Space of modular forms of level 2200 and weight 2

• Label: 2200.2
• Level: 2200
• Weight: 2
• Dimension: 72673
• Nonzero newspaces: 63
• Sturm bound: 576000
• Trace bound: 27

Defining parameters

Level:	\( N \)	=	\( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 63 \)
Sturm bound:			\(576000\)
Trace bound:			\(27\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2200))\).

	Total	New	Old
Modular forms	147360	74149	73211
Cusp forms	140641	72673	67968
Eisenstein series	6719	1476	5243

Trace form

72673 * q - 106 * q^2 - 106 * q^3 - 106 * q^4 - 2 * q^5 - 170 * q^6 - 122 * q^7 - 106 * q^8 - 232 * q^9 - 128 * q^10 - 198 * q^11 - 188 * q^12 - 8 * q^13 - 58 * q^14 - 112 * q^15 - 106 * q^16 - 214 * q^17 + 6 * q^18 - 57 * q^19 - 88 * q^20 + 12 * q^21 - 78 * q^22 - 230 * q^23 + 6 * q^24 - 266 * q^25 - 266 * q^26 - 73 * q^27 - 122 * q^28 - 34 * q^29 - 120 * q^30 - 148 * q^31 - 176 * q^32 - 221 * q^33 - 324 * q^34 - 104 * q^35 - 218 * q^36 + 34 * q^37 - 136 * q^38 + 82 * q^39 - 208 * q^40 - 278 * q^41 - 76 * q^42 + 110 * q^43 - 72 * q^44 + 158 * q^45 - 196 * q^46 + 116 * q^47 - 12 * q^48 - 32 * q^49 - 88 * q^50 - 91 * q^51 + 40 * q^52 + 94 * q^53 + 86 * q^54 - 72 * q^55 - 116 * q^56 + 19 * q^57 + 96 * q^58 + 35 * q^59 - 40 * q^60 - 68 * q^61 + 134 * q^62 - 52 * q^63 + 38 * q^64 - 202 * q^65 - 142 * q^66 - 340 * q^67 - 10 * q^68 - 8 * q^69 - 120 * q^70 - 254 * q^71 - 308 * q^72 - 66 * q^73 - 220 * q^74 - 272 * q^75 - 506 * q^76 - 42 * q^77 - 596 * q^78 - 330 * q^79 - 168 * q^80 - 239 * q^81 - 494 * q^82 - 355 * q^83 - 658 * q^84 - 146 * q^85 - 406 * q^86 - 412 * q^87 - 510 * q^88 - 384 * q^89 - 728 * q^90 - 252 * q^91 - 634 * q^92 + 30 * q^93 - 722 * q^94 - 304 * q^95 - 416 * q^96 - 101 * q^97 - 712 * q^98 + 132 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2200))\)

