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Properties

Label 6600.2
Level 6600
Weight 2
Dimension 438988
Nonzero newspaces 126
Sturm bound 4608000

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Defining parameters

Level: \( N \) = \( 6600 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 126 \)
Sturm bound: \(4608000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6600))\).

Total New Old
Modular forms 1165440 441940 723500
Cusp forms 1138561 438988 699573
Eisenstein series 26879 2952 23927

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6600))\)

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
6600.2.a \(\chi_{6600}(1, \cdot)\) 6600.2.a.a 1 1
6600.2.a.b 1
6600.2.a.c 1
6600.2.a.d 1
6600.2.a.e 1
6600.2.a.f 1
6600.2.a.g 1
6600.2.a.h 1
6600.2.a.i 1
6600.2.a.j 1
6600.2.a.k 1
6600.2.a.l 1
6600.2.a.m 1
6600.2.a.n 1
6600.2.a.o 1
6600.2.a.p 1
6600.2.a.q 1
6600.2.a.r 1
6600.2.a.s 1
6600.2.a.t 1
6600.2.a.u 1
6600.2.a.v 1
6600.2.a.w 1
6600.2.a.x 1
6600.2.a.y 1
6600.2.a.z 1
6600.2.a.ba 1
6600.2.a.bb 1
6600.2.a.bc 1
6600.2.a.bd 1
6600.2.a.be 1
6600.2.a.bf 1
6600.2.a.bg 2
6600.2.a.bh 2
6600.2.a.bi 2
6600.2.a.bj 2
6600.2.a.bk 2
6600.2.a.bl 2
6600.2.a.bm 2
6600.2.a.bn 3
6600.2.a.bo 3
6600.2.a.bp 3
6600.2.a.bq 3
6600.2.a.br 3
6600.2.a.bs 3
6600.2.a.bt 3
6600.2.a.bu 3
6600.2.a.bv 3
6600.2.a.bw 3
6600.2.a.bx 5
6600.2.a.by 5
6600.2.a.bz 5
6600.2.a.ca 5
6600.2.d \(\chi_{6600}(1849, \cdot)\) 6600.2.d.a 2 1
6600.2.d.b 2
6600.2.d.c 2
6600.2.d.d 2
6600.2.d.e 2
6600.2.d.f 2
6600.2.d.g 2
6600.2.d.h 2
6600.2.d.i 2
6600.2.d.j 2
6600.2.d.k 2
6600.2.d.l 2
6600.2.d.m 2
6600.2.d.n 2
6600.2.d.o 2
6600.2.d.p 2
6600.2.d.q 2
6600.2.d.r 2
6600.2.d.s 2
6600.2.d.t 2
6600.2.d.u 2
6600.2.d.v 2
6600.2.d.w 2
6600.2.d.x 2
6600.2.d.y 2
6600.2.d.z 4
6600.2.d.ba 4
6600.2.d.bb 4
6600.2.d.bc 4
6600.2.d.bd 4
6600.2.d.be 6
6600.2.d.bf 6
6600.2.d.bg 6
6600.2.e \(\chi_{6600}(3851, \cdot)\) n/a 760 1
6600.2.f \(\chi_{6600}(6401, \cdot)\) n/a 228 1
6600.2.g \(\chi_{6600}(1099, \cdot)\) n/a 432 1
6600.2.j \(\chi_{6600}(5149, \cdot)\) n/a 360 1
6600.2.k \(\chi_{6600}(551, \cdot)\) None 0 1
6600.2.p \(\chi_{6600}(3101, \cdot)\) n/a 900 1
6600.2.q \(\chi_{6600}(4399, \cdot)\) None 0 1
6600.2.t \(\chi_{6600}(2551, \cdot)\) None 0 1
6600.2.u \(\chi_{6600}(4949, \cdot)\) n/a 856 1
6600.2.v \(\chi_{6600}(2399, \cdot)\) None 0 1
6600.2.w \(\chi_{6600}(3301, \cdot)\) n/a 380 1
6600.2.z \(\chi_{6600}(5851, \cdot)\) n/a 456 1
6600.2.ba \(\chi_{6600}(1649, \cdot)\) n/a 216 1
6600.2.bf \(\chi_{6600}(5699, \cdot)\) n/a 720 1
