Properties

Label 8400.2
Level 8400
Weight 2
Dimension 684980
Nonzero newspaces 112
Sturm bound 7372800

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Defining parameters

Level: \( N \) = \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 112 \)
Sturm bound: \(7372800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8400))\).

Total New Old
Modular forms 1862016 688672 1173344
Cusp forms 1824385 684980 1139405
Eisenstein series 37631 3692 33939

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8400))\)

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
8400.2.a \(\chi_{8400}(1, \cdot)\) 8400.2.a.a 1 1
8400.2.a.b 1
8400.2.a.c 1
8400.2.a.d 1
8400.2.a.e 1
8400.2.a.f 1
8400.2.a.g 1
8400.2.a.h 1
8400.2.a.i 1
8400.2.a.j 1
8400.2.a.k 1
8400.2.a.l 1
8400.2.a.m 1
8400.2.a.n 1
8400.2.a.o 1
8400.2.a.p 1
8400.2.a.q 1
8400.2.a.r 1
8400.2.a.s 1
8400.2.a.t 1
8400.2.a.u 1
8400.2.a.v 1
8400.2.a.w 1
8400.2.a.x 1
8400.2.a.y 1
8400.2.a.z 1
8400.2.a.ba 1
8400.2.a.bb 1
8400.2.a.bc 1
8400.2.a.bd 1
8400.2.a.be 1
8400.2.a.bf 1
8400.2.a.bg 1
8400.2.a.bh 1
8400.2.a.bi 1
8400.2.a.bj 1
8400.2.a.bk 1
8400.2.a.bl 1
8400.2.a.bm 1
8400.2.a.bn 1
8400.2.a.bo 1
8400.2.a.bp 1
8400.2.a.bq 1
8400.2.a.br 1
8400.2.a.bs 1
8400.2.a.bt 1
8400.2.a.bu 1
8400.2.a.bv 1
8400.2.a.bw 1
8400.2.a.bx 1
8400.2.a.by 1
8400.2.a.bz 1
8400.2.a.ca 1
8400.2.a.cb 1
8400.2.a.cc 1
8400.2.a.cd 1
8400.2.a.ce 1
8400.2.a.cf 1
8400.2.a.cg 1
8400.2.a.ch 1
8400.2.a.ci 1
8400.2.a.cj 1
8400.2.a.ck 1
8400.2.a.cl 1
8400.2.a.cm 1
8400.2.a.cn 1
8400.2.a.co 1
8400.2.a.cp 1
8400.2.a.cq 1
8400.2.a.cr 1
8400.2.a.cs 1
8400.2.a.ct 1
8400.2.a.cu 2
8400.2.a.cv 2
8400.2.a.cw 2
8400.2.a.cx 2
8400.2.a.cy 2
8400.2.a.cz 2
8400.2.a.da 2
8400.2.a.db 2
8400.2.a.dc 2
8400.2.a.dd 2
8400.2.a.de 2
8400.2.a.df 2
8400.2.a.dg 3
8400.2.a.dh 3
8400.2.a.di 3
8400.2.a.dj 3
8400.2.a.dk 3
8400.2.a.dl 3
8400.2.d \(\chi_{8400}(7951, \cdot)\) n/a 152 1
8400.2.e \(\chi_{8400}(1751, \cdot)\) None 0 1
8400.2.f \(\chi_{8400}(7601, \cdot)\) n/a 298 1
8400.2.g \(\chi_{8400}(4201, \cdot)\) None 0 1
8400.2.j \(\chi_{8400}(1849, \cdot)\) None 0 1
8400.2.k \(\chi_{8400}(5249, \cdot)\) n/a 284 1
8400.2.p \(\chi_{8400}(7799, \cdot)\) None 0 1
8400.2.q \(\chi_{8400}(5599, \cdot)\) n/a 144 1
8400.2.t \(\chi_{8400}(6049, \cdot)\) n/a 108 1
8400.2.u \(\chi_{8400}(1049, \cdot)\) None 0 1
8400.2.v \(\chi_{8400}(3599, \cdot)\) n/a 216 1
8400.2.w \(\chi_{8400}(1399, \cdot)\) None 0 1
