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Properties

Label 9999.2
Level 9999
Weight 2
Dimension 2849970
Nonzero newspaces 144
Sturm bound 14688000

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Defining parameters

Level: \( N \) = \( 9999 = 3^{2} \cdot 11 \cdot 101 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 144 \)
Sturm bound: \(14688000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9999))\).

Total New Old
Modular forms 3688000 2866010 821990
Cusp forms 3656001 2849970 806031
Eisenstein series 31999 16040 15959

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9999))\)

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
9999.2.a \(\chi_{9999}(1, \cdot)\) 9999.2.a.a 1 1
9999.2.a.b 1
9999.2.a.c 1
9999.2.a.d 1
9999.2.a.e 1
9999.2.a.f 1
9999.2.a.g 1
9999.2.a.h 1
9999.2.a.i 1
9999.2.a.j 1
9999.2.a.k 1
9999.2.a.l 1
9999.2.a.m 1
9999.2.a.n 2
9999.2.a.o 2
9999.2.a.p 2
9999.2.a.q 2
9999.2.a.r 5
9999.2.a.s 8
9999.2.a.t 9
9999.2.a.u 14
9999.2.a.v 15
9999.2.a.w 16
9999.2.a.x 16
9999.2.a.y 21
9999.2.a.z 24
9999.2.a.ba 24
9999.2.a.bb 25
9999.2.a.bc 27
9999.2.a.bd 29
9999.2.a.be 29
9999.2.a.bf 29
9999.2.a.bg 53
9999.2.a.bh 53
9999.2.b \(\chi_{9999}(9998, \cdot)\) n/a 408 1
9999.2.e \(\chi_{9999}(100, \cdot)\) n/a 424 1
9999.2.f \(\chi_{9999}(9899, \cdot)\) n/a 400 1
9999.2.i \(\chi_{9999}(3334, \cdot)\) n/a 2000 2
9999.2.j \(\chi_{9999}(8999, \cdot)\) n/a 680 2
9999.2.m \(\chi_{9999}(10, \cdot)\) n/a 1016 2
9999.2.n \(\chi_{9999}(4438, \cdot)\) n/a 2032 4
9999.2.o \(\chi_{9999}(2359, \cdot)\) n/a 2032 4
9999.2.p \(\chi_{9999}(1819, \cdot)\) n/a 2000 4
9999.2.q \(\chi_{9999}(892, \cdot)\) n/a 1704 4
9999.2.r \(\chi_{9999}(289, \cdot)\) n/a 2032 4
9999.2.s \(\chi_{9999}(1450, \cdot)\) n/a 2032 4
9999.2.v \(\chi_{9999}(3233, \cdot)\) n/a 2400 2
9999.2.w \(\chi_{9999}(3433, \cdot)\) n/a 2040 2
9999.2.z \(\chi_{9999}(3332, \cdot)\) n/a 2440 2
9999.2.ba \(\chi_{9999}(107, \cdot)\) n/a 1632 4
9999.2.bd \(\chi_{9999}(1027, \cdot)\) n/a 2032 4
9999.2.bk \(\chi_{9999}(1097, \cdot)\) n/a 1632 4
9999.2.bp \(\chi_{9999}(791, \cdot)\) n/a 1632 4
9999.2.bq \(\chi_{9999}(809, \cdot)\) n/a 1600 4
9999.2.br \(\chi_{9999}(3428, \cdot)\) n/a 1632 4
9999.2.bs \(\chi_{9999}(2609, \cdot)\) n/a 1632 4
9999.2.bt \(\chi_{9999}(2935, \cdot)\) n/a 2032 4
9999.2.bv \(\chi_{9999}(2539, \cdot)\) n/a 2032 4
9999.2.bw \(\chi_{9999}(1378, \cdot)\) n/a 2032 4
9999.2.bx \(\chi_{9999}(1918, \cdot)\) n/a 2032 4
9999.2.by \(\chi_{9999}(4357, \cdot)\) n/a 1696 4
9999.2.ch \(\chi_{9999}(4256, \cdot)\) n/a 1632 4
9999.2.ci \(\chi_{9999}(908, \cdot)\) n/a 1632 4
9999.2.cj \(\chi_{9999}(926, \cdot)\) n/a 1632 4
9999.2.ck \(\chi_{9999}(2834, \cdot)\) n/a 1632 4
9999.2.cm \(\chi_{9999}(17, \cdot)\) n/a 1632 4
9999.2.cn \(\chi_{9999}(701, \cdot)\) n/a 1632 4
9999.2.cq \(\chi_{9999}(3343, \cdot)\) n/a 4880 4
9999.2.ct \(\chi_{9999}(2333, \cdot)\) n/a 4080 4
9999.2.cu \(\chi_{9999}(1501, \cdot)\) n/a 9760 8
