Properties

Label 14400.2
Level 14400
Weight 2
Dimension 2265453
Nonzero newspaces 112
Sturm bound 22118400

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Defining parameters

Level: \( N \) = \( 14400 = 2^{6} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 112 \)
Sturm bound: \(22118400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(14400))\).

Total New Old
Modular forms 5561856 2273571 3288285
Cusp forms 5497345 2265453 3231892
Eisenstein series 64511 8118 56393

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(14400))\)

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
14400.2.a \(\chi_{14400}(1, \cdot)\) 14400.2.a.a 1 1
14400.2.a.b 1
14400.2.a.c 1
14400.2.a.d 1
14400.2.a.e 1
14400.2.a.f 1
14400.2.a.g 1
14400.2.a.h 1
14400.2.a.i 1
14400.2.a.j 1
14400.2.a.k 1
14400.2.a.l 1
14400.2.a.m 1
14400.2.a.n 1
14400.2.a.o 1
14400.2.a.p 1
14400.2.a.q 1
14400.2.a.r 1
14400.2.a.s 1
14400.2.a.t 1
14400.2.a.u 1
14400.2.a.v 1
14400.2.a.w 1
14400.2.a.x 1
14400.2.a.y 1
14400.2.a.z 1
14400.2.a.ba 1
14400.2.a.bb 1
14400.2.a.bc 1
14400.2.a.bd 1
14400.2.a.be 1
14400.2.a.bf 1
14400.2.a.bg 1
14400.2.a.bh 1
14400.2.a.bi 1
14400.2.a.bj 1
14400.2.a.bk 1
14400.2.a.bl 1
14400.2.a.bm 1
14400.2.a.bn 1
14400.2.a.bo 1
14400.2.a.bp 1
14400.2.a.bq 1
14400.2.a.br 1
14400.2.a.bs 1
14400.2.a.bt 1
14400.2.a.bu 1
14400.2.a.bv 1
14400.2.a.bw 1
14400.2.a.bx 1
14400.2.a.by 1
14400.2.a.bz 1
14400.2.a.ca 1
14400.2.a.cb 1
14400.2.a.cc 1
14400.2.a.cd 1
14400.2.a.ce 1
14400.2.a.cf 1
14400.2.a.cg 1
14400.2.a.ch 1
14400.2.a.ci 1
14400.2.a.cj 1
14400.2.a.ck 1
14400.2.a.cl 1
14400.2.a.cm 1
14400.2.a.cn 1
14400.2.a.co 1
14400.2.a.cp 1
14400.2.a.cq 1
14400.2.a.cr 1
14400.2.a.cs 1
14400.2.a.ct 1
14400.2.a.cu 1
14400.2.a.cv 1
14400.2.a.cw 1
14400.2.a.cx 1
14400.2.a.cy 1
14400.2.a.cz 1
14400.2.a.da 1
14400.2.a.db 1
14400.2.a.dc 1
14400.2.a.dd 1
14400.2.a.de 1
14400.2.a.df 1
14400.2.a.dg 1
14400.2.a.dh 1
14400.2.a.di 1
14400.2.a.dj 1
14400.2.a.dk 1
14400.2.a.dl 1
14400.2.a.dm 1
14400.2.a.dn 1
14400.2.a.do 1
14400.2.a.dp 1
14400.2.a.dq 1
14400.2.a.dr 1
14400.2.a.ds 1
14400.2.a.dt 1
14400.2.a.du 1
14400.2.a.dv 1
14400.2.a.dw 1
14400.2.a.dx 1
14400.2.a.dy 1
14400.2.a.dz 1
14400.2.a.ea 1
14400.2.a.eb 1
14400.2.a.ec 1
14400.2.a.ed 1
14400.2.a.ee 1
14400.2.a.ef 1
14400.2.a.eg 1
14400.2.a.eh 1
14400.2.a.ei 1
14400.2.a.ej 1
14400.2.a.ek 1
