Properties

Label 9600.2
Level 9600
Weight 2
Dimension 953616
Nonzero newspaces 72
Sturm bound 9830400

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Defining parameters

Level: \( N \) = \( 9600 = 2^{7} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(9830400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9600))\).

Total New Old
Modular forms 2475520 957552 1517968
Cusp forms 2439681 953616 1486065
Eisenstein series 35839 3936 31903

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9600))\)

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
9600.2.a \(\chi_{9600}(1, \cdot)\) 9600.2.a.a 1 1
9600.2.a.b 1
9600.2.a.c 1
9600.2.a.d 1
9600.2.a.e 1
9600.2.a.f 1
9600.2.a.g 1
9600.2.a.h 1
9600.2.a.i 1
9600.2.a.j 1
9600.2.a.k 1
9600.2.a.l 1
9600.2.a.m 1
9600.2.a.n 1
9600.2.a.o 1
9600.2.a.p 1
9600.2.a.q 1
9600.2.a.r 1
9600.2.a.s 1
9600.2.a.t 1
9600.2.a.u 1
9600.2.a.v 1
9600.2.a.w 1
9600.2.a.x 1
9600.2.a.y 1
9600.2.a.z 1
9600.2.a.ba 1
9600.2.a.bb 1
9600.2.a.bc 1
9600.2.a.bd 1
9600.2.a.be 1
9600.2.a.bf 1
9600.2.a.bg 1
9600.2.a.bh 1
9600.2.a.bi 1
9600.2.a.bj 1
9600.2.a.bk 1
9600.2.a.bl 1
9600.2.a.bm 1
9600.2.a.bn 1
9600.2.a.bo 1
9600.2.a.bp 1
9600.2.a.bq 1
9600.2.a.br 1
9600.2.a.bs 1
9600.2.a.bt 1
9600.2.a.bu 1
9600.2.a.bv 1
9600.2.a.bw 1
9600.2.a.bx 1
9600.2.a.by 1
9600.2.a.bz 1
9600.2.a.ca 1
9600.2.a.cb 1
9600.2.a.cc 1
9600.2.a.cd 1
9600.2.a.ce 2
9600.2.a.cf 2
9600.2.a.cg 2
9600.2.a.ch 2
9600.2.a.ci 2
9600.2.a.cj 2
9600.2.a.ck 2
9600.2.a.cl 2
9600.2.a.cm 2
9600.2.a.cn 2
9600.2.a.co 2
9600.2.a.cp 2
9600.2.a.cq 2
9600.2.a.cr 2
9600.2.a.cs 2
9600.2.a.ct 2
9600.2.a.cu 2
9600.2.a.cv 2
9600.2.a.cw 2
9600.2.a.cx 2
9600.2.a.cy 2
9600.2.a.cz 2
9600.2.a.da 2
9600.2.a.db 2
9600.2.a.dc 2
9600.2.a.dd 2
9600.2.a.de 2
9600.2.a.df 2
9600.2.a.dg 2
9600.2.a.dh 2
9600.2.a.di 2
9600.2.a.dj 2
9600.2.a.dk 2
9600.2.a.dl 2
9600.2.a.dm 2
9600.2.a.dn 2
9600.2.a.do 3
9600.2.a.dp 3
9600.2.a.dq 3
9600.2.a.dr 3
9600.2.a.ds 3
9600.2.a.dt 3
9600.2.a.du 3
9600.2.a.dv 3
9600.2.b \(\chi_{9600}(5951, \cdot)\) n/a 304 1
9600.2.d \(\chi_{9600}(3649, \cdot)\) n/a 144 1
9600.2.f \(\chi_{9600}(8449, \cdot)\) n/a 144 1
9600.2.h \(\chi_{9600}(1151, \cdot)\) n/a 304 1
9600.2.k \(\chi_{9600}(4801, \cdot)\) n/a 152 1
9600.2.m \(\chi_{9600}(4799, \cdot)\) n/a 288 1
9600.2.o \(\chi_{9600}(9599, \cdot)\) n/a 288 1
9600.2.s \(\chi_{9600}(2401, \cdot)\) n/a 304 2
9600.2.t \(\chi_{9600}(2399, \cdot)\) n/a 560 2
9600.2.v \(\chi_{9600}(257, \cdot)\) n/a 576 2
9600.2.w \(\chi_{9600}(7807, \cdot)\) n/a 288 2
9600.2.y \(\chi_{9600}(2143, \cdot)\) n/a 288 2
9600.2.bb \(\chi_{9600}(2657, \cdot)\) n/a 560 2
9600.2.bc \(\chi_{9600}(607, \cdot)\) n/a 288 2
9600.2.bf \(\chi_{9600}(4193, \cdot)\) n/a 560 2
9600.2.bh \(\chi_{9600}(3007, \cdot)\) n/a 288 2
9600.2.bi \(\chi_{9600}(5057, \cdot)\) n/a 576 2
9600.2.bk \(\chi_{9600}(3551, \cdot)\) n/a 584 2
9600.2.bl \(\chi_{9600}(1249, \cdot)\) n/a 288 2
9600.2.bo \(\chi_{9600}(1921, \cdot)\) n/a 960 4
9600.2.bp \(\chi_{9600}(3343, \cdot)\) n/a 576 4
9600.2.bs \(\chi_{9600}(593, \cdot)\) n/a 1136 4
9600.2.bt \(\chi_{9600}(1199, \cdot)\) n/a 1136 4
9600.2.bw \(\chi_{9600}(1201, \cdot)\) n/a 608 4
9600.2.by \(\chi_{9600}(2351, \cdot)\) n/a 1192 4
