Space of modular forms of level 2800 and weight 2

• Label: 2800.2
• Level: 2800
• Weight: 2
• Dimension: 113549
• Nonzero newspaces: 56
• Sturm bound: 921600
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(921600\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2800))\).

	Total	New	Old
Modular forms	235104	115393	119711
Cusp forms	225697	113549	112148
Eisenstein series	9407	1844	7563

Trace form

113549 * q - 104 * q^2 - 77 * q^3 - 108 * q^4 - 160 * q^5 - 180 * q^6 - 99 * q^7 - 272 * q^8 - 35 * q^9 - 128 * q^10 - 133 * q^11 - 100 * q^12 - 150 * q^13 - 128 * q^14 - 264 * q^15 - 156 * q^16 - 267 * q^17 - 112 * q^18 - 139 * q^19 - 128 * q^20 - 313 * q^21 - 264 * q^22 - 147 * q^23 - 108 * q^24 - 48 * q^25 - 340 * q^26 - 110 * q^27 - 76 * q^28 - 346 * q^29 - 64 * q^30 - 89 * q^31 + 36 * q^32 - 155 * q^33 + 140 * q^34 - 108 * q^35 - 160 * q^36 + q^37 + 140 * q^38 + 26 * q^39 + 32 * q^40 + 82 * q^41 + 100 * q^42 - 148 * q^43 + 172 * q^44 - 100 * q^45 + 120 * q^46 - 95 * q^47 + 252 * q^48 - 231 * q^49 - 240 * q^50 - 291 * q^51 + 136 * q^52 - 131 * q^53 + 252 * q^54 - 124 * q^55 - 120 * q^56 - 122 * q^57 - 181 * q^59 - 192 * q^60 - 195 * q^61 - 32 * q^62 + 7 * q^63 - 276 * q^64 - 344 * q^65 - 316 * q^66 + 95 * q^67 - 272 * q^68 - 74 * q^69 - 232 * q^70 - 124 * q^71 - 500 * q^72 - 131 * q^73 - 460 * q^74 + 160 * q^75 - 612 * q^76 - 197 * q^77 - 800 * q^78 + 253 * q^79 - 288 * q^80 - 400 * q^81 - 364 * q^82 + 344 * q^83 - 428 * q^84 - 192 * q^85 - 428 * q^86 + 602 * q^87 - 476 * q^88 - 3 * q^89 - 368 * q^90 + 84 * q^91 - 388 * q^92 + 61 * q^93 - 372 * q^94 + 236 * q^95 - 516 * q^96 - 54 * q^97 - 244 * q^98 + 556 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2800))\)