9999.2.cv \(\chi_{9999}(196, \cdot)\) n/a 9760 8
9999.2.cw \(\chi_{9999}(2014, \cdot)\) n/a 8160 8
9999.2.cx \(\chi_{9999}(1213, \cdot)\) n/a 9600 8
9999.2.cy \(\chi_{9999}(895, \cdot)\) n/a 9760 8
9999.2.cz \(\chi_{9999}(499, \cdot)\) n/a 9760 8
9999.2.da \(\chi_{9999}(1070, \cdot)\) n/a 3264 8
9999.2.dd \(\chi_{9999}(145, \cdot)\) n/a 4064 8
9999.2.de \(\chi_{9999}(2089, \cdot)\) n/a 4064 8
9999.2.df \(\chi_{9999}(865, \cdot)\) n/a 4064 8
9999.2.dg \(\chi_{9999}(919, \cdot)\) n/a 4064 8
9999.2.dh \(\chi_{9999}(739, \cdot)\) n/a 4064 8
9999.2.di \(\chi_{9999}(1657, \cdot)\) n/a 4064 8
9999.2.dt \(\chi_{9999}(1556, \cdot)\) n/a 3264 8
9999.2.du \(\chi_{9999}(746, \cdot)\) n/a 3264 8
9999.2.dv \(\chi_{9999}(818, \cdot)\) n/a 3264 8
9999.2.dw \(\chi_{9999}(170, \cdot)\) n/a 3264 8
9999.2.dx \(\chi_{9999}(1079, \cdot)\) n/a 2720 8
9999.2.dy \(\chi_{9999}(280, \cdot)\) n/a 10160 20
9999.2.dz \(\chi_{9999}(496, \cdot)\) n/a 8520 20
9999.2.ea \(\chi_{9999}(37, \cdot)\) n/a 10160 20
9999.2.eb \(\chi_{9999}(3349, \cdot)\) n/a 10160 20
9999.2.ec \(\chi_{9999}(181, \cdot)\) n/a 10160 20
9999.2.ef \(\chi_{9999}(1652, \cdot)\) n/a 9760 8
9999.2.eg \(\chi_{9999}(1580, \cdot)\) n/a 9760 8
9999.2.ei \(\chi_{9999}(2228, \cdot)\) n/a 9760 8
9999.2.ej \(\chi_{9999}(974, \cdot)\) n/a 9760 8
9999.2.ek \(\chi_{9999}(1514, \cdot)\) n/a 9760 8
9999.2.el \(\chi_{9999}(65, \cdot)\) n/a 9760 8
9999.2.eu \(\chi_{9999}(166, \cdot)\) n/a 8160 8
9999.2.ev \(\chi_{9999}(1312, \cdot)\) n/a 9760 8
9999.2.ew \(\chi_{9999}(421, \cdot)\) n/a 9760 8
9999.2.ex \(\chi_{9999}(511, \cdot)\) n/a 9760 8
9999.2.ez \(\chi_{9999}(1633, \cdot)\) n/a 9760 8
9999.2.fa \(\chi_{9999}(95, \cdot)\) n/a 9760 8
9999.2.fb \(\chi_{9999}(491, \cdot)\) n/a 9760 8
9999.2.fc \(\chi_{9999}(1415, \cdot)\) n/a 9600 8
9999.2.fd \(\chi_{9999}(1913, \cdot)\) n/a 9760 8
9999.2.fi \(\chi_{9999}(398, \cdot)\) n/a 9760 8
9999.2.fp \(\chi_{9999}(115, \cdot)\) n/a 9760 8
9999.2.fs \(\chi_{9999}(623, \cdot)\) n/a 9760 8
9999.2.fu \(\chi_{9999}(1304, \cdot)\) n/a 8160 20
9999.2.fv \(\chi_{9999}(64, \cdot)\) n/a 10160 20
9999.2.fw \(\chi_{9999}(388, \cdot)\) n/a 10160 20
9999.2.fx \(\chi_{9999}(298, \cdot)\) n/a 8480 20
9999.2.fy \(\chi_{9999}(82, \cdot)\) n/a 10160 20
9999.2.gd \(\chi_{9999}(233, \cdot)\) n/a 8160 20
9999.2.ge \(\chi_{9999}(395, \cdot)\) n/a 8160 20
9999.2.gf \(\chi_{9999}(530, \cdot)\) n/a 8160 20
9999.2.gg \(\chi_{9999}(260, \cdot)\) n/a 8160 20
9999.2.gm \(\chi_{9999}(379, \cdot)\) n/a 10160 20
9999.2.go \(\chi_{9999}(134, \cdot)\) n/a 8160 20
9999.2.gt \(\chi_{9999}(629, \cdot)\) n/a 8160 20
9999.2.gu \(\chi_{9999}(728, \cdot)\) n/a 8160 20
9999.2.gv \(\chi_{9999}(197, \cdot)\) n/a 8160 20
9999.2.gw \(\chi_{9999}(206, \cdot)\) n/a 8160 20
9999.2.hc \(\chi_{9999}(650, \cdot)\) n/a 16320 16
9999.2.hd \(\chi_{9999}(212, \cdot)\) n/a 19520 16
9999.2.he \(\chi_{9999}(950, \cdot)\) n/a 19520 16
9999.2.hf \(\chi_{9999}(1049, \cdot)\) n/a 19520 16
