↑

Properties

Label 9900.2
Level 9900
Weight 2
Dimension 1081525
Nonzero newspaces 168
Sturm bound 10368000

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 9900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 168 \)
Sturm bound: \(10368000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9900))\).

Total New Old
Modular forms 2614400 1088169 1526231
Cusp forms 2569601 1081525 1488076
Eisenstein series 44799 6644 38155

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9900))\)

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
9900.2.a \(\chi_{9900}(1, \cdot)\) 9900.2.a.a 1 1
9900.2.a.b 1
9900.2.a.c 1
9900.2.a.d 1
9900.2.a.e 1
9900.2.a.f 1
9900.2.a.g 1
9900.2.a.h 1
9900.2.a.i 1
9900.2.a.j 1
9900.2.a.k 1
9900.2.a.l 1
9900.2.a.m 1
9900.2.a.n 1
9900.2.a.o 1
9900.2.a.p 1
9900.2.a.q 1
9900.2.a.r 1
9900.2.a.s 1
9900.2.a.t 1
9900.2.a.u 1
9900.2.a.v 1
9900.2.a.w 1
9900.2.a.x 1
9900.2.a.y 1
9900.2.a.z 1
9900.2.a.ba 1
9900.2.a.bb 1
9900.2.a.bc 1
9900.2.a.bd 1
9900.2.a.be 1
9900.2.a.bf 2
9900.2.a.bg 2
9900.2.a.bh 2
9900.2.a.bi 2
9900.2.a.bj 2
9900.2.a.bk 2
9900.2.a.bl 2
9900.2.a.bm 2
9900.2.a.bn 2
9900.2.a.bo 2
9900.2.a.bp 2
9900.2.a.bq 2
9900.2.a.br 2
9900.2.a.bs 2
9900.2.a.bt 2
9900.2.a.bu 2
9900.2.a.bv 2
9900.2.a.bw 2
9900.2.a.bx 2
9900.2.a.by 2
9900.2.a.bz 2
9900.2.a.ca 2
9900.2.a.cb 4
9900.2.c \(\chi_{9900}(5149, \cdot)\) 9900.2.c.a 2 1
9900.2.c.b 2
9900.2.c.c 2
9900.2.c.d 2
9900.2.c.e 2
9900.2.c.f 2
9900.2.c.g 2
9900.2.c.h 2
9900.2.c.i 2
9900.2.c.j 2
9900.2.c.k 2
9900.2.c.l 2
9900.2.c.m 2
9900.2.c.n 2
9900.2.c.o 2
9900.2.c.p 4
9900.2.c.q 4
9900.2.c.r 4
9900.2.c.s 4
9900.2.c.t 4
9900.2.c.u 4
9900.2.c.v 4
9900.2.c.w 4
9900.2.c.x 4
9900.2.c.y 4
9900.2.c.z 4
9900.2.d \(\chi_{9900}(9701, \cdot)\) 9900.2.d.a 2 1
9900.2.d.b 2
9900.2.d.c 16
9900.2.d.d 16
9900.2.d.e 16
9900.2.d.f 24
9900.2.f \(\chi_{9900}(3851, \cdot)\) n/a 380 1
9900.2.i \(\chi_{9900}(1099, \cdot)\) n/a 536 1
9900.2.k \(\chi_{9900}(5851, \cdot)\) n/a 564 1
9900.2.l \(\chi_{9900}(8999, \cdot)\) n/a 360 1
9900.2.n \(\chi_{9900}(4949, \cdot)\) 9900.2.n.a 4 1
9900.2.n.b 4
9900.2.n.c 16
9900.2.n.d 16
9900.2.n.e 32
9900.2.q \(\chi_{9900}(3301, \cdot)\) n/a 380 2
9900.2.r \(\chi_{9900}(5543, \cdot)\) n/a 864 2
9900.2.u \(\chi_{9900}(3257, \cdot)\) n/a 120 2
9900.2.v \(\chi_{9900}(5743, \cdot)\) n/a 900 2
9900.2.y \(\chi_{9900}(1693, \cdot)\) n/a 180 2
9900.2.z \(\chi_{9900}(361, \cdot)\) n/a 600 4
9900.2.ba \(\chi_{9900}(3601, \cdot)\) n/a 380 4
9900.2.bb \(\chi_{9900}(5041, \cdot)\) n/a 600 4
9900.2.bc \(\chi_{9900}(2161, \cdot)\) n/a 600 4
9900.2.bd \(\chi_{9900}(181, \cdot)\) n/a 600 4