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
2200.2.a	\(\chi_{2200}(1, \cdot)\)	2200.2.a.a	1	1
		2200.2.a.b	1
		2200.2.a.c	1
		2200.2.a.d	1
		2200.2.a.e	1
		2200.2.a.f	1
		2200.2.a.g	1
		2200.2.a.h	1
		2200.2.a.i	1
		2200.2.a.j	1
		2200.2.a.k	1
		2200.2.a.l	2
		2200.2.a.m	2
		2200.2.a.n	2
		2200.2.a.o	2
		2200.2.a.p	2
		2200.2.a.q	2
		2200.2.a.r	2
		2200.2.a.s	2
		2200.2.a.t	3
		2200.2.a.u	3
		2200.2.a.v	3
		2200.2.a.w	3
		2200.2.a.x	4
		2200.2.a.y	4
2200.2.b	\(\chi_{2200}(1849, \cdot)\)	2200.2.b.a	2	1
		2200.2.b.b	2
		2200.2.b.c	2
		2200.2.b.d	2
		2200.2.b.e	2
		2200.2.b.f	4
		2200.2.b.g	4
		2200.2.b.h	4
		2200.2.b.i	4
		2200.2.b.j	4
		2200.2.b.k	4
		2200.2.b.l	6
		2200.2.b.m	6
2200.2.c	\(\chi_{2200}(1099, \cdot)\)	n/a	212	1
2200.2.f	\(\chi_{2200}(351, \cdot)\)	None	0	1
2200.2.g	\(\chi_{2200}(1101, \cdot)\)	n/a	190	1
2200.2.l	\(\chi_{2200}(749, \cdot)\)	n/a	180	1
2200.2.m	\(\chi_{2200}(2199, \cdot)\)	None	0	1
2200.2.p	\(\chi_{2200}(1451, \cdot)\)	n/a	222	1
2200.2.r	\(\chi_{2200}(243, \cdot)\)	n/a	360	2
2200.2.t	\(\chi_{2200}(1693, \cdot)\)	n/a	424	2
2200.2.v	\(\chi_{2200}(593, \cdot)\)	n/a	108	2
2200.2.x	\(\chi_{2200}(1343, \cdot)\)	None	0	2
2200.2.y	\(\chi_{2200}(361, \cdot)\)	n/a	360	4
2200.2.z	\(\chi_{2200}(201, \cdot)\)	n/a	228	4
2200.2.ba	\(\chi_{2200}(641, \cdot)\)	n/a	360	4
2200.2.bb	\(\chi_{2200}(81, \cdot)\)	n/a	360	4
2200.2.bc	\(\chi_{2200}(441, \cdot)\)	n/a	304	4
2200.2.bd	\(\chi_{2200}(1281, \cdot)\)	n/a	360	4
2200.2.be	\(\chi_{2200}(181, \cdot)\)	n/a	1424	4
2200.2.bf	\(\chi_{2200}(831, \cdot)\)	None	0	4
2200.2.bi	\(\chi_{2200}(1179, \cdot)\)	n/a	1424	4
2200.2.bj	\(\chi_{2200}(289, \cdot)\)	n/a	360	4
2200.2.bm	\(\chi_{2200}(439, \cdot)\)	None	0	4
2200.2.bn	\(\chi_{2200}(309, \cdot)\)	n/a	1200	4
2200.2.bq	\(\chi_{2200}(371, \cdot)\)	n/a	1424	4
2200.2.br	\(\chi_{2200}(171, \cdot)\)	n/a	1424	4
2200.2.bs	\(\chi_{2200}(211, \cdot)\)	n/a	1424	4
2200.2.bt	\(\chi_{2200}(51, \cdot)\)	n/a	888	4
2200.2.cc	\(\chi_{2200}(1109, \cdot)\)	n/a	1424	4
2200.2.cd	\(\chi_{2200}(799, \cdot)\)	None	0	4
2200.2.ce	\(\chi_{2200}(1119, \cdot)\)	None	0	4
2200.2.cf	\(\chi_{2200}(479, \cdot)\)	None	0	4
2200.2.cg	\(\chi_{2200}(389, \cdot)\)	n/a	1424	4
2200.2.ch	\(\chi_{2200}(949, \cdot)\)	n/a	848	4
2200.2.ci	\(\chi_{2200}(69, \cdot)\)	n/a	1424	4
2200.2.cj	\(\chi_{2200}(39, \cdot)\)	None	0	4