8400.2.z \(\chi_{8400}(3751, \cdot)\) None 0 1
8400.2.ba \(\chi_{8400}(5951, \cdot)\) n/a 228 1
8400.2.bf \(\chi_{8400}(3401, \cdot)\) None 0 1
8400.2.bg \(\chi_{8400}(1201, \cdot)\) n/a 304 2
8400.2.bj \(\chi_{8400}(7657, \cdot)\) None 0 2
8400.2.bk \(\chi_{8400}(1457, \cdot)\) n/a 432 2
8400.2.bl \(\chi_{8400}(1807, \cdot)\) n/a 216 2
8400.2.bm \(\chi_{8400}(5207, \cdot)\) None 0 2
8400.2.bp \(\chi_{8400}(4243, \cdot)\) n/a 864 2
8400.2.bs \(\chi_{8400}(1357, \cdot)\) n/a 1152 2
8400.2.bu \(\chi_{8400}(3557, \cdot)\) n/a 1728 2
8400.2.bv \(\chi_{8400}(3107, \cdot)\) n/a 2288 2
8400.2.bx \(\chi_{8400}(3149, \cdot)\) n/a 2288 2
8400.2.ca \(\chi_{8400}(3851, \cdot)\) n/a 1824 2
8400.2.cb \(\chi_{8400}(3949, \cdot)\) n/a 864 2
8400.2.ce \(\chi_{8400}(1651, \cdot)\) n/a 1216 2
8400.2.cg \(\chi_{8400}(2101, \cdot)\) n/a 912 2
8400.2.ch \(\chi_{8400}(3499, \cdot)\) n/a 1152 2
8400.2.ck \(\chi_{8400}(1301, \cdot)\) n/a 2408 2
8400.2.cl \(\chi_{8400}(1499, \cdot)\) n/a 1728 2
8400.2.co \(\chi_{8400}(1693, \cdot)\) n/a 1152 2
8400.2.cp \(\chi_{8400}(43, \cdot)\) n/a 864 2
8400.2.cr \(\chi_{8400}(3443, \cdot)\) n/a 2288 2
8400.2.cu \(\chi_{8400}(3893, \cdot)\) n/a 1728 2
8400.2.cx \(\chi_{8400}(6007, \cdot)\) None 0 2
8400.2.cy \(\chi_{8400}(1007, \cdot)\) n/a 576 2
8400.2.cz \(\chi_{8400}(3457, \cdot)\) n/a 288 2
8400.2.da \(\chi_{8400}(5657, \cdot)\) None 0 2
8400.2.dd \(\chi_{8400}(1681, \cdot)\) n/a 720 4
8400.2.dg \(\chi_{8400}(199, \cdot)\) None 0 2
8400.2.dh \(\chi_{8400}(1199, \cdot)\) n/a 576 2
8400.2.di \(\chi_{8400}(3449, \cdot)\) None 0 2
8400.2.dj \(\chi_{8400}(3649, \cdot)\) n/a 288 2
8400.2.dm \(\chi_{8400}(2201, \cdot)\) None 0 2
8400.2.dr \(\chi_{8400}(3551, \cdot)\) n/a 608 2
8400.2.ds \(\chi_{8400}(2551, \cdot)\) None 0 2
8400.2.dv \(\chi_{8400}(1801, \cdot)\) None 0 2
8400.2.dw \(\chi_{8400}(1601, \cdot)\) n/a 596 2
8400.2.dx \(\chi_{8400}(2951, \cdot)\) None 0 2
8400.2.dy \(\chi_{8400}(1951, \cdot)\) n/a 304 2
8400.2.eb \(\chi_{8400}(4399, \cdot)\) n/a 288 2
8400.2.ec \(\chi_{8400}(599, \cdot)\) None 0 2
8400.2.eh \(\chi_{8400}(4049, \cdot)\) n/a 568 2
8400.2.ei \(\chi_{8400}(3049, \cdot)\) None 0 2
8400.2.ej \(\chi_{8400}(41, \cdot)\) None 0 4
8400.2.eo \(\chi_{8400}(911, \cdot)\) n/a 1440 4
8400.2.ep \(\chi_{8400}(391, \cdot)\) None 0 4
8400.2.es \(\chi_{8400}(3079, \cdot)\) None 0 4
8400.2.et \(\chi_{8400}(239, \cdot)\) n/a 1440 4
8400.2.eu \(\chi_{8400}(2729, \cdot)\) None 0 4
