Properties

Label 5600.2
Level 5600
Weight 2
Dimension 455834
Nonzero newspaces 80
Sturm bound 3686400

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Defining parameters

Level: \( N \) = \( 5600 = 2^{5} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(3686400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5600))\).

Total New Old
Modular forms 932352 459934 472418
Cusp forms 910849 455834 455015
Eisenstein series 21503 4100 17403

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5600))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5600.2.a \(\chi_{5600}(1, \cdot)\) 5600.2.a.a 1 1
5600.2.a.b 1
5600.2.a.c 1
5600.2.a.d 1
5600.2.a.e 1
5600.2.a.f 1
5600.2.a.g 1
5600.2.a.h 1
5600.2.a.i 1
5600.2.a.j 1
5600.2.a.k 1
5600.2.a.l 1
5600.2.a.m 1
5600.2.a.n 1
5600.2.a.o 1
5600.2.a.p 1
5600.2.a.q 1
5600.2.a.r 1
5600.2.a.s 1
5600.2.a.t 1
5600.2.a.u 1
5600.2.a.v 1
5600.2.a.w 2
5600.2.a.x 2
5600.2.a.y 2
5600.2.a.z 2
5600.2.a.ba 2
5600.2.a.bb 2
5600.2.a.bc 2
5600.2.a.bd 2
5600.2.a.be 2
5600.2.a.bf 2
5600.2.a.bg 2
5600.2.a.bh 2
5600.2.a.bi 2
5600.2.a.bj 2
5600.2.a.bk 2
5600.2.a.bl 2
5600.2.a.bm 3
5600.2.a.bn 3
5600.2.a.bo 3
5600.2.a.bp 3
5600.2.a.bq 4
5600.2.a.br 4
5600.2.a.bs 4
5600.2.a.bt 4
5600.2.a.bu 5
5600.2.a.bv 5
5600.2.a.bw 5
5600.2.a.bx 5
5600.2.a.by 6
5600.2.a.bz 6
5600.2.b \(\chi_{5600}(2801, \cdot)\) n/a 114 1
5600.2.e \(\chi_{5600}(5599, \cdot)\) n/a 144 1
5600.2.g \(\chi_{5600}(449, \cdot)\) n/a 108 1
5600.2.h \(\chi_{5600}(2351, \cdot)\) n/a 146 1
5600.2.k \(\chi_{5600}(5151, \cdot)\) n/a 152 1
5600.2.l \(\chi_{5600}(3249, \cdot)\) n/a 108 1
5600.2.n \(\chi_{5600}(2799, \cdot)\) n/a 140 1
5600.2.q \(\chi_{5600}(3201, \cdot)\) n/a 304 2
5600.2.r \(\chi_{5600}(2057, \cdot)\) None 0 2
5600.2.t \(\chi_{5600}(407, \cdot)\) None 0 2
5600.2.w \(\chi_{5600}(657, \cdot)\) n/a 280 2
5600.2.x \(\chi_{5600}(2143, \cdot)\) n/a 216 2
5600.2.bb \(\chi_{5600}(1849, \cdot)\) None 0 2
5600.2.bc \(\chi_{5600}(951, \cdot)\) None 0 2
5600.2.bd \(\chi_{5600}(1401, \cdot)\) None 0 2
5600.2.be \(\chi_{5600}(1399, \cdot)\) None 0 2
5600.2.bi \(\chi_{5600}(1807, \cdot)\) n/a 216 2
5600.2.bj \(\chi_{5600}(993, \cdot)\) n/a 288 2
5600.2.bl \(\chi_{5600}(3207, \cdot)\) None 0 2
5600.2.bn \(\chi_{5600}(4857, \cdot)\) None 0 2