2200.2.cs	\(\chi_{2200}(131, \cdot)\)	n/a	1424	4
2200.2.cx	\(\chi_{2200}(219, \cdot)\)	n/a	1424	4
2200.2.cy	\(\chi_{2200}(89, \cdot)\)	n/a	296	4
2200.2.dh	\(\chi_{2200}(1471, \cdot)\)	None	0	4
2200.2.di	\(\chi_{2200}(581, \cdot)\)	n/a	1424	4
2200.2.dj	\(\chi_{2200}(301, \cdot)\)	n/a	888	4
2200.2.dk	\(\chi_{2200}(1461, \cdot)\)	n/a	1424	4
2200.2.dl	\(\chi_{2200}(151, \cdot)\)	None	0	4
2200.2.dm	\(\chi_{2200}(271, \cdot)\)	None	0	4
2200.2.dn	\(\chi_{2200}(431, \cdot)\)	None	0	4
2200.2.do	\(\chi_{2200}(141, \cdot)\)	n/a	1424	4
2200.2.dx	\(\chi_{2200}(9, \cdot)\)	n/a	360	4
2200.2.dy	\(\chi_{2200}(139, \cdot)\)	n/a	1424	4
2200.2.dz	\(\chi_{2200}(19, \cdot)\)	n/a	1424	4
2200.2.ea	\(\chi_{2200}(299, \cdot)\)	n/a	848	4
2200.2.eb	\(\chi_{2200}(889, \cdot)\)	n/a	360	4
2200.2.ec	\(\chi_{2200}(49, \cdot)\)	n/a	216	4
2200.2.ed	\(\chi_{2200}(929, \cdot)\)	n/a	360	4
2200.2.ee	\(\chi_{2200}(1019, \cdot)\)	n/a	1424	4
2200.2.eh	\(\chi_{2200}(221, \cdot)\)	n/a	1200	4
2200.2.ei	\(\chi_{2200}(791, \cdot)\)	None	0	4
2200.2.el	\(\chi_{2200}(491, \cdot)\)	n/a	1424	4
2200.2.eo	\(\chi_{2200}(79, \cdot)\)	None	0	4
2200.2.ep	\(\chi_{2200}(229, \cdot)\)	n/a	1424	4
2200.2.er	\(\chi_{2200}(223, \cdot)\)	None	0	8
2200.2.et	\(\chi_{2200}(17, \cdot)\)	n/a	720	8
2200.2.ev	\(\chi_{2200}(173, \cdot)\)	n/a	2848	8
2200.2.ex	\(\chi_{2200}(467, \cdot)\)	n/a	2848	8
2200.2.ey	\(\chi_{2200}(437, \cdot)\)	n/a	2848	8
2200.2.fa	\(\chi_{2200}(203, \cdot)\)	n/a	2848	8
2200.2.fc	\(\chi_{2200}(57, \cdot)\)	n/a	432	8
2200.2.fe	\(\chi_{2200}(103, \cdot)\)	None	0	8
2200.2.fg	\(\chi_{2200}(23, \cdot)\)	None	0	8
2200.2.fh	\(\chi_{2200}(47, \cdot)\)	None	0	8
2200.2.fk	\(\chi_{2200}(153, \cdot)\)	n/a	720	8
2200.2.fl	\(\chi_{2200}(937, \cdot)\)	n/a	720	8
2200.2.fo	\(\chi_{2200}(217, \cdot)\)	n/a	720	8
2200.2.fq	\(\chi_{2200}(207, \cdot)\)	None	0	8
2200.2.fs	\(\chi_{2200}(443, \cdot)\)	n/a	1696	8
2200.2.fu	\(\chi_{2200}(197, \cdot)\)	n/a	2848	8
2200.2.fv	\(\chi_{2200}(13, \cdot)\)	n/a	2848	8
2200.2.fy	\(\chi_{2200}(237, \cdot)\)	n/a	2848	8
2200.2.ga	\(\chi_{2200}(147, \cdot)\)	n/a	2848	8
2200.2.gc	\(\chi_{2200}(67, \cdot)\)	n/a	2400	8
2200.2.gd	\(\chi_{2200}(3, \cdot)\)	n/a	2848	8
2200.2.gg	\(\chi_{2200}(293, \cdot)\)	n/a	1696	8
2200.2.gi	\(\chi_{2200}(247, \cdot)\)	None	0	8
2200.2.gk	\(\chi_{2200}(73, \cdot)\)	n/a	720	8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 2}\)