	1712	4
3600.2.dr	\(\chi_{3600}(301, \cdot)\)	n/a	1800	4
3600.2.ds	\(\chi_{3600}(241, \cdot)\)	n/a	1424	8
3600.2.dt	\(\chi_{3600}(179, \cdot)\)	n/a	1920	8
3600.2.du	\(\chi_{3600}(181, \cdot)\)	n/a	2384	8
3600.2.dy	\(\chi_{3600}(233, \cdot)\)	None	0	8
3600.2.dz	\(\chi_{3600}(487, \cdot)\)	None	0	8
3600.2.eb	\(\chi_{3600}(53, \cdot)\)	n/a	1920	8
3600.2.ee	\(\chi_{3600}(523, \cdot)\)	n/a	2384	8
3600.2.ef	\(\chi_{3600}(197, \cdot)\)	n/a	1920	8
3600.2.ei	\(\chi_{3600}(163, \cdot)\)	n/a	2384	8
3600.2.ek	\(\chi_{3600}(127, \cdot)\)	n/a	600	8
3600.2.el	\(\chi_{3600}(17, \cdot)\)	n/a	480	8
3600.2.ep	\(\chi_{3600}(109, \cdot)\)	n/a	2384	8
3600.2.eq	\(\chi_{3600}(611, \cdot)\)	n/a	1920	8
3600.2.er	\(\chi_{3600}(121, \cdot)\)	None	0	8
3600.2.et	\(\chi_{3600}(119, \cdot)\)	None	0	8
3600.2.ev	\(\chi_{3600}(239, \cdot)\)	n/a	1440	8
3600.2.ez	\(\chi_{3600}(311, \cdot)\)	None	0	8
3600.2.fb	\(\chi_{3600}(169, \cdot)\)	None	0	8
3600.2.fd	\(\chi_{3600}(529, \cdot)\)	n/a	1424	8
3600.2.ff	\(\chi_{3600}(191, \cdot)\)	n/a	1440	8
3600.2.fi	\(\chi_{3600}(11, \cdot)\)	n/a	11456	16
3600.2.fj	\(\chi_{3600}(229, \cdot)\)	n/a	11456	16
3600.2.fk	\(\chi_{3600}(223, \cdot)\)	n/a	2880	16
3600.2.fn	\(\chi_{3600}(113, \cdot)\)	n/a	2848	16
3600.2.fo	\(\chi_{3600}(187, \cdot)\)	n/a	11456	16
3600.2.fr	\(\chi_{3600}(173, \cdot)\)	n/a	11456	16
3600.2.fs	\(\chi_{3600}(67, \cdot)\)	n/a	11456	16
3600.2.fv	\(\chi_{3600}(77, \cdot)\)	n/a	11456	16
3600.2.fw	\(\chi_{3600}(137, \cdot)\)	None	0	16
3600.2.fz	\(\chi_{3600}(103, \cdot)\)	None	0	16
3600.2.ga	\(\chi_{3600}(61, \cdot)\)	n/a	11456	16
3600.2.gb	\(\chi_{3600}(59, \cdot)\)	n/a	11456	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 45}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1800))\)\(^{\oplus 2}\)