6600.2.bh \(\chi_{6600}(5543, \cdot)\) None 0 2
6600.2.bi \(\chi_{6600}(1693, \cdot)\) n/a 864 2
6600.2.bl \(\chi_{6600}(2443, \cdot)\) n/a 720 2
6600.2.bm \(\chi_{6600}(2993, \cdot)\) n/a 360 2
6600.2.bp \(\chi_{6600}(5743, \cdot)\) None 0 2
6600.2.bq \(\chi_{6600}(6293, \cdot)\) n/a 1440 2
6600.2.bt \(\chi_{6600}(2243, \cdot)\) n/a 1712 2
6600.2.bu \(\chi_{6600}(4993, \cdot)\) n/a 216 2
6600.2.bw \(\chi_{6600}(361, \cdot)\) n/a 720 4
6600.2.bx \(\chi_{6600}(2401, \cdot)\) n/a 456 4
6600.2.by \(\chi_{6600}(961, \cdot)\) n/a 720 4
6600.2.bz \(\chi_{6600}(2161, \cdot)\) n/a 720 4
6600.2.ca \(\chi_{6600}(3481, \cdot)\) n/a 720 4
6600.2.cb \(\chi_{6600}(1321, \cdot)\) n/a 592 4
6600.2.cc \(\chi_{6600}(439, \cdot)\) None 0 4
6600.2.cd \(\chi_{6600}(461, \cdot)\) n/a 5728 4
6600.2.ci \(\chi_{6600}(1871, \cdot)\) None 0 4
6600.2.cj \(\chi_{6600}(1189, \cdot)\) n/a 2400 4
6600.2.cm \(\chi_{6600}(2419, \cdot)\) n/a 2880 4
6600.2.cn \(\chi_{6600}(1121, \cdot)\) n/a 1440 4
6600.2.co \(\chi_{6600}(1211, \cdot)\) n/a 4800 4
6600.2.cp \(\chi_{6600}(529, \cdot)\) n/a 608 4
6600.2.cu \(\chi_{6600}(181, \cdot)\) n/a 2880 4
6600.2.cv \(\chi_{6600}(839, \cdot)\) None 0 4
6600.2.cw \(\chi_{6600}(629, \cdot)\) n/a 5728 4
6600.2.cx \(\chi_{6600}(871, \cdot)\) None 0 4
6600.2.dc \(\chi_{6600}(2609, \cdot)\) n/a 1440 4
6600.2.dd \(\chi_{6600}(931, \cdot)\) n/a 2880 4
6600.2.dg \(\chi_{6600}(1499, \cdot)\) n/a 3424 4
6600.2.dh \(\chi_{6600}(1259, \cdot)\) n/a 5728 4
6600.2.dm \(\chi_{6600}(2579, \cdot)\) n/a 5728 4
6600.2.dn \(\chi_{6600}(689, \cdot)\) n/a 1440 4
6600.2.do \(\chi_{6600}(1531, \cdot)\) n/a 2880 4
6600.2.dt \(\chi_{6600}(1051, \cdot)\) n/a 1824 4
6600.2.du \(\chi_{6600}(569, \cdot)\) n/a 1440 4
6600.2.dv \(\chi_{6600}(211, \cdot)\) n/a 2880 4
6600.2.dw \(\chi_{6600}(3449, \cdot)\) n/a 864 4
6600.2.dz \(\chi_{6600}(179, \cdot)\) n/a 5728 4
6600.2.ec \(\chi_{6600}(1229, \cdot)\) n/a 5728 4
6600.2.ed \(\chi_{6600}(1471, \cdot)\) None 0 4
6600.2.eg \(\chi_{6600}(1741, \cdot)\) n/a 2880 4
6600.2.eh \(\chi_{6600}(119, \cdot)\) None 0 4
6600.2.em \(\chi_{6600}(599, \cdot)\) None 0 4
6600.2.en \(\chi_{6600}(1621, \cdot)\) n/a 2880 4
6600.2.eo \(\chi_{6600}(1439, \cdot)\) None 0 4
6600.2.ep \(\chi_{6600}(301, \cdot)\) n/a 1824 4
6600.2.eu \(\chi_{6600}(151, \cdot)\) None 0 4
6600.2.ev \(\chi_{6600}(29, \cdot)\) n/a 5728 4
6600.2.ew \(\chi_{6600}(271, \cdot)\) None 0 4
6600.2.ex \(\chi_{6600}(149, \cdot)\) n/a 3424 4
6600.2.fc \(\chi_{6600}(3269, \cdot)\) n/a 5728 4
6600.2.fd \(\chi_{6600}(2791, \cdot)\) None 0 4
