Properties

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

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

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