9900.2.be \(\chi_{9900}(1981, \cdot)\) n/a 496 4
9900.2.bf \(\chi_{9900}(1649, \cdot)\) n/a 432 2
9900.2.bj \(\chi_{9900}(2551, \cdot)\) n/a 2712 2
9900.2.bk \(\chi_{9900}(2399, \cdot)\) n/a 2160 2
9900.2.bm \(\chi_{9900}(551, \cdot)\) n/a 2280 2
9900.2.bp \(\chi_{9900}(4399, \cdot)\) n/a 2576 2
9900.2.br \(\chi_{9900}(1849, \cdot)\) n/a 360 2
9900.2.bs \(\chi_{9900}(3101, \cdot)\) n/a 456 2
9900.2.bu \(\chi_{9900}(3079, \cdot)\) n/a 3584 4
9900.2.bx \(\chi_{9900}(1871, \cdot)\) n/a 2400 4
9900.2.bz \(\chi_{9900}(1781, \cdot)\) n/a 480 4
9900.2.ca \(\chi_{9900}(1189, \cdot)\) n/a 504 4
9900.2.cd \(\chi_{9900}(4139, \cdot)\) n/a 2880 4
9900.2.ce \(\chi_{9900}(811, \cdot)\) n/a 3584 4
9900.2.ch \(\chi_{9900}(2609, \cdot)\) n/a 480 4
9900.2.cl \(\chi_{9900}(6569, \cdot)\) n/a 480 4
9900.2.co \(\chi_{9900}(809, \cdot)\) n/a 480 4
9900.2.cp \(\chi_{9900}(1349, \cdot)\) n/a 288 4
9900.2.cs \(\chi_{9900}(1711, \cdot)\) n/a 3584 4
9900.2.cu \(\chi_{9900}(2159, \cdot)\) n/a 2880 4
9900.2.cx \(\chi_{9900}(2699, \cdot)\) n/a 1728 4
9900.2.cy \(\chi_{9900}(1259, \cdot)\) n/a 2880 4
9900.2.db \(\chi_{9900}(2251, \cdot)\) n/a 2256 4
9900.2.dc \(\chi_{9900}(271, \cdot)\) n/a 3584 4
9900.2.df \(\chi_{9900}(1531, \cdot)\) n/a 3584 4
9900.2.dh \(\chi_{9900}(179, \cdot)\) n/a 2880 4
9900.2.dk \(\chi_{9900}(629, \cdot)\) n/a 480 4
9900.2.dm \(\chi_{9900}(1421, \cdot)\) n/a 480 4
9900.2.dn \(\chi_{9900}(289, \cdot)\) n/a 600 4
9900.2.dq \(\chi_{9900}(971, \cdot)\) n/a 2880 4
9900.2.ds \(\chi_{9900}(19, \cdot)\) n/a 3584 4
9900.2.dt \(\chi_{9900}(1999, \cdot)\) n/a 2144 4
9900.2.dw \(\chi_{9900}(2719, \cdot)\) n/a 3584 4
9900.2.dx \(\chi_{9900}(71, \cdot)\) n/a 2880 4
9900.2.ea \(\chi_{9900}(4211, \cdot)\) n/a 2880 4
9900.2.eb \(\chi_{9900}(251, \cdot)\) n/a 1824 4
9900.2.ed \(\chi_{9900}(3979, \cdot)\) n/a 3584 4
9900.2.ef \(\chi_{9900}(5509, \cdot)\) n/a 600 4
9900.2.eh \(\chi_{9900}(161, \cdot)\) n/a 480 4
9900.2.ek \(\chi_{9900}(701, \cdot)\) n/a 304 4
9900.2.el \(\chi_{9900}(2681, \cdot)\) n/a 480 4
9900.2.eo \(\chi_{9900}(1549, \cdot)\) n/a 360 4
9900.2.ep \(\chi_{9900}(829, \cdot)\) n/a 600 4
9900.2.es \(\chi_{9900}(4789, \cdot)\) n/a 600 4
9900.2.eu \(\chi_{9900}(5561, \cdot)\) n/a 480 4
9900.2.ev \(\chi_{9900}(919, \cdot)\) n/a 3584 4
9900.2.ey \(\chi_{9900}(3491, \cdot)\) n/a 2880 4
9900.2.fb \(\chi_{9900}(989, \cdot)\) n/a 480 4
9900.2.fd \(\chi_{9900}(1079, \cdot)\) n/a 2400 4
9900.2.fe \(\chi_{9900}(1891, \cdot)\) n/a 3584 4
9900.2.fg \(\chi_{9900}(2993, \cdot)\) n/a 720 4
9900.2.fj \(\chi_{9900}(2243, \cdot)\) n/a 5152 4