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
2800.2.a	\(\chi_{2800}(1, \cdot)\)	2800.2.a.a	1	1
		2800.2.a.b	1
		2800.2.a.c	1
		2800.2.a.d	1
		2800.2.a.e	1
		2800.2.a.f	1
		2800.2.a.g	1
		2800.2.a.h	1
		2800.2.a.i	1
		2800.2.a.j	1
		2800.2.a.k	1
		2800.2.a.l	1
		2800.2.a.m	1
		2800.2.a.n	1
		2800.2.a.o	1
		2800.2.a.p	1
		2800.2.a.q	1
		2800.2.a.r	1
		2800.2.a.s	1
		2800.2.a.t	1
		2800.2.a.u	1
		2800.2.a.v	1
		2800.2.a.w	1
		2800.2.a.x	1
		2800.2.a.y	1
		2800.2.a.z	1
		2800.2.a.ba	1
		2800.2.a.bb	1
		2800.2.a.bc	1
		2800.2.a.bd	1
		2800.2.a.be	1
		2800.2.a.bf	1
		2800.2.a.bg	1
		2800.2.a.bh	2
		2800.2.a.bi	2
		2800.2.a.bj	2
		2800.2.a.bk	2
		2800.2.a.bl	2
		2800.2.a.bm	2
		2800.2.a.bn	2
		2800.2.a.bo	2
		2800.2.a.bp	2
		2800.2.a.bq	3
		2800.2.a.br	3
2800.2.b	\(\chi_{2800}(1401, \cdot)\)	None	0	1
2800.2.e	\(\chi_{2800}(2799, \cdot)\)	2800.2.e.a	4	1
		2800.2.e.b	4
		2800.2.e.c	4
		2800.2.e.d	4
		2800.2.e.e	8
		2800.2.e.f	8
		2800.2.e.g	8
		2800.2.e.h	8
		2800.2.e.i	8
		2800.2.e.j	8
		2800.2.e.k	8
2800.2.g	\(\chi_{2800}(449, \cdot)\)	2800.2.g.a	2	1
		2800.2.g.b	2
		2800.2.g.c	2
		2800.2.g.d	2
		2800.2.g.e	2
		2800.2.g.f	2
		2800.2.g.g	2
		2800.2.g.h	2
		2800.2.g.i	2
		2800.2.g.j	2
		2800.2.g.k	2
		2800.2.g.l	2
		2800.2.g.m	2
		2800.2.g.n	2
		2800.2.g.o	2
		2800.2.g.p	2
		2800.2.g.q	2
		2800.2.g.r	4
		2800.2.g.s	4
		2800.2.g.t	4
		2800.2.g.u	4
		2800.2.g.v	4
2800.2.h	\(\chi_{2800}(951, \cdot)\)	None	0	1
2800.2.k	\(\chi_{2800}(2351, \cdot)\)	2800.2.k.a	2	1
		2800.2.k.b	2
		2800.2.k.c	2
		2800.2.k.d	2
		2800.2.k.e	2
		2800.2.k.f	2
		2800.2.k.g	4
		2800.2.k.h	4
		2800.2.k.i	4
		2800.2.k.j	4
		2800.2.k.k	8
		2800.2.k.l	8
		2800.2.k.m	8
		2800.2.k.n	8
		2800.2.k.o	8
		2800.2.k.p	8
2800.2.l	\(\chi_{2800}(1849, \cdot)\)	None	0	1
2800.2.n	\(\chi_{2800}(1399, \cdot)\)	None	0	1
2800.2.q	\(\chi_{2800}(401, \cdot)\)	n/a	146	2
2800.2.r	\(\chi_{2800}(293, \cdot)\)	n/a	568	2
2800.2.t	\(\chi_{2800}(43, \cdot)\)	n/a	432	2
2800.2.w	\(\chi_{2800}(2057, \cdot)\)	None	0	2
2800.2.x	\(\chi_{2800}(1807, \cdot)\)	n/a	108	2
2800.2.bb	\(\chi_{2800}(1149, \cdot)\)	n/a	432	2
2800.2.bc	\(\chi_{2800}(251, \cdot)\)	n/a	596	2
2800.2.bd	\(\chi_{2800}(701, \cdot)\)	n/a	456	2
2800.2.be	\(\chi_{2800}(699, \cdot)\)	n/a	568	2
2800.2.bi	\(\chi_{2800}(407, \cdot)\)	None	0	2
2800.2.bj	\(\chi_{2800}(657, \cdot)\)	n/a	140	2
2800.2.bl	\(\chi_{2800}(1443, \cdot)\)	n/a	432	2
2800.2.bn	\(\chi_{2800}(1693, \cdot)\)	n/a	568	2
2800.2.bp	\(\chi_{2800}(561, \cdot)\)	n/a	360	4
2800.2.br	\(\chi_{2800}(199, \cdot)\)	None	0	2
2800.2.bt	\(\chi_{2800}(1151, \cdot)\)	n/a	152	2
2800.2.bw	\(\chi_{2800}(249, \cdot)\)	None	0	2
2800.2.bx	\(\chi_{2800}(849, \cdot)\)	n/a	140	2
2800.2.ca	\(\chi_{2800}(551, \cdot)\)	None	0	2