9999.2.hg \(\chi_{9999}(158, \cdot)\) n/a 19520 16
9999.2.hr \(\chi_{9999}(1960, \cdot)\) n/a 19520 16
9999.2.hs \(\chi_{9999}(259, \cdot)\) n/a 19520 16
9999.2.ht \(\chi_{9999}(448, \cdot)\) n/a 19520 16
9999.2.hu \(\chi_{9999}(1525, \cdot)\) n/a 19520 16
9999.2.hv \(\chi_{9999}(142, \cdot)\) n/a 19520 16
9999.2.hw \(\chi_{9999}(436, \cdot)\) n/a 19520 16
9999.2.hz \(\chi_{9999}(344, \cdot)\) n/a 19520 16
9999.2.ia \(\chi_{9999}(97, \cdot)\) n/a 48800 40
9999.2.ib \(\chi_{9999}(16, \cdot)\) n/a 48800 40
9999.2.ic \(\chi_{9999}(31, \cdot)\) n/a 48800 40
9999.2.id \(\chi_{9999}(529, \cdot)\) n/a 40800 40
9999.2.ie \(\chi_{9999}(328, \cdot)\) n/a 48800 40
9999.2.ig \(\chi_{9999}(46, \cdot)\) n/a 20320 40
9999.2.ih \(\chi_{9999}(152, \cdot)\) n/a 16320 40
9999.2.ii \(\chi_{9999}(53, \cdot)\) n/a 16320 40
9999.2.ij \(\chi_{9999}(89, \cdot)\) n/a 13600 40
9999.2.ik \(\chi_{9999}(26, \cdot)\) n/a 16320 40
9999.2.ip \(\chi_{9999}(28, \cdot)\) n/a 20320 40
9999.2.iq \(\chi_{9999}(109, \cdot)\) n/a 20320 40
9999.2.ir \(\chi_{9999}(73, \cdot)\) n/a 20320 40
9999.2.is \(\chi_{9999}(217, \cdot)\) n/a 20320 40
9999.2.iy \(\chi_{9999}(422, \cdot)\) n/a 16320 40
9999.2.ja \(\chi_{9999}(49, \cdot)\) n/a 48800 40
9999.2.jb \(\chi_{9999}(281, \cdot)\) n/a 48800 40
9999.2.jc \(\chi_{9999}(182, \cdot)\) n/a 48800 40
9999.2.jd \(\chi_{9999}(428, \cdot)\) n/a 48800 40
9999.2.je \(\chi_{9999}(524, \cdot)\) n/a 48800 40
9999.2.jj \(\chi_{9999}(247, \cdot)\) n/a 48800 40
9999.2.jk \(\chi_{9999}(232, \cdot)\) n/a 40800 40
9999.2.jl \(\chi_{9999}(691, \cdot)\) n/a 48800 40
9999.2.jm \(\chi_{9999}(4, \cdot)\) n/a 48800 40
9999.2.js \(\chi_{9999}(68, \cdot)\) n/a 48800 40
9999.2.ju \(\chi_{9999}(272, \cdot)\) n/a 48800 40
9999.2.jv \(\chi_{9999}(131, \cdot)\) n/a 48800 40
9999.2.jw \(\chi_{9999}(425, \cdot)\) n/a 48800 40
9999.2.jx \(\chi_{9999}(266, \cdot)\) n/a 48800 40
9999.2.kh \(\chi_{9999}(569, \cdot)\) n/a 48800 40
9999.2.kj \(\chi_{9999}(59, \cdot)\) n/a 97600 80
9999.2.kk \(\chi_{9999}(61, \cdot)\) n/a 97600 80
9999.2.kl \(\chi_{9999}(175, \cdot)\) n/a 97600 80
9999.2.km \(\chi_{9999}(40, \cdot)\) n/a 97600 80
9999.2.kn \(\chi_{9999}(310, \cdot)\) n/a 97600 80
9999.2.ks \(\chi_{9999}(353, \cdot)\) n/a 81600 80
9999.2.kt \(\chi_{9999}(38, \cdot)\) n/a 97600 80
9999.2.ku \(\chi_{9999}(104, \cdot)\) n/a 97600 80
9999.2.kv \(\chi_{9999}(119, \cdot)\) n/a 97600 80
9999.2.lb \(\chi_{9999}(7, \cdot)\) n/a 97600 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9999))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9999)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(101))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(303))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(909))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1111))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3333))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9999))\)\(^{\oplus 1}\)