9900.2.fk \(\chi_{9900}(1957, \cdot)\) n/a 864 4
9900.2.fn \(\chi_{9900}(2443, \cdot)\) n/a 4320 4
9900.2.fo \(\chi_{9900}(661, \cdot)\) n/a 2400 8
9900.2.fp \(\chi_{9900}(1021, \cdot)\) n/a 2880 8
9900.2.fq \(\chi_{9900}(301, \cdot)\) n/a 1824 8
9900.2.fr \(\chi_{9900}(841, \cdot)\) n/a 2880 8
9900.2.fs \(\chi_{9900}(961, \cdot)\) n/a 2880 8
9900.2.ft \(\chi_{9900}(421, \cdot)\) n/a 2880 8
9900.2.fv \(\chi_{9900}(1403, \cdot)\) n/a 5760 8
9900.2.fw \(\chi_{9900}(1853, \cdot)\) n/a 960 8
9900.2.fz \(\chi_{9900}(1297, \cdot)\) n/a 1200 8
9900.2.ga \(\chi_{9900}(937, \cdot)\) n/a 1200 8
9900.2.gb \(\chi_{9900}(1117, \cdot)\) n/a 1200 8
9900.2.gc \(\chi_{9900}(1657, \cdot)\) n/a 720 8
9900.2.gh \(\chi_{9900}(217, \cdot)\) n/a 1200 8
9900.2.gi \(\chi_{9900}(883, \cdot)\) n/a 7168 8
9900.2.gn \(\chi_{9900}(1387, \cdot)\) n/a 6000 8
9900.2.go \(\chi_{9900}(2143, \cdot)\) n/a 4288 8
9900.2.gp \(\chi_{9900}(1567, \cdot)\) n/a 7168 8
9900.2.gq \(\chi_{9900}(163, \cdot)\) n/a 7168 8
9900.2.gt \(\chi_{9900}(1277, \cdot)\) n/a 800 8
9900.2.gu \(\chi_{9900}(1457, \cdot)\) n/a 576 8
9900.2.gv \(\chi_{9900}(53, \cdot)\) n/a 960 8
9900.2.gw \(\chi_{9900}(917, \cdot)\) n/a 960 8
9900.2.hb \(\chi_{9900}(2897, \cdot)\) n/a 960 8
9900.2.hc \(\chi_{9900}(827, \cdot)\) n/a 5760 8
9900.2.hh \(\chi_{9900}(1187, \cdot)\) n/a 5760 8
9900.2.hi \(\chi_{9900}(503, \cdot)\) n/a 5760 8
9900.2.hj \(\chi_{9900}(3203, \cdot)\) n/a 5760 8
9900.2.hk \(\chi_{9900}(107, \cdot)\) n/a 3456 8
9900.2.hn \(\chi_{9900}(487, \cdot)\) n/a 7168 8
9900.2.ho \(\chi_{9900}(73, \cdot)\) n/a 1200 8
9900.2.hr \(\chi_{9900}(419, \cdot)\) n/a 14400 8
9900.2.hs \(\chi_{9900}(571, \cdot)\) n/a 17216 8
9900.2.hw \(\chi_{9900}(329, \cdot)\) n/a 2880 8
9900.2.hx \(\chi_{9900}(79, \cdot)\) n/a 17216 8
9900.2.ia \(\chi_{9900}(191, \cdot)\) n/a 17216 8
9900.2.ib \(\chi_{9900}(169, \cdot)\) n/a 2880 8
9900.2.id \(\chi_{9900}(41, \cdot)\) n/a 2880 8
9900.2.ig \(\chi_{9900}(761, \cdot)\) n/a 2880 8
9900.2.ih \(\chi_{9900}(101, \cdot)\) n/a 1824 8
9900.2.ik \(\chi_{9900}(709, \cdot)\) n/a 2880 8
9900.2.il \(\chi_{9900}(49, \cdot)\) n/a 1728 8
9900.2.io \(\chi_{9900}(1489, \cdot)\) n/a 2880 8
9900.2.iq \(\chi_{9900}(1481, \cdot)\) n/a 2880 8
9900.2.is \(\chi_{9900}(2711, \cdot)\) n/a 17216 8
9900.2.iu \(\chi_{9900}(799, \cdot)\) n/a 10304 8
9900.2.iv \(\chi_{9900}(259, \cdot)\) n/a 17216 8
9900.2.iy \(\chi_{9900}(139, \cdot)\) n/a 17216 8
9900.2.iz \(\chi_{9900}(2291, \cdot)\) n/a 17216 8
9900.2.jc \(\chi_{9900}(851, \cdot)\) n/a 10848 8
9900.2.jd \(\chi_{9900}(911, \cdot)\) n/a 17216 8
9900.2.jf \(\chi_{9900}(679, \cdot)\) n/a 17216 8