14400.2.a.el 1
14400.2.a.em 1
14400.2.a.en 1
14400.2.a.eo 1
14400.2.a.ep 1
14400.2.a.eq 1
14400.2.a.er 1
14400.2.a.es 1
14400.2.a.et 1
14400.2.a.eu 1
14400.2.a.ev 1
14400.2.a.ew 1
14400.2.a.ex 1
14400.2.a.ey 1
14400.2.a.ez 1
14400.2.a.fa 1
14400.2.a.fb 1
14400.2.a.fc 1
14400.2.a.fd 1
14400.2.a.fe 1
14400.2.a.ff 1
14400.2.a.fg 1
14400.2.a.fh 1
14400.2.a.fi 1
14400.2.a.fj 1
14400.2.a.fk 1
14400.2.a.fl 2
14400.2.a.fm 2
14400.2.a.fn 2
14400.2.a.fo 2
14400.2.a.fp 2
14400.2.a.fq 2
14400.2.a.fr 2
14400.2.a.fs 2
14400.2.a.ft 2
14400.2.a.fu 2
14400.2.a.fv 2
14400.2.a.fw 2
14400.2.a.fx 2
14400.2.a.fy 2
14400.2.a.fz 2
14400.2.a.ga 2
14400.2.a.gb 2
14400.2.a.gc 2
14400.2.a.gd 2
14400.2.a.ge 4
14400.2.a.gf 4
14400.2.b \(\chi_{14400}(8351, \cdot)\) n/a 152 1
14400.2.d \(\chi_{14400}(6049, \cdot)\) n/a 180 1
14400.2.f \(\chi_{14400}(13249, \cdot)\) n/a 178 1
14400.2.h \(\chi_{14400}(1151, \cdot)\) n/a 152 1
14400.2.k \(\chi_{14400}(7201, \cdot)\) n/a 190 1
14400.2.m \(\chi_{14400}(7199, \cdot)\) n/a 144 1
14400.2.o \(\chi_{14400}(14399, \cdot)\) n/a 144 1
14400.2.q \(\chi_{14400}(4801, \cdot)\) n/a 900 2
14400.2.t \(\chi_{14400}(3601, \cdot)\) n/a 374 2
14400.2.u \(\chi_{14400}(3599, \cdot)\) n/a 288 2
14400.2.w \(\chi_{14400}(5057, \cdot)\) n/a 288 2
14400.2.x \(\chi_{14400}(3007, \cdot)\) n/a 356 2
14400.2.z \(\chi_{14400}(5743, \cdot)\) n/a 356 2
14400.2.bc \(\chi_{14400}(593, \cdot)\) n/a 288 2
14400.2.bd \(\chi_{14400}(12943, \cdot)\) n/a 356 2
14400.2.bg \(\chi_{14400}(7793, \cdot)\) n/a 288 2
14400.2.bi \(\chi_{14400}(2143, \cdot)\) n/a 360 2
14400.2.bj \(\chi_{14400}(4193, \cdot)\) n/a 288 2
14400.2.bl \(\chi_{14400}(4751, \cdot)\) n/a 304 2
14400.2.bm \(\chi_{14400}(2449, \cdot)\) n/a 356 2
14400.2.bp \(\chi_{14400}(2881, \cdot)\) n/a 1192 4
14400.2.bs \(\chi_{14400}(4799, \cdot)\) n/a 856 2
14400.2.bu \(\chi_{14400}(2399, \cdot)\) n/a 864 2
14400.2.bw \(\chi_{14400}(2401, \cdot)\) n/a 912 2
14400.2.bx \(\chi_{14400}(5951, \cdot)\) n/a 900 2
14400.2.bz \(\chi_{14400}(3649, \cdot)\) n/a 856 2
14400.2.cb \(\chi_{14400}(1249, \cdot)\) n/a 864 2
14400.2.cd \(\chi_{14400}(3551, \cdot)\) n/a 912 2
14400.2.cw \(\chi_{14400}(4031, \cdot)\) n/a 960 4
14400.2.cy \(\chi_{14400}(1729, \cdot)\) n/a 1192 4
14400.2.da \(\chi_{14400}(289, \cdot)\) n/a 1200 4
14400.2.dc \(\chi_{14400}(2591, \cdot)\) n/a 960 4
