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Properties

Label 4200.2
Level 4200
Weight 2
Dimension 170886
Nonzero newspaces 72
Sturm bound 1843200

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Defining parameters

Level: \( N \) = \( 4200 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(1843200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4200))\).

Total New Old
Modular forms 468864 172526 296338
Cusp forms 452737 170886 281851
Eisenstein series 16127 1640 14487

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4200))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4200.2.a \(\chi_{4200}(1, \cdot)\) 4200.2.a.a 1 1
4200.2.a.b 1
4200.2.a.c 1
4200.2.a.d 1
4200.2.a.e 1
4200.2.a.f 1
4200.2.a.g 1
4200.2.a.h 1
4200.2.a.i 1
4200.2.a.j 1
4200.2.a.k 1
4200.2.a.l 1
4200.2.a.m 1
4200.2.a.n 1
4200.2.a.o 1
4200.2.a.p 1
4200.2.a.q 1
4200.2.a.r 1
4200.2.a.s 1
4200.2.a.t 1
4200.2.a.u 1
4200.2.a.v 1
4200.2.a.w 1
4200.2.a.x 1
4200.2.a.y 1
4200.2.a.z 1
4200.2.a.ba 1
4200.2.a.bb 1
4200.2.a.bc 1
4200.2.a.bd 1
4200.2.a.be 1
4200.2.a.bf 1
4200.2.a.bg 2
4200.2.a.bh 2
4200.2.a.bi 2
4200.2.a.bj 2
4200.2.a.bk 2
4200.2.a.bl 2
4200.2.a.bm 2
4200.2.a.bn 3
4200.2.a.bo 3
4200.2.a.bp 3
4200.2.a.bq 3
4200.2.d \(\chi_{4200}(3751, \cdot)\) None 0 1
4200.2.e \(\chi_{4200}(3851, \cdot)\) n/a 456 1
4200.2.f \(\chi_{4200}(3401, \cdot)\) n/a 152 1
4200.2.g \(\chi_{4200}(2101, \cdot)\) n/a 228 1
4200.2.j \(\chi_{4200}(3949, \cdot)\) n/a 216 1
4200.2.k \(\chi_{4200}(1049, \cdot)\) n/a 144 1
4200.2.p \(\chi_{4200}(1499, \cdot)\) n/a 432 1
4200.2.q \(\chi_{4200}(1399, \cdot)\) None 0 1
4200.2.t \(\chi_{4200}(1849, \cdot)\) 4200.2.t.a 2 1
4200.2.t.b 2
4200.2.t.c 2
4200.2.t.d 2
4200.2.t.e 2
4200.2.t.f 2
4200.2.t.g 2
4200.2.t.h 2
4200.2.t.i 2
4200.2.t.j 2
4200.2.t.k 2
4200.2.t.l 2
4200.2.t.m 2
4200.2.t.n 2
4200.2.t.o 2
4200.2.t.p 2
4200.2.t.q 2
4200.2.t.r 2
4200.2.t.s 2
4200.2.t.t 2
4200.2.t.u 4
4200.2.t.v 4
4200.2.t.w 4
4200.2.u \(\chi_{4200}(3149, \cdot)\) n/a 568 1
4200.2.v \(\chi_{4200}(3599, \cdot)\) None 0 1
4200.2.w \(\chi_{4200}(3499, \cdot)\) n/a 288 1
4200.2.z \(\chi_{4200}(1651, \cdot)\) n/a 304 1
4200.2.ba \(\chi_{4200}(1751, \cdot)\) None 0 1
4200.2.bf \(\chi_{4200}(1301, \cdot)\) n/a 596 1
4200.2.bg \(\chi_{4200}(1201, \cdot)\) n/a 152 2
4200.2.bj \(\chi_{4200}(1357, \cdot)\) n/a 576 2
4200.2.bk \(\chi_{4200}(1457, \cdot)\) n/a 216 2
4200.2.bl \(\chi_{4200}(1807, \cdot)\) None 0 2
4200.2.bm \(\chi_{4200}(3107, \cdot)\) n/a 1136 2
4200.2.br \(\chi_{4200}(43, \cdot)\) n/a 432 2
4200.2.bs \(\chi_{4200}(1007, \cdot)\) None 0 2
4200.2.bt \(\chi_{4200}(3457, \cdot)\) n/a 144 2
4200.2.bu \(\chi_{4200}(3557, \cdot)\) n/a 864 2
4200.2.bx \(\chi_{4200}(841, \cdot)\) n/a 352 4
4200.2.ca \(\chi_{4200}(1699, \cdot)\) n/a 576 2
4200.2.cb \(\chi_{4200}(599, \cdot)\) None 0 2
4200.2.cc \(\chi_{4200}(1349, \cdot)\) n/a 1136 2
4200.2.cd \(\chi_{4200}(3049, \cdot)\) n/a 144 2
4200.2.cg \(\chi_{4200}(101, \cdot)\) n/a 1192 2
4200.2.cl \(\chi_{4200}(2951, \cdot)\) None 0 2
4200.2.cm \(\chi_{4200}(451, \cdot)\) n/a 608 2
4200.2.cp \(\chi_{4200}(3301, \cdot)\) n/a 608 2