6600.2.fg \(\chi_{6600}(421, \cdot)\) n/a 2880 4
6600.2.fh \(\chi_{6600}(719, \cdot)\) None 0 4
6600.2.fi \(\chi_{6600}(59, \cdot)\) n/a 5728 4
6600.2.fn \(\chi_{6600}(1889, \cdot)\) n/a 1440 4
6600.2.fo \(\chi_{6600}(811, \cdot)\) n/a 2880 4
6600.2.fr \(\chi_{6600}(1339, \cdot)\) n/a 2880 4
6600.2.fs \(\chi_{6600}(281, \cdot)\) n/a 1440 4
6600.2.ft \(\chi_{6600}(731, \cdot)\) n/a 5728 4
6600.2.fu \(\chi_{6600}(289, \cdot)\) n/a 720 4
6600.2.fz \(\chi_{6600}(2711, \cdot)\) None 0 4
6600.2.ga \(\chi_{6600}(3469, \cdot)\) n/a 2880 4
6600.2.gd \(\chi_{6600}(101, \cdot)\) n/a 3600 4
6600.2.ge \(\chi_{6600}(3319, \cdot)\) None 0 4
6600.2.gf \(\chi_{6600}(821, \cdot)\) n/a 5728 4
6600.2.gg \(\chi_{6600}(799, \cdot)\) None 0 4
6600.2.gl \(\chi_{6600}(2719, \cdot)\) None 0 4
6600.2.gm \(\chi_{6600}(3341, \cdot)\) n/a 5728 4
6600.2.gn \(\chi_{6600}(71, \cdot)\) None 0 4
6600.2.go \(\chi_{6600}(2029, \cdot)\) n/a 2880 4
6600.2.gt \(\chi_{6600}(949, \cdot)\) n/a 1728 4
6600.2.gu \(\chi_{6600}(911, \cdot)\) None 0 4
6600.2.gv \(\chi_{6600}(709, \cdot)\) n/a 2880 4
6600.2.gw \(\chi_{6600}(2951, \cdot)\) None 0 4
6600.2.gz \(\chi_{6600}(679, \cdot)\) None 0 4
6600.2.ha \(\chi_{6600}(2021, \cdot)\) n/a 5728 4
6600.2.hd \(\chi_{6600}(971, \cdot)\) n/a 5728 4
6600.2.he \(\chi_{6600}(169, \cdot)\) n/a 720 4
6600.2.hh \(\chi_{6600}(139, \cdot)\) n/a 2880 4
6600.2.hi \(\chi_{6600}(41, \cdot)\) n/a 1440 4
6600.2.hn \(\chi_{6600}(1601, \cdot)\) n/a 912 4
6600.2.ho \(\chi_{6600}(19, \cdot)\) n/a 2880 4
6600.2.hp \(\chi_{6600}(761, \cdot)\) n/a 1440 4
6600.2.hq \(\chi_{6600}(2899, \cdot)\) n/a 1728 4
6600.2.hv \(\chi_{6600}(49, \cdot)\) n/a 432 4
6600.2.hw \(\chi_{6600}(2171, \cdot)\) n/a 5728 4
6600.2.hx \(\chi_{6600}(889, \cdot)\) n/a 720 4
6600.2.hy \(\chi_{6600}(251, \cdot)\) n/a 3600 4
6600.2.id \(\chi_{6600}(2291, \cdot)\) n/a 5728 4
6600.2.ie \(\chi_{6600}(1489, \cdot)\) n/a 720 4
6600.2.ih \(\chi_{6600}(2059, \cdot)\) n/a 2880 4
6600.2.ii \(\chi_{6600}(1481, \cdot)\) n/a 1440 4
6600.2.ij \(\chi_{6600}(79, \cdot)\) None 0 4
6600.2.ik \(\chi_{6600}(1421, \cdot)\) n/a 5728 4
6600.2.ip \(\chi_{6600}(191, \cdot)\) None 0 4
6600.2.iq \(\chi_{6600}(229, \cdot)\) n/a 2880 4
6600.2.ir \(\chi_{6600}(419, \cdot)\) n/a 4800 4
6600.2.iw \(\chi_{6600}(329, \cdot)\) n/a 1440 4
6600.2.ix \(\chi_{6600}(571, \cdot)\) n/a 2880 4
6600.2.ja \(\chi_{6600}(661, \cdot)\) n/a 2400 4
6600.2.jb \(\chi_{6600}(1079, \cdot)\) None 0 4
6600.2.jc \(\chi_{6600}(989, \cdot)\) n/a 5728 4
6600.2.jd \(\chi_{6600}(1231, \cdot)\) None 0 4
6600.2.jh \(\chi_{6600}(613, \cdot)\) n/a 5760 8
