Properties

Label 4400.2
Level 4400
Weight 2
Dimension 291983
Nonzero newspaces 98
Sturm bound 2304000

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Defining parameters

Level: \( N \) = \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 98 \)
Sturm bound: \(2304000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4400))\).

Total New Old
Modular forms 583840 295303 288537
Cusp forms 568161 291983 276178
Eisenstein series 15679 3320 12359

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4400))\)

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
4400.2.a \(\chi_{4400}(1, \cdot)\) 4400.2.a.a 1 1
4400.2.a.b 1
4400.2.a.c 1
4400.2.a.d 1
4400.2.a.e 1
4400.2.a.f 1
4400.2.a.g 1
4400.2.a.h 1
4400.2.a.i 1
4400.2.a.j 1
4400.2.a.k 1
4400.2.a.l 1
4400.2.a.m 1
4400.2.a.n 1
4400.2.a.o 1
4400.2.a.p 1
4400.2.a.q 1
4400.2.a.r 1
4400.2.a.s 1
4400.2.a.t 1
4400.2.a.u 1
4400.2.a.v 1
4400.2.a.w 1
4400.2.a.x 1
4400.2.a.y 1
4400.2.a.z 1
4400.2.a.ba 1
4400.2.a.bb 1
4400.2.a.bc 1
4400.2.a.bd 1
4400.2.a.be 1
4400.2.a.bf 2
4400.2.a.bg 2
4400.2.a.bh 2
4400.2.a.bi 2
4400.2.a.bj 2
4400.2.a.bk 2
4400.2.a.bl 2
4400.2.a.bm 2
4400.2.a.bn 2
4400.2.a.bo 2
4400.2.a.bp 2
4400.2.a.bq 2
4400.2.a.br 2
4400.2.a.bs 2
4400.2.a.bt 2
4400.2.a.bu 2
4400.2.a.bv 2
4400.2.a.bw 2
4400.2.a.bx 3
4400.2.a.by 3
4400.2.a.bz 3
4400.2.a.ca 3
4400.2.a.cb 4
4400.2.a.cc 4
4400.2.a.cd 4
4400.2.a.ce 4
4400.2.b \(\chi_{4400}(4049, \cdot)\) 4400.2.b.a 2 1
4400.2.b.b 2
4400.2.b.c 2
4400.2.b.d 2
4400.2.b.e 2
4400.2.b.f 2
4400.2.b.g 2
4400.2.b.h 2
4400.2.b.i 2
4400.2.b.j 2
4400.2.b.k 2
4400.2.b.l 2
4400.2.b.m 2
4400.2.b.n 2
4400.2.b.o 2
4400.2.b.p 4
4400.2.b.q 4
4400.2.b.r 4
4400.2.b.s 4
4400.2.b.t 4
4400.2.b.u 4
4400.2.b.v 4
4400.2.b.w 4
4400.2.b.x 4
4400.2.b.y 4
4400.2.b.z 4
4400.2.b.ba 4
4400.2.b.bb 6
4400.2.b.bc 6
4400.2.c \(\chi_{4400}(2199, \cdot)\) None 0 1
4400.2.f \(\chi_{4400}(351, \cdot)\) n/a 114 1
4400.2.g \(\chi_{4400}(2201, \cdot)\) None 0 1
4400.2.l \(\chi_{4400}(1849, \cdot)\) None 0 1
4400.2.m \(\chi_{4400}(4399, \cdot)\) n/a 108 1
4400.2.p \(\chi_{4400}(2551, \cdot)\) None 0 1
4400.2.s \(\chi_{4400}(2443, \cdot)\) n/a 720 2
4400.2.t \(\chi_{4400}(1693, \cdot)\) n/a 856 2
4400.2.v \(\chi_{4400}(1451, \cdot)\) n/a 900 2
4400.2.w \(\chi_{4400}(1101, \cdot)\) n/a 760 2
4400.2.z \(\chi_{4400}(1607, \cdot)\) None 0 2
4400.2.bb \(\chi_{4400}(857, \cdot)\) None 0 2
4400.2.bd \(\chi_{4400}(593, \cdot)\) n/a 212 2
4400.2.bf \(\chi_{4400}(1343, \cdot)\) n/a 180 2
4400.2.bh \(\chi_{4400}(749, \cdot)\) n/a 720 2
4400.2.bi \(\chi_{4400}(1099, \cdot)\) n/a 856 2
4400.2.bk \(\chi_{4400}(243, \cdot)\) n/a 720 2
4400.2.bl \(\chi_{4400}(3893, \cdot)\) n/a 856 2
4400.2.bo \(\chi_{4400}(2561, \cdot)\) n/a 712 4
4400.2.bp \(\chi_{4400}(401, \cdot)\) n/a 444 4
4400.2.bq \(\chi_{4400}(641, \cdot)\) n/a 712 4
4400.2.br \(\chi_{4400}(81, \cdot)\) n/a 712 4