2800.2.cc	\(\chi_{2800}(1801, \cdot)\)	None	0	2
2800.2.cd	\(\chi_{2800}(1599, \cdot)\)	n/a	144	2
2800.2.ch	\(\chi_{2800}(279, \cdot)\)	None	0	4
2800.2.cj	\(\chi_{2800}(169, \cdot)\)	None	0	4
2800.2.ck	\(\chi_{2800}(111, \cdot)\)	n/a	480	4
2800.2.cn	\(\chi_{2800}(391, \cdot)\)	None	0	4
2800.2.co	\(\chi_{2800}(1009, \cdot)\)	n/a	360	4
2800.2.cq	\(\chi_{2800}(559, \cdot)\)	n/a	480	4
2800.2.ct	\(\chi_{2800}(281, \cdot)\)	None	0	4
2800.2.cv	\(\chi_{2800}(107, \cdot)\)	n/a	1136	4
2800.2.cx	\(\chi_{2800}(493, \cdot)\)	n/a	1136	4
2800.2.cy	\(\chi_{2800}(257, \cdot)\)	n/a	280	4
2800.2.db	\(\chi_{2800}(807, \cdot)\)	None	0	4
2800.2.de	\(\chi_{2800}(299, \cdot)\)	n/a	1136	4
2800.2.df	\(\chi_{2800}(501, \cdot)\)	n/a	1192	4
2800.2.dg	\(\chi_{2800}(451, \cdot)\)	n/a	1192	4
2800.2.dh	\(\chi_{2800}(149, \cdot)\)	n/a	1136	4
2800.2.dk	\(\chi_{2800}(207, \cdot)\)	n/a	288	4
2800.2.dn	\(\chi_{2800}(857, \cdot)\)	None	0	4
2800.2.dp	\(\chi_{2800}(157, \cdot)\)	n/a	1136	4
2800.2.dr	\(\chi_{2800}(443, \cdot)\)	n/a	1136	4
2800.2.ds	\(\chi_{2800}(81, \cdot)\)	n/a	944	8
2800.2.du	\(\chi_{2800}(13, \cdot)\)	n/a	3808	8
2800.2.dw	\(\chi_{2800}(267, \cdot)\)	n/a	2880	8
2800.2.dy	\(\chi_{2800}(97, \cdot)\)	n/a	944	8
2800.2.dz	\(\chi_{2800}(183, \cdot)\)	None	0	8
2800.2.ed	\(\chi_{2800}(139, \cdot)\)	n/a	3808	8
2800.2.ee	\(\chi_{2800}(141, \cdot)\)	n/a	2880	8
2800.2.ef	\(\chi_{2800}(531, \cdot)\)	n/a	3808	8
2800.2.eg	\(\chi_{2800}(29, \cdot)\)	n/a	2880	8
2800.2.ek	\(\chi_{2800}(127, \cdot)\)	n/a	720	8
2800.2.el	\(\chi_{2800}(153, \cdot)\)	None	0	8
2800.2.eo	\(\chi_{2800}(547, \cdot)\)	n/a	2880	8
2800.2.eq	\(\chi_{2800}(237, \cdot)\)	n/a	3808	8
2800.2.es	\(\chi_{2800}(159, \cdot)\)	n/a	960	8
2800.2.et	\(\chi_{2800}(121, \cdot)\)	None	0	8
2800.2.ev	\(\chi_{2800}(311, \cdot)\)	None	0	8
2800.2.ey	\(\chi_{2800}(289, \cdot)\)	n/a	944	8
2800.2.ez	\(\chi_{2800}(9, \cdot)\)	None	0	8
2800.2.fc	\(\chi_{2800}(31, \cdot)\)	n/a	960	8
2800.2.fe	\(\chi_{2800}(439, \cdot)\)	None	0	8
2800.2.fg	\(\chi_{2800}(67, \cdot)\)	n/a	7616	16
2800.2.fi	\(\chi_{2800}(213, \cdot)\)	n/a	7616	16
2800.2.fk	\(\chi_{2800}(73, \cdot)\)	None	0	16
2800.2.fn	\(\chi_{2800}(303, \cdot)\)	n/a	1920	16
2800.2.fq	\(\chi_{2800}(109, \cdot)\)	n/a	7616	16
2800.2.fr	\(\chi_{2800}(131, \cdot)\)	n/a	7616	16
2800.2.fs	\(\chi_{2800}(221, \cdot)\)	n/a	7616	16
2800.2.ft	\(\chi_{2800}(19, \cdot)\)	n/a	7616	16
2800.2.fw	\(\chi_{2800}(23, \cdot)\)	None	0	16
2800.2.fz	\(\chi_{2800}(17, \cdot)\)	n/a	1888	16
2800.2.ga	\(\chi_{2800}(117, \cdot)\)	n/a	7616	16
2800.2.gc	\(\chi_{2800}(163, \cdot)\)	n/a	7616	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2800))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1400))\)\(^{\oplus 2}\)