8400.2.ev \(\chi_{8400}(1009, \cdot)\) n/a 720 4
8400.2.ey \(\chi_{8400}(559, \cdot)\) n/a 960 4
8400.2.ez \(\chi_{8400}(1079, \cdot)\) None 0 4
8400.2.fe \(\chi_{8400}(209, \cdot)\) n/a 1904 4
8400.2.ff \(\chi_{8400}(169, \cdot)\) None 0 4
8400.2.fi \(\chi_{8400}(841, \cdot)\) None 0 4
8400.2.fj \(\chi_{8400}(881, \cdot)\) n/a 1904 4
8400.2.fk \(\chi_{8400}(71, \cdot)\) None 0 4
8400.2.fl \(\chi_{8400}(1231, \cdot)\) n/a 960 4
8400.2.fo \(\chi_{8400}(3257, \cdot)\) None 0 4
8400.2.fp \(\chi_{8400}(2257, \cdot)\) n/a 576 4
8400.2.fu \(\chi_{8400}(143, \cdot)\) n/a 1152 4
8400.2.fv \(\chi_{8400}(3607, \cdot)\) None 0 4
8400.2.fw \(\chi_{8400}(1643, \cdot)\) n/a 4576 4
8400.2.fz \(\chi_{8400}(893, \cdot)\) n/a 4576 4
8400.2.gb \(\chi_{8400}(157, \cdot)\) n/a 2304 4
8400.2.gc \(\chi_{8400}(907, \cdot)\) n/a 2304 4
8400.2.ge \(\chi_{8400}(101, \cdot)\) n/a 4816 4
8400.2.gh \(\chi_{8400}(2699, \cdot)\) n/a 4576 4
8400.2.gi \(\chi_{8400}(3301, \cdot)\) n/a 2432 4
8400.2.gl \(\chi_{8400}(1699, \cdot)\) n/a 2304 4
8400.2.gn \(\chi_{8400}(949, \cdot)\) n/a 2304 4
8400.2.go \(\chi_{8400}(451, \cdot)\) n/a 2432 4
8400.2.gr \(\chi_{8400}(1349, \cdot)\) n/a 4576 4
8400.2.gs \(\chi_{8400}(851, \cdot)\) n/a 4816 4
8400.2.gv \(\chi_{8400}(557, \cdot)\) n/a 4576 4
8400.2.gw \(\chi_{8400}(1307, \cdot)\) n/a 4576 4
8400.2.gy \(\chi_{8400}(1243, \cdot)\) n/a 2304 4
8400.2.hb \(\chi_{8400}(493, \cdot)\) n/a 2304 4
8400.2.hc \(\chi_{8400}(4007, \cdot)\) None 0 4
8400.2.hd \(\chi_{8400}(3007, \cdot)\) n/a 576 4
8400.2.hi \(\chi_{8400}(2657, \cdot)\) n/a 1136 4
8400.2.hj \(\chi_{8400}(1657, \cdot)\) None 0 4
8400.2.hk \(\chi_{8400}(961, \cdot)\) n/a 1920 8
8400.2.hn \(\chi_{8400}(617, \cdot)\) None 0 8
8400.2.ho \(\chi_{8400}(97, \cdot)\) n/a 1920 8
8400.2.hp \(\chi_{8400}(2687, \cdot)\) n/a 3840 8
8400.2.hq \(\chi_{8400}(967, \cdot)\) None 0 8
8400.2.ht \(\chi_{8400}(533, \cdot)\) n/a 11520 8
8400.2.hw \(\chi_{8400}(83, \cdot)\) n/a 15296 8
8400.2.hy \(\chi_{8400}(547, \cdot)\) n/a 5760 8
8400.2.hz \(\chi_{8400}(13, \cdot)\) n/a 7680 8
8400.2.ic \(\chi_{8400}(659, \cdot)\) n/a 11520 8
8400.2.id \(\chi_{8400}(461, \cdot)\) n/a 15296 8
8400.2.ig \(\chi_{8400}(139, \cdot)\) n/a 7680 8
8400.2.ih \(\chi_{8400}(421, \cdot)\) n/a 5760 8
8400.2.ij \(\chi_{8400}(811, \cdot)\) n/a 7680 8
8400.2.im \(\chi_{8400}(589, \cdot)\) n/a 5760 8
8400.2.in \(\chi_{8400}(491, \cdot)\) n/a 11520 8