9900.2.ji \(\chi_{9900}(281, \cdot)\) n/a 2880 8
9900.2.jj \(\chi_{9900}(229, \cdot)\) n/a 2880 8
9900.2.jn \(\chi_{9900}(1469, \cdot)\) n/a 2880 8
9900.2.jo \(\chi_{9900}(931, \cdot)\) n/a 17216 8
9900.2.jq \(\chi_{9900}(119, \cdot)\) n/a 17216 8
9900.2.jt \(\chi_{9900}(1379, \cdot)\) n/a 17216 8
9900.2.ju \(\chi_{9900}(599, \cdot)\) n/a 10304 8
9900.2.jx \(\chi_{9900}(211, \cdot)\) n/a 17216 8
9900.2.jy \(\chi_{9900}(151, \cdot)\) n/a 10848 8
9900.2.kb \(\chi_{9900}(2371, \cdot)\) n/a 17216 8
9900.2.kd \(\chi_{9900}(2759, \cdot)\) n/a 17216 8
9900.2.kf \(\chi_{9900}(1229, \cdot)\) n/a 2880 8
9900.2.kj \(\chi_{9900}(689, \cdot)\) n/a 2880 8
9900.2.km \(\chi_{9900}(149, \cdot)\) n/a 1728 8
9900.2.kn \(\chi_{9900}(29, \cdot)\) n/a 2880 8
9900.2.kr \(\chi_{9900}(59, \cdot)\) n/a 17216 8
9900.2.ks \(\chi_{9900}(871, \cdot)\) n/a 17216 8
9900.2.kv \(\chi_{9900}(461, \cdot)\) n/a 2880 8
9900.2.kw \(\chi_{9900}(529, \cdot)\) n/a 2400 8
9900.2.ky \(\chi_{9900}(439, \cdot)\) n/a 17216 8
9900.2.lb \(\chi_{9900}(1211, \cdot)\) n/a 14400 8
9900.2.ld \(\chi_{9900}(113, \cdot)\) n/a 5760 16
9900.2.le \(\chi_{9900}(167, \cdot)\) n/a 34432 16
9900.2.lh \(\chi_{9900}(367, \cdot)\) n/a 34432 16
9900.2.li \(\chi_{9900}(223, \cdot)\) n/a 34432 16
9900.2.lj \(\chi_{9900}(643, \cdot)\) n/a 20608 16
9900.2.lk \(\chi_{9900}(67, \cdot)\) n/a 28800 16
9900.2.lp \(\chi_{9900}(103, \cdot)\) n/a 34432 16
9900.2.lq \(\chi_{9900}(277, \cdot)\) n/a 5760 16
9900.2.lv \(\chi_{9900}(193, \cdot)\) n/a 3456 16
9900.2.lw \(\chi_{9900}(337, \cdot)\) n/a 5760 16
9900.2.lx \(\chi_{9900}(13, \cdot)\) n/a 5760 16
9900.2.ly \(\chi_{9900}(373, \cdot)\) n/a 5760 16
9900.2.mb \(\chi_{9900}(743, \cdot)\) n/a 20608 16
9900.2.mc \(\chi_{9900}(83, \cdot)\) n/a 34432 16
9900.2.md \(\chi_{9900}(563, \cdot)\) n/a 34432 16
9900.2.me \(\chi_{9900}(263, \cdot)\) n/a 34432 16
9900.2.mj \(\chi_{9900}(767, \cdot)\) n/a 34432 16
9900.2.mk \(\chi_{9900}(137, \cdot)\) n/a 5760 16
9900.2.mp \(\chi_{9900}(713, \cdot)\) n/a 5760 16
9900.2.mq \(\chi_{9900}(533, \cdot)\) n/a 5760 16
9900.2.mr \(\chi_{9900}(257, \cdot)\) n/a 3456 16
9900.2.ms \(\chi_{9900}(353, \cdot)\) n/a 4800 16
9900.2.mv \(\chi_{9900}(853, \cdot)\) n/a 5760 16
9900.2.mw \(\chi_{9900}(247, \cdot)\) n/a 34432 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(825))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(990))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1650))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2475))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4950))\)\(^{\oplus 2}\)