9600.2.bz \(\chi_{9600}(49, \cdot)\) n/a 576 4
9600.2.cc \(\chi_{9600}(2993, \cdot)\) n/a 1136 4
9600.2.cd \(\chi_{9600}(943, \cdot)\) n/a 576 4
9600.2.cg \(\chi_{9600}(3071, \cdot)\) n/a 1920 4
9600.2.ci \(\chi_{9600}(769, \cdot)\) n/a 960 4
9600.2.ck \(\chi_{9600}(1729, \cdot)\) n/a 960 4
9600.2.cm \(\chi_{9600}(191, \cdot)\) n/a 1920 4
9600.2.co \(\chi_{9600}(1919, \cdot)\) n/a 1920 4
9600.2.cq \(\chi_{9600}(959, \cdot)\) n/a 1920 4
9600.2.cs \(\chi_{9600}(961, \cdot)\) n/a 960 4
9600.2.cv \(\chi_{9600}(857, \cdot)\) None 0 8
9600.2.cw \(\chi_{9600}(1207, \cdot)\) None 0 8
9600.2.cy \(\chi_{9600}(601, \cdot)\) None 0 8
9600.2.da \(\chi_{9600}(649, \cdot)\) None 0 8
9600.2.dd \(\chi_{9600}(551, \cdot)\) None 0 8
9600.2.df \(\chi_{9600}(599, \cdot)\) None 0 8
9600.2.dh \(\chi_{9600}(2057, \cdot)\) None 0 8
9600.2.di \(\chi_{9600}(7, \cdot)\) None 0 8
9600.2.dk \(\chi_{9600}(479, \cdot)\) n/a 3776 8
9600.2.dl \(\chi_{9600}(481, \cdot)\) n/a 1920 8
9600.2.dp \(\chi_{9600}(833, \cdot)\) n/a 3840 8
9600.2.dq \(\chi_{9600}(703, \cdot)\) n/a 1920 8
9600.2.ds \(\chi_{9600}(353, \cdot)\) n/a 3776 8
9600.2.dv \(\chi_{9600}(1183, \cdot)\) n/a 1920 8
9600.2.dw \(\chi_{9600}(737, \cdot)\) n/a 3776 8
9600.2.dz \(\chi_{9600}(223, \cdot)\) n/a 1920 8
9600.2.eb \(\chi_{9600}(127, \cdot)\) n/a 1920 8
9600.2.ec \(\chi_{9600}(2177, \cdot)\) n/a 3840 8
9600.2.eg \(\chi_{9600}(289, \cdot)\) n/a 1920 8
9600.2.eh \(\chi_{9600}(671, \cdot)\) n/a 3776 8
9600.2.ek \(\chi_{9600}(893, \cdot)\) n/a 18368 16
9600.2.el \(\chi_{9600}(643, \cdot)\) n/a 9216 16
9600.2.em \(\chi_{9600}(251, \cdot)\) n/a 19360 16
9600.2.en \(\chi_{9600}(349, \cdot)\) n/a 9216 16
9600.2.eq \(\chi_{9600}(301, \cdot)\) n/a 9728 16
9600.2.er \(\chi_{9600}(299, \cdot)\) n/a 18368 16
9600.2.ew \(\chi_{9600}(43, \cdot)\) n/a 9216 16
9600.2.ex \(\chi_{9600}(293, \cdot)\) n/a 18368 16
9600.2.ey \(\chi_{9600}(497, \cdot)\) n/a 7616 16
9600.2.fb \(\chi_{9600}(367, \cdot)\) n/a 3840 16
9600.2.fd \(\chi_{9600}(529, \cdot)\) n/a 3840 16
9600.2.fe \(\chi_{9600}(431, \cdot)\) n/a 7616 16
9600.2.fg \(\chi_{9600}(241, \cdot)\) n/a 3840 16
9600.2.fj \(\chi_{9600}(239, \cdot)\) n/a 7616 16
9600.2.fl \(\chi_{9600}(847, \cdot)\) n/a 3840 16
9600.2.fm \(\chi_{9600}(17, \cdot)\) n/a 7616 16
9600.2.fp \(\chi_{9600}(487, \cdot)\) None 0 32
9600.2.fq \(\chi_{9600}(137, \cdot)\) None 0 32
9600.2.fs \(\chi_{9600}(119, \cdot)\) None 0 32
9600.2.fu \(\chi_{9600}(71, \cdot)\) None 0 32
9600.2.fx \(\chi_{9600}(169, \cdot)\) None 0 32
9600.2.fz \(\chi_{9600}(121, \cdot)\) None 0 32
9600.2.gb \(\chi_{9600}(103, \cdot)\) None 0 32
9600.2.gc \(\chi_{9600}(233, \cdot)\) None 0 32
9600.2.ge \(\chi_{9600}(53, \cdot)\) n/a 122624 64
9600.2.gf \(\chi_{9600}(67, \cdot)\) n/a 61440 64
9600.2.gk \(\chi_{9600}(61, \cdot)\) n/a 61440 64
9600.2.gl \(\chi_{9600}(59, \cdot)\) n/a 122624 64
9600.2.go \(\chi_{9600}(11, \cdot)\) n/a 122624 64
9600.2.gp \(\chi_{9600}(109, \cdot)\) n/a 61440 64
9600.2.gq \(\chi_{9600}(163, \cdot)\) n/a 61440 64
9600.2.gr \(\chi_{9600}(173, \cdot)\) n/a 122624 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(640))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4800))\)\(^{\oplus 2}\)