6600.2.ji \(\chi_{6600}(167, \cdot)\) None 0 8
6600.2.jl \(\chi_{6600}(113, \cdot)\) n/a 2880 8
6600.2.jm \(\chi_{6600}(1027, \cdot)\) n/a 5760 8
6600.2.jp \(\chi_{6600}(827, \cdot)\) n/a 11456 8
6600.2.ju \(\chi_{6600}(1033, \cdot)\) n/a 1440 8
6600.2.jv \(\chi_{6600}(937, \cdot)\) n/a 1440 8
6600.2.jw \(\chi_{6600}(337, \cdot)\) n/a 1440 8
6600.2.jx \(\chi_{6600}(193, \cdot)\) n/a 864 8
6600.2.jy \(\chi_{6600}(923, \cdot)\) n/a 11456 8
6600.2.jz \(\chi_{6600}(107, \cdot)\) n/a 6848 8
6600.2.ka \(\chi_{6600}(83, \cdot)\) n/a 11456 8
6600.2.kb \(\chi_{6600}(563, \cdot)\) n/a 11456 8
6600.2.kg \(\chi_{6600}(217, \cdot)\) n/a 1440 8
6600.2.kj \(\chi_{6600}(103, \cdot)\) None 0 8
6600.2.ko \(\chi_{6600}(1013, \cdot)\) n/a 9600 8
6600.2.kp \(\chi_{6600}(917, \cdot)\) n/a 11456 8
6600.2.kq \(\chi_{6600}(53, \cdot)\) n/a 11456 8
6600.2.kr \(\chi_{6600}(2093, \cdot)\) n/a 6848 8
6600.2.ks \(\chi_{6600}(463, \cdot)\) None 0 8
6600.2.kt \(\chi_{6600}(1543, \cdot)\) None 0 8
6600.2.ku \(\chi_{6600}(223, \cdot)\) None 0 8
6600.2.kv \(\chi_{6600}(367, \cdot)\) None 0 8
6600.2.la \(\chi_{6600}(653, \cdot)\) n/a 11456 8
6600.2.ld \(\chi_{6600}(427, \cdot)\) n/a 5760 8
6600.2.li \(\chi_{6600}(353, \cdot)\) n/a 2400 8
6600.2.lj \(\chi_{6600}(257, \cdot)\) n/a 1728 8
6600.2.lk \(\chi_{6600}(377, \cdot)\) n/a 2880 8
6600.2.ll \(\chi_{6600}(713, \cdot)\) n/a 2880 8
6600.2.lm \(\chi_{6600}(67, \cdot)\) n/a 4800 8
6600.2.ln \(\chi_{6600}(163, \cdot)\) n/a 5760 8
6600.2.lo \(\chi_{6600}(763, \cdot)\) n/a 5760 8
6600.2.lp \(\chi_{6600}(643, \cdot)\) n/a 3456 8
6600.2.lu \(\chi_{6600}(137, \cdot)\) n/a 2880 8
6600.2.lx \(\chi_{6600}(767, \cdot)\) None 0 8
6600.2.mc \(\chi_{6600}(373, \cdot)\) n/a 5760 8
6600.2.md \(\chi_{6600}(3493, \cdot)\) n/a 3456 8
6600.2.me \(\chi_{6600}(877, \cdot)\) n/a 5760 8
6600.2.mf \(\chi_{6600}(13, \cdot)\) n/a 5760 8
6600.2.mg \(\chi_{6600}(263, \cdot)\) None 0 8
6600.2.mh \(\chi_{6600}(503, \cdot)\) None 0 8
6600.2.mi \(\chi_{6600}(887, \cdot)\) None 0 8
6600.2.mj \(\chi_{6600}(743, \cdot)\) None 0 8
6600.2.mo \(\chi_{6600}(277, \cdot)\) n/a 5760 8
6600.2.mr \(\chi_{6600}(317, \cdot)\) n/a 11456 8
6600.2.ms \(\chi_{6600}(247, \cdot)\) None 0 8
6600.2.mv \(\chi_{6600}(73, \cdot)\) n/a 1440 8
6600.2.mw \(\chi_{6600}(227, \cdot)\) n/a 11456 8

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(660))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(825))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1650))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3300))\)\(^{\oplus 2}\)