14400.2.de \(\chi_{14400}(2879, \cdot)\) n/a 960 4
14400.2.dg \(\chi_{14400}(1439, \cdot)\) n/a 960 4
14400.2.di \(\chi_{14400}(1441, \cdot)\) n/a 1200 4
14400.2.dk \(\chi_{14400}(49, \cdot)\) n/a 1712 4
14400.2.dl \(\chi_{14400}(2351, \cdot)\) n/a 1800 4
14400.2.do \(\chi_{14400}(607, \cdot)\) n/a 1728 4
14400.2.dr \(\chi_{14400}(2657, \cdot)\) n/a 1728 4
14400.2.ds \(\chi_{14400}(2993, \cdot)\) n/a 1712 4
14400.2.dv \(\chi_{14400}(3343, \cdot)\) n/a 1712 4
14400.2.dw \(\chi_{14400}(5393, \cdot)\) n/a 1712 4
14400.2.dz \(\chi_{14400}(943, \cdot)\) n/a 1712 4
14400.2.ea \(\chi_{14400}(257, \cdot)\) n/a 1712 4
14400.2.ed \(\chi_{14400}(4543, \cdot)\) n/a 1712 4
14400.2.eg \(\chi_{14400}(1199, \cdot)\) n/a 1712 4
14400.2.eh \(\chi_{14400}(1201, \cdot)\) n/a 1800 4
14400.2.ei \(\chi_{14400}(961, \cdot)\) n/a 5728 8
14400.2.ek \(\chi_{14400}(2357, \cdot)\) n/a 4608 8
14400.2.el \(\chi_{14400}(307, \cdot)\) n/a 5744 8
14400.2.en \(\chi_{14400}(901, \cdot)\) n/a 6056 8
14400.2.ep \(\chi_{14400}(1549, \cdot)\) n/a 5744 8
14400.2.es \(\chi_{14400}(251, \cdot)\) n/a 4864 8
14400.2.eu \(\chi_{14400}(899, \cdot)\) n/a 4608 8
14400.2.ew \(\chi_{14400}(557, \cdot)\) n/a 4608 8
14400.2.ex \(\chi_{14400}(2107, \cdot)\) n/a 5744 8
14400.2.ez \(\chi_{14400}(719, \cdot)\) n/a 1920 8
14400.2.fa \(\chi_{14400}(721, \cdot)\) n/a 2384 8
14400.2.fe \(\chi_{14400}(737, \cdot)\) n/a 1920 8
14400.2.ff \(\chi_{14400}(1567, \cdot)\) n/a 2400 8
14400.2.fh \(\chi_{14400}(17, \cdot)\) n/a 1920 8
14400.2.fk \(\chi_{14400}(1423, \cdot)\) n/a 2384 8
14400.2.fl \(\chi_{14400}(3473, \cdot)\) n/a 1920 8
14400.2.fo \(\chi_{14400}(847, \cdot)\) n/a 2384 8
14400.2.fq \(\chi_{14400}(127, \cdot)\) n/a 2384 8
14400.2.fr \(\chi_{14400}(2177, \cdot)\) n/a 1920 8
14400.2.fv \(\chi_{14400}(1009, \cdot)\) n/a 2384 8
14400.2.fw \(\chi_{14400}(431, \cdot)\) n/a 1920 8
14400.2.gn \(\chi_{14400}(481, \cdot)\) n/a 5760 8
14400.2.gp \(\chi_{14400}(479, \cdot)\) n/a 5760 8
14400.2.gr \(\chi_{14400}(959, \cdot)\) n/a 5728 8
14400.2.gv \(\chi_{14400}(671, \cdot)\) n/a 5760 8
14400.2.gx \(\chi_{14400}(2209, \cdot)\) n/a 5760 8
14400.2.gz \(\chi_{14400}(769, \cdot)\) n/a 5728 8
14400.2.hb \(\chi_{14400}(191, \cdot)\) n/a 5728 8
14400.2.hs \(\chi_{14400}(43, \cdot)\) n/a 27584 16
14400.2.hv \(\chi_{14400}(893, \cdot)\) n/a 27584 16
14400.2.hx \(\chi_{14400}(299, \cdot)\) n/a 27584 16