5600.2.bp \(\chi_{5600}(1121, \cdot)\) n/a 720 4
5600.2.br \(\chi_{5600}(4399, \cdot)\) n/a 280 2
5600.2.bt \(\chi_{5600}(1151, \cdot)\) n/a 304 2
5600.2.bw \(\chi_{5600}(849, \cdot)\) n/a 280 2
5600.2.bx \(\chi_{5600}(3649, \cdot)\) n/a 288 2
5600.2.ca \(\chi_{5600}(3951, \cdot)\) n/a 292 2
5600.2.cc \(\chi_{5600}(401, \cdot)\) n/a 292 2
5600.2.cd \(\chi_{5600}(1599, \cdot)\) n/a 288 2
5600.2.ch \(\chi_{5600}(701, \cdot)\) n/a 1824 4
5600.2.ci \(\chi_{5600}(699, \cdot)\) n/a 2288 4
5600.2.cj \(\chi_{5600}(1693, \cdot)\) n/a 2288 4
5600.2.ck \(\chi_{5600}(43, \cdot)\) n/a 1728 4
5600.2.cn \(\chi_{5600}(1443, \cdot)\) n/a 1728 4
5600.2.co \(\chi_{5600}(293, \cdot)\) n/a 2288 4
5600.2.ct \(\chi_{5600}(251, \cdot)\) n/a 2408 4
5600.2.cu \(\chi_{5600}(1149, \cdot)\) n/a 1728 4
5600.2.cx \(\chi_{5600}(559, \cdot)\) n/a 944 4
5600.2.cz \(\chi_{5600}(1009, \cdot)\) n/a 720 4
5600.2.da \(\chi_{5600}(671, \cdot)\) n/a 960 4
5600.2.dd \(\chi_{5600}(111, \cdot)\) n/a 944 4
5600.2.de \(\chi_{5600}(1569, \cdot)\) n/a 720 4
5600.2.dg \(\chi_{5600}(1119, \cdot)\) n/a 960 4
5600.2.dj \(\chi_{5600}(561, \cdot)\) n/a 720 4
5600.2.dl \(\chi_{5600}(807, \cdot)\) None 0 4
5600.2.dn \(\chi_{5600}(857, \cdot)\) None 0 4
5600.2.do \(\chi_{5600}(257, \cdot)\) n/a 576 4
5600.2.dr \(\chi_{5600}(207, \cdot)\) n/a 560 4
5600.2.du \(\chi_{5600}(199, \cdot)\) None 0 4
5600.2.dv \(\chi_{5600}(1801, \cdot)\) None 0 4
5600.2.dw \(\chi_{5600}(551, \cdot)\) None 0 4
5600.2.dx \(\chi_{5600}(249, \cdot)\) None 0 4
5600.2.ea \(\chi_{5600}(543, \cdot)\) n/a 576 4
5600.2.ed \(\chi_{5600}(593, \cdot)\) n/a 560 4
5600.2.ef \(\chi_{5600}(3657, \cdot)\) None 0 4
5600.2.eh \(\chi_{5600}(3607, \cdot)\) None 0 4
5600.2.ei \(\chi_{5600}(641, \cdot)\) n/a 1920 8
5600.2.ek \(\chi_{5600}(377, \cdot)\) None 0 8
5600.2.em \(\chi_{5600}(183, \cdot)\) None 0 8
5600.2.eo \(\chi_{5600}(97, \cdot)\) n/a 1920 8
5600.2.ep \(\chi_{5600}(463, \cdot)\) n/a 1440 8
5600.2.et \(\chi_{5600}(279, \cdot)\) None 0 8
5600.2.eu \(\chi_{5600}(281, \cdot)\) None 0 8
5600.2.ev \(\chi_{5600}(391, \cdot)\) None 0 8
5600.2.ew \(\chi_{5600}(169, \cdot)\) None 0 8
5600.2.fa \(\chi_{5600}(127, \cdot)\) n/a 1440 8
5600.2.fb \(\chi_{5600}(433, \cdot)\) n/a 1888 8
5600.2.fe \(\chi_{5600}(1527, \cdot)\) None 0 8