4200.2.cq \(\chi_{4200}(1601, \cdot)\) n/a 304 2
4200.2.cr \(\chi_{4200}(851, \cdot)\) n/a 1192 2
4200.2.cs \(\chi_{4200}(1951, \cdot)\) None 0 2
4200.2.cv \(\chi_{4200}(199, \cdot)\) None 0 2
4200.2.cw \(\chi_{4200}(2699, \cdot)\) n/a 1136 2
4200.2.db \(\chi_{4200}(3449, \cdot)\) n/a 288 2
4200.2.dc \(\chi_{4200}(949, \cdot)\) n/a 576 2
4200.2.dd \(\chi_{4200}(461, \cdot)\) n/a 3808 4
4200.2.di \(\chi_{4200}(71, \cdot)\) None 0 4
4200.2.dj \(\chi_{4200}(811, \cdot)\) n/a 1920 4
4200.2.dm \(\chi_{4200}(139, \cdot)\) n/a 1920 4
4200.2.dn \(\chi_{4200}(239, \cdot)\) None 0 4
4200.2.do \(\chi_{4200}(629, \cdot)\) n/a 3808 4
4200.2.dp \(\chi_{4200}(169, \cdot)\) n/a 368 4
4200.2.ds \(\chi_{4200}(559, \cdot)\) None 0 4
4200.2.dt \(\chi_{4200}(659, \cdot)\) n/a 2880 4
4200.2.dy \(\chi_{4200}(209, \cdot)\) n/a 960 4
4200.2.dz \(\chi_{4200}(589, \cdot)\) n/a 1440 4
4200.2.ec \(\chi_{4200}(421, \cdot)\) n/a 1440 4
4200.2.ed \(\chi_{4200}(41, \cdot)\) n/a 960 4
4200.2.ee \(\chi_{4200}(491, \cdot)\) n/a 2880 4
4200.2.ef \(\chi_{4200}(391, \cdot)\) None 0 4
4200.2.ei \(\chi_{4200}(557, \cdot)\) n/a 2272 4
4200.2.ej \(\chi_{4200}(1657, \cdot)\) n/a 288 4
4200.2.eo \(\chi_{4200}(143, \cdot)\) None 0 4
4200.2.ep \(\chi_{4200}(907, \cdot)\) n/a 1152 4
4200.2.eq \(\chi_{4200}(1307, \cdot)\) n/a 2272 4
4200.2.er \(\chi_{4200}(3007, \cdot)\) None 0 4
4200.2.ew \(\chi_{4200}(2657, \cdot)\) n/a 576 4
4200.2.ex \(\chi_{4200}(157, \cdot)\) n/a 1152 4
4200.2.ey \(\chi_{4200}(121, \cdot)\) n/a 960 8
4200.2.fb \(\chi_{4200}(197, \cdot)\) n/a 5760 8
4200.2.fc \(\chi_{4200}(97, \cdot)\) n/a 960 8
4200.2.fd \(\chi_{4200}(167, \cdot)\) None 0 8
4200.2.fe \(\chi_{4200}(547, \cdot)\) n/a 2880 8
4200.2.fj \(\chi_{4200}(83, \cdot)\) n/a 7616 8
4200.2.fk \(\chi_{4200}(127, \cdot)\) None 0 8
4200.2.fl \(\chi_{4200}(113, \cdot)\) n/a 1440 8
4200.2.fm \(\chi_{4200}(13, \cdot)\) n/a 3840 8
4200.2.fp \(\chi_{4200}(109, \cdot)\) n/a 3840 8
4200.2.fq \(\chi_{4200}(89, \cdot)\) n/a 1920 8
4200.2.fv \(\chi_{4200}(179, \cdot)\) n/a 7616 8
4200.2.fw \(\chi_{4200}(439, \cdot)\) None 0 8
4200.2.fz \(\chi_{4200}(31, \cdot)\) None 0 8
4200.2.ga \(\chi_{4200}(11, \cdot)\) n/a 7616 8
4200.2.gb \(\chi_{4200}(521, \cdot)\) n/a 1920 8
4200.2.gc \(\chi_{4200}(541, \cdot)\) n/a 3840 8
4200.2.gf \(\chi_{4200}(691, \cdot)\) n/a 3840 8
4200.2.gg \(\chi_{4200}(191, \cdot)\) None 0 8
4200.2.gl \(\chi_{4200}(341, \cdot)\) n/a 7616 8
4200.2.go \(\chi_{4200}(289, \cdot)\) n/a 960 8
4200.2.gp \(\chi_{4200}(269, \cdot)\) n/a 7616 8
4200.2.gq \(\chi_{4200}(359, \cdot)\) None 0 8
4200.2.gr \(\chi_{4200}(19, \cdot)\) n/a 3840 8
4200.2.gu \(\chi_{4200}(397, \cdot)\) n/a 7680 16
4200.2.gv \(\chi_{4200}(137, \cdot)\) n/a 3840 16
4200.2.ha \(\chi_{4200}(247, \cdot)\) None 0 16
4200.2.hb \(\chi_{4200}(227, \cdot)\) n/a 15232 16
4200.2.hc \(\chi_{4200}(67, \cdot)\) n/a 7680 16
4200.2.hd \(\chi_{4200}(47, \cdot)\) None 0 16
4200.2.hi \(\chi_{4200}(73, \cdot)\) n/a 1920 16
4200.2.hj \(\chi_{4200}(53, \cdot)\) n/a 15232 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2100))\)\(^{\oplus 2}\)