14400.2.hz \(\chi_{14400}(851, \cdot)\) n/a 29088 16
14400.2.ia \(\chi_{14400}(349, \cdot)\) n/a 27584 16
14400.2.ic \(\chi_{14400}(301, \cdot)\) n/a 29088 16
14400.2.ie \(\chi_{14400}(643, \cdot)\) n/a 27584 16
14400.2.ih \(\chi_{14400}(293, \cdot)\) n/a 27584 16
14400.2.ik \(\chi_{14400}(911, \cdot)\) n/a 11456 16
14400.2.il \(\chi_{14400}(529, \cdot)\) n/a 11456 16
14400.2.im \(\chi_{14400}(1087, \cdot)\) n/a 11456 16
14400.2.ip \(\chi_{14400}(833, \cdot)\) n/a 11456 16
14400.2.iq \(\chi_{14400}(1903, \cdot)\) n/a 11456 16
14400.2.it \(\chi_{14400}(497, \cdot)\) n/a 11456 16
14400.2.iu \(\chi_{14400}(367, \cdot)\) n/a 11456 16
14400.2.ix \(\chi_{14400}(113, \cdot)\) n/a 11456 16
14400.2.iy \(\chi_{14400}(353, \cdot)\) n/a 11520 16
14400.2.jb \(\chi_{14400}(223, \cdot)\) n/a 11520 16
14400.2.jc \(\chi_{14400}(241, \cdot)\) n/a 11456 16
14400.2.jd \(\chi_{14400}(239, \cdot)\) n/a 11456 16
14400.2.jh \(\chi_{14400}(163, \cdot)\) n/a 38336 32
14400.2.ji \(\chi_{14400}(53, \cdot)\) n/a 30720 32
14400.2.jk \(\chi_{14400}(179, \cdot)\) n/a 30720 32
14400.2.jm \(\chi_{14400}(611, \cdot)\) n/a 30720 32
14400.2.jp \(\chi_{14400}(109, \cdot)\) n/a 38336 32
14400.2.jr \(\chi_{14400}(181, \cdot)\) n/a 38336 32
14400.2.jt \(\chi_{14400}(523, \cdot)\) n/a 38336 32
14400.2.ju \(\chi_{14400}(197, \cdot)\) n/a 30720 32
14400.2.km \(\chi_{14400}(77, \cdot)\) n/a 184064 64
14400.2.kp \(\chi_{14400}(187, \cdot)\) n/a 184064 64
14400.2.kr \(\chi_{14400}(61, \cdot)\) n/a 184064 64
14400.2.kt \(\chi_{14400}(229, \cdot)\) n/a 184064 64
14400.2.ku \(\chi_{14400}(11, \cdot)\) n/a 184064 64
14400.2.kw \(\chi_{14400}(59, \cdot)\) n/a 184064 64
14400.2.ky \(\chi_{14400}(173, \cdot)\) n/a 184064 64
14400.2.lb \(\chi_{14400}(67, \cdot)\) n/a 184064 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(14400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(14400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 63}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 54}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 42}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 45}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 42}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(720))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1800))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7200))\)\(^{\oplus 2}\)