5600.2.fg \(\chi_{5600}(153, \cdot)\) None 0 8
5600.2.fh \(\chi_{5600}(149, \cdot)\) n/a 4576 8
5600.2.fi \(\chi_{5600}(451, \cdot)\) n/a 4816 8
5600.2.fn \(\chi_{5600}(107, \cdot)\) n/a 4576 8
5600.2.fo \(\chi_{5600}(157, \cdot)\) n/a 4576 8
5600.2.fr \(\chi_{5600}(493, \cdot)\) n/a 4576 8
5600.2.fs \(\chi_{5600}(443, \cdot)\) n/a 4576 8
5600.2.ft \(\chi_{5600}(299, \cdot)\) n/a 4576 8
5600.2.fu \(\chi_{5600}(501, \cdot)\) n/a 4816 8
5600.2.fy \(\chi_{5600}(159, \cdot)\) n/a 1920 8
5600.2.fz \(\chi_{5600}(81, \cdot)\) n/a 1888 8
5600.2.gb \(\chi_{5600}(271, \cdot)\) n/a 1888 8
5600.2.ge \(\chi_{5600}(289, \cdot)\) n/a 1920 8
5600.2.gf \(\chi_{5600}(529, \cdot)\) n/a 1888 8
5600.2.gi \(\chi_{5600}(31, \cdot)\) n/a 1920 8
5600.2.gk \(\chi_{5600}(719, \cdot)\) n/a 1888 8
5600.2.gm \(\chi_{5600}(29, \cdot)\) n/a 11520 16
5600.2.gn \(\chi_{5600}(531, \cdot)\) n/a 15296 16
5600.2.gs \(\chi_{5600}(267, \cdot)\) n/a 11520 16
5600.2.gt \(\chi_{5600}(237, \cdot)\) n/a 15296 16
5600.2.gw \(\chi_{5600}(13, \cdot)\) n/a 15296 16
5600.2.gx \(\chi_{5600}(547, \cdot)\) n/a 11520 16
5600.2.gy \(\chi_{5600}(139, \cdot)\) n/a 15296 16
5600.2.gz \(\chi_{5600}(141, \cdot)\) n/a 11520 16
5600.2.hc \(\chi_{5600}(247, \cdot)\) None 0 16
5600.2.he \(\chi_{5600}(297, \cdot)\) None 0 16
5600.2.hg \(\chi_{5600}(17, \cdot)\) n/a 3776 16
5600.2.hj \(\chi_{5600}(767, \cdot)\) n/a 3840 16
5600.2.hm \(\chi_{5600}(9, \cdot)\) None 0 16
5600.2.hn \(\chi_{5600}(311, \cdot)\) None 0 16
5600.2.ho \(\chi_{5600}(121, \cdot)\) None 0 16
5600.2.hp \(\chi_{5600}(439, \cdot)\) None 0 16
5600.2.hs \(\chi_{5600}(303, \cdot)\) n/a 3776 16
5600.2.hv \(\chi_{5600}(33, \cdot)\) n/a 3840 16
5600.2.hw \(\chi_{5600}(73, \cdot)\) None 0 16
5600.2.hy \(\chi_{5600}(23, \cdot)\) None 0 16
5600.2.ic \(\chi_{5600}(221, \cdot)\) n/a 30592 32
5600.2.id \(\chi_{5600}(19, \cdot)\) n/a 30592 32
5600.2.ie \(\chi_{5600}(117, \cdot)\) n/a 30592 32
5600.2.if \(\chi_{5600}(67, \cdot)\) n/a 30592 32
5600.2.ii \(\chi_{5600}(163, \cdot)\) n/a 30592 32
5600.2.ij \(\chi_{5600}(213, \cdot)\) n/a 30592 32
5600.2.io \(\chi_{5600}(131, \cdot)\) n/a 30592 32
5600.2.ip \(\chi_{5600}(109, \cdot)\) n/a 30592 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2800))\)\(^{\oplus 2}\)