4400.2.bs \(\chi_{4400}(881, \cdot)\) n/a 600 4
4400.2.bt \(\chi_{4400}(1281, \cdot)\) n/a 712 4
4400.2.bu \(\chi_{4400}(1961, \cdot)\) None 0 4
4400.2.bv \(\chi_{4400}(831, \cdot)\) n/a 720 4
4400.2.by \(\chi_{4400}(359, \cdot)\) None 0 4
4400.2.bz \(\chi_{4400}(289, \cdot)\) n/a 712 4
4400.2.cc \(\chi_{4400}(879, \cdot)\) n/a 720 4
4400.2.cd \(\chi_{4400}(89, \cdot)\) None 0 4
4400.2.cg \(\chi_{4400}(3671, \cdot)\) None 0 4
4400.2.ch \(\chi_{4400}(711, \cdot)\) None 0 4
4400.2.ci \(\chi_{4400}(391, \cdot)\) None 0 4
4400.2.cj \(\chi_{4400}(151, \cdot)\) None 0 4
4400.2.cs \(\chi_{4400}(9, \cdot)\) None 0 4
4400.2.ct \(\chi_{4400}(799, \cdot)\) n/a 432 4
4400.2.cu \(\chi_{4400}(1119, \cdot)\) n/a 720 4
4400.2.cv \(\chi_{4400}(479, \cdot)\) n/a 720 4
4400.2.cw \(\chi_{4400}(1609, \cdot)\) None 0 4
4400.2.cx \(\chi_{4400}(1049, \cdot)\) None 0 4
4400.2.cy \(\chi_{4400}(889, \cdot)\) None 0 4
4400.2.cz \(\chi_{4400}(959, \cdot)\) n/a 720 4
4400.2.di \(\chi_{4400}(791, \cdot)\) None 0 4
4400.2.dn \(\chi_{4400}(439, \cdot)\) None 0 4
4400.2.do \(\chi_{4400}(529, \cdot)\) n/a 600 4
4400.2.dx \(\chi_{4400}(1471, \cdot)\) n/a 720 4
4400.2.dy \(\chi_{4400}(1721, \cdot)\) None 0 4
4400.2.dz \(\chi_{4400}(201, \cdot)\) None 0 4
4400.2.ea \(\chi_{4400}(361, \cdot)\) None 0 4
4400.2.eb \(\chi_{4400}(1151, \cdot)\) n/a 456 4
4400.2.ec \(\chi_{4400}(271, \cdot)\) n/a 720 4
4400.2.ed \(\chi_{4400}(431, \cdot)\) n/a 720 4
4400.2.ee \(\chi_{4400}(1241, \cdot)\) None 0 4
4400.2.en \(\chi_{4400}(2209, \cdot)\) n/a 712 4
4400.2.eo \(\chi_{4400}(519, \cdot)\) None 0 4
4400.2.ep \(\chi_{4400}(3319, \cdot)\) None 0 4
4400.2.eq \(\chi_{4400}(1399, \cdot)\) None 0 4
4400.2.er \(\chi_{4400}(1169, \cdot)\) n/a 712 4
4400.2.es \(\chi_{4400}(49, \cdot)\) n/a 424 4
4400.2.et \(\chi_{4400}(929, \cdot)\) n/a 712 4
4400.2.eu \(\chi_{4400}(39, \cdot)\) None 0 4
4400.2.ex \(\chi_{4400}(441, \cdot)\) None 0 4
4400.2.ey \(\chi_{4400}(1231, \cdot)\) n/a 720 4
4400.2.fb \(\chi_{4400}(871, \cdot)\) None 0 4
4400.2.fe \(\chi_{4400}(79, \cdot)\) n/a 720 4
4400.2.ff \(\chi_{4400}(1369, \cdot)\) None 0 4
4400.2.fi \(\chi_{4400}(173, \cdot)\) n/a 5728 8
4400.2.fj \(\chi_{4400}(467, \cdot)\) n/a 5728 8
4400.2.fu \(\chi_{4400}(267, \cdot)\) n/a 5728 8
4400.2.fv \(\chi_{4400}(373, \cdot)\) n/a 5728 8
4400.2.fw \(\chi_{4400}(293, \cdot)\) n/a 3424 8
4400.2.fx \(\chi_{4400}(613, \cdot)\) n/a 5728 8
4400.2.fy \(\chi_{4400}(2213, \cdot)\) n/a 5728 8
4400.2.fz \(\chi_{4400}(3, \cdot)\) n/a 5728 8
4400.2.ga \(\chi_{4400}(1123, \cdot)\) n/a 4800 8
4400.2.gb \(\chi_{4400}(643, \cdot)\) n/a 3424 8
4400.2.gc \(\chi_{4400}(323, \cdot)\) n/a 5728 8
4400.2.gd \(\chi_{4400}(237, \cdot)\) n/a 5728 8
4400.2.gf \(\chi_{4400}(221, \cdot)\) n/a 4800 8
4400.2.gg \(\chi_{4400}(131, \cdot)\) n/a 5728 8
4400.2.gj \(\chi_{4400}(1179, \cdot)\) n/a 5728 8