8400.2.iq \(\chi_{8400}(629, \cdot)\) n/a 15296 8
8400.2.is \(\chi_{8400}(923, \cdot)\) n/a 15296 8
8400.2.it \(\chi_{8400}(197, \cdot)\) n/a 11520 8
8400.2.iv \(\chi_{8400}(853, \cdot)\) n/a 7680 8
8400.2.iy \(\chi_{8400}(883, \cdot)\) n/a 5760 8
8400.2.jb \(\chi_{8400}(167, \cdot)\) None 0 8
8400.2.jc \(\chi_{8400}(127, \cdot)\) n/a 1440 8
8400.2.jd \(\chi_{8400}(113, \cdot)\) n/a 2880 8
8400.2.je \(\chi_{8400}(937, \cdot)\) None 0 8
8400.2.jh \(\chi_{8400}(1129, \cdot)\) None 0 8
8400.2.ji \(\chi_{8400}(689, \cdot)\) n/a 3808 8
8400.2.jn \(\chi_{8400}(359, \cdot)\) None 0 8
8400.2.jo \(\chi_{8400}(1039, \cdot)\) n/a 1920 8
8400.2.jr \(\chi_{8400}(31, \cdot)\) n/a 1920 8
8400.2.js \(\chi_{8400}(1031, \cdot)\) None 0 8
8400.2.jt \(\chi_{8400}(1361, \cdot)\) n/a 3808 8
8400.2.ju \(\chi_{8400}(121, \cdot)\) None 0 8
8400.2.jx \(\chi_{8400}(871, \cdot)\) None 0 8
8400.2.jy \(\chi_{8400}(191, \cdot)\) n/a 3840 8
8400.2.kd \(\chi_{8400}(521, \cdot)\) None 0 8
8400.2.kg \(\chi_{8400}(289, \cdot)\) n/a 1920 8
8400.2.kh \(\chi_{8400}(89, \cdot)\) None 0 8
8400.2.ki \(\chi_{8400}(1439, \cdot)\) n/a 3840 8
8400.2.kj \(\chi_{8400}(439, \cdot)\) None 0 8
8400.2.km \(\chi_{8400}(73, \cdot)\) None 0 16
8400.2.kn \(\chi_{8400}(737, \cdot)\) n/a 7616 16
8400.2.ks \(\chi_{8400}(1087, \cdot)\) n/a 3840 16
8400.2.kt \(\chi_{8400}(647, \cdot)\) None 0 16
8400.2.ku \(\chi_{8400}(733, \cdot)\) n/a 15360 16
8400.2.kx \(\chi_{8400}(67, \cdot)\) n/a 15360 16
8400.2.kz \(\chi_{8400}(563, \cdot)\) n/a 30592 16
8400.2.la \(\chi_{8400}(53, \cdot)\) n/a 30592 16
8400.2.ld \(\chi_{8400}(11, \cdot)\) n/a 30592 16
8400.2.le \(\chi_{8400}(269, \cdot)\) n/a 30592 16
8400.2.lh \(\chi_{8400}(691, \cdot)\) n/a 15360 16
8400.2.li \(\chi_{8400}(109, \cdot)\) n/a 15360 16
8400.2.lk \(\chi_{8400}(19, \cdot)\) n/a 15360 16
8400.2.ln \(\chi_{8400}(541, \cdot)\) n/a 15360 16
8400.2.lo \(\chi_{8400}(179, \cdot)\) n/a 30592 16
8400.2.lr \(\chi_{8400}(341, \cdot)\) n/a 30592 16
8400.2.lt \(\chi_{8400}(163, \cdot)\) n/a 15360 16
8400.2.lu \(\chi_{8400}(397, \cdot)\) n/a 15360 16
8400.2.lw \(\chi_{8400}(653, \cdot)\) n/a 30592 16
8400.2.lz \(\chi_{8400}(227, \cdot)\) n/a 30592 16
8400.2.ma \(\chi_{8400}(247, \cdot)\) None 0 16
8400.2.mb \(\chi_{8400}(47, \cdot)\) n/a 7680 16
8400.2.mg \(\chi_{8400}(577, \cdot)\) n/a 3840 16
8400.2.mh \(\chi_{8400}(137, \cdot)\) None 0 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4200))\)\(^{\oplus 2}\)