4400.2.gk \(\chi_{4400}(229, \cdot)\) n/a 5728 8
4400.2.gm \(\chi_{4400}(1109, \cdot)\) n/a 5728 8
4400.2.go \(\chi_{4400}(299, \cdot)\) n/a 3424 8
4400.2.gr \(\chi_{4400}(19, \cdot)\) n/a 5728 8
4400.2.gs \(\chi_{4400}(139, \cdot)\) n/a 5728 8
4400.2.gv \(\chi_{4400}(389, \cdot)\) n/a 5728 8
4400.2.gw \(\chi_{4400}(69, \cdot)\) n/a 5728 8
4400.2.gz \(\chi_{4400}(949, \cdot)\) n/a 3424 8
4400.2.hb \(\chi_{4400}(1019, \cdot)\) n/a 5728 8
4400.2.hd \(\chi_{4400}(223, \cdot)\) n/a 1440 8
4400.2.hf \(\chi_{4400}(17, \cdot)\) n/a 1424 8
4400.2.hh \(\chi_{4400}(633, \cdot)\) None 0 8
4400.2.hj \(\chi_{4400}(647, \cdot)\) None 0 8
4400.2.hk \(\chi_{4400}(73, \cdot)\) None 0 8
4400.2.hm \(\chi_{4400}(247, \cdot)\) None 0 8
4400.2.ho \(\chi_{4400}(193, \cdot)\) n/a 848 8
4400.2.hq \(\chi_{4400}(687, \cdot)\) n/a 1440 8
4400.2.hs \(\chi_{4400}(287, \cdot)\) n/a 1200 8
4400.2.ht \(\chi_{4400}(47, \cdot)\) n/a 1440 8
4400.2.hw \(\chi_{4400}(417, \cdot)\) n/a 1424 8
4400.2.hx \(\chi_{4400}(1073, \cdot)\) n/a 1424 8
4400.2.ia \(\chi_{4400}(673, \cdot)\) n/a 1424 8
4400.2.ic \(\chi_{4400}(207, \cdot)\) n/a 864 8
4400.2.ie \(\chi_{4400}(807, \cdot)\) None 0 8
4400.2.ig \(\chi_{4400}(153, \cdot)\) None 0 8
4400.2.ih \(\chi_{4400}(937, \cdot)\) None 0 8
4400.2.ik \(\chi_{4400}(217, \cdot)\) None 0 8
4400.2.im \(\chi_{4400}(103, \cdot)\) None 0 8
4400.2.io \(\chi_{4400}(23, \cdot)\) None 0 8
4400.2.ip \(\chi_{4400}(423, \cdot)\) None 0 8
4400.2.is \(\chi_{4400}(57, \cdot)\) None 0 8
4400.2.iu \(\chi_{4400}(383, \cdot)\) n/a 1440 8
4400.2.iw \(\chi_{4400}(897, \cdot)\) n/a 1424 8
4400.2.iz \(\chi_{4400}(181, \cdot)\) n/a 5728 8
4400.2.ja \(\chi_{4400}(491, \cdot)\) n/a 5728 8
4400.2.jc \(\chi_{4400}(371, \cdot)\) n/a 5728 8
4400.2.je \(\chi_{4400}(301, \cdot)\) n/a 3600 8
4400.2.jh \(\chi_{4400}(581, \cdot)\) n/a 5728 8
4400.2.ji \(\chi_{4400}(1461, \cdot)\) n/a 5728 8
4400.2.jl \(\chi_{4400}(211, \cdot)\) n/a 5728 8
4400.2.jm \(\chi_{4400}(171, \cdot)\) n/a 5728 8
4400.2.jp \(\chi_{4400}(51, \cdot)\) n/a 3600 8
4400.2.jr \(\chi_{4400}(141, \cdot)\) n/a 5728 8
4400.2.jt \(\chi_{4400}(219, \cdot)\) n/a 5728 8
4400.2.ju \(\chi_{4400}(309, \cdot)\) n/a 4800 8
4400.2.jw \(\chi_{4400}(147, \cdot)\) n/a 5728 8
4400.2.jx \(\chi_{4400}(13, \cdot)\) n/a 5728 8
4400.2.jy \(\chi_{4400}(197, \cdot)\) n/a 5728 8
4400.2.jz \(\chi_{4400}(437, \cdot)\) n/a 5728 8
4400.2.ka \(\chi_{4400}(893, \cdot)\) n/a 3424 8
4400.2.kb \(\chi_{4400}(67, \cdot)\) n/a 4800 8
4400.2.kc \(\chi_{4400}(203, \cdot)\) n/a 5728 8
4400.2.kd \(\chi_{4400}(443, \cdot)\) n/a 3424 8
4400.2.ke \(\chi_{4400}(2203, \cdot)\) n/a 5728 8
4400.2.kf \(\chi_{4400}(277, \cdot)\) n/a 5728 8
4400.2.kq \(\chi_{4400}(453, \cdot)\) n/a 5728 8
4400.2.kr \(\chi_{4400}(587, \cdot)\) n/a 5728 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4400))\)\(^{\oplus 1}\)