↑

Properties

Label 9075.2
Level 9075
Weight 2
Dimension 1968589
Nonzero newspaces 84
Sturm bound 11616000

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(11616000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9075))\).

Total New Old
Modular forms 2921920 1980109 941811
Cusp forms 2886081 1968589 917492
Eisenstein series 35839 11520 24319

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9075))\)

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
9075.2.a \(\chi_{9075}(1, \cdot)\) 9075.2.a.a 1 1
9075.2.a.b 1
9075.2.a.c 1
9075.2.a.d 1
9075.2.a.e 1
9075.2.a.f 1
9075.2.a.g 1
9075.2.a.h 1
9075.2.a.i 1
9075.2.a.j 1
9075.2.a.k 1
9075.2.a.l 1
9075.2.a.m 1
9075.2.a.n 1
9075.2.a.o 1
9075.2.a.p 1
9075.2.a.q 1
9075.2.a.r 1
9075.2.a.s 1
9075.2.a.t 1
9075.2.a.u 2
9075.2.a.v 2
9075.2.a.w 2
9075.2.a.x 2
9075.2.a.y 2
9075.2.a.z 2
9075.2.a.ba 2
9075.2.a.bb 2
9075.2.a.bc 2
9075.2.a.bd 2
9075.2.a.be 2
9075.2.a.bf 2
9075.2.a.bg 2
9075.2.a.bh 2
9075.2.a.bi 2
9075.2.a.bj 2
9075.2.a.bk 2
9075.2.a.bl 2
9075.2.a.bm 2
9075.2.a.bn 2
9075.2.a.bo 2
9075.2.a.bp 2
9075.2.a.bq 2
9075.2.a.br 2
9075.2.a.bs 2
9075.2.a.bt 2
9075.2.a.bu 2
9075.2.a.bv 2
9075.2.a.bw 2
9075.2.a.bx 2
9075.2.a.by 2
9075.2.a.bz 2
9075.2.a.ca 2
9075.2.a.cb 2
9075.2.a.cc 3
9075.2.a.cd 3
9075.2.a.ce 3
9075.2.a.cf 3
9075.2.a.cg 3
9075.2.a.ch 3
9075.2.a.ci 3
9075.2.a.cj 3
9075.2.a.ck 3
9075.2.a.cl 4
9075.2.a.cm 4
9075.2.a.cn 4
9075.2.a.co 4
9075.2.a.cp 4
9075.2.a.cq 4
9075.2.a.cr 4
9075.2.a.cs 4
9075.2.a.ct 4
9075.2.a.cu 4
9075.2.a.cv 4
9075.2.a.cw 4
9075.2.a.cx 4
9075.2.a.cy 4
9075.2.a.cz 4
9075.2.a.da 4
9075.2.a.db 4
9075.2.a.dc 4
9075.2.a.dd 4
9075.2.a.de 4
9075.2.a.df 4
9075.2.a.dg 4
9075.2.a.dh 4
9075.2.a.di 4
9075.2.a.dj 4
9075.2.a.dk 5
9075.2.a.dl 5
9075.2.a.dm 5
9075.2.a.dn 5
9075.2.a.do 6
9075.2.a.dp 6
9075.2.a.dq 6
9075.2.a.dr 6
9075.2.a.ds 6
9075.2.a.dt 8
9075.2.a.du 8
9075.2.a.dv 8
9075.2.a.dw 8
9075.2.a.dx 12
9075.2.a.dy 12
9075.2.a.dz 12
9075.2.a.ea 12
9075.2.c \(\chi_{9075}(7624, \cdot)\) n/a 328 1
9075.2.d \(\chi_{9075}(9074, \cdot)\) n/a 632 1
9075.2.f \(\chi_{9075}(1451, \cdot)\) n/a 660 1
9075.2.j \(\chi_{9075}(1693, \cdot)\) n/a 648 2
9075.2.k \(\chi_{9075}(6293, \cdot)\) n/a 1272 2
9075.2.m \(\chi_{9075}(4141, \cdot)\) n/a 2160 4
9075.2.n \(\chi_{9075}(1576, \cdot)\) n/a 1368 4
9075.2.o \(\chi_{9075}(511, \cdot)\) n/a 2160 4
9075.2.p \(\chi_{9075}(1291, \cdot)\) n/a 2160 4
9075.2.q \(\chi_{9075}(1816, \cdot)\) n/a 2184 4
9075.2.r \(\chi_{9075}(856, \cdot)\) n/a 2160 4
9075.2.s \(\chi_{9075}(1304, \cdot)\) n/a 4256 4
9075.2.v \(\chi_{9075}(1219, \cdot)\) n/a 2160 4
9075.2.x \(\chi_{9075}(3266, \cdot)\) n/a 4256 4
9075.2.bd \(\chi_{9075}(596, \cdot)\) n/a 4256 4
9075.2.bf \(\chi_{9075}(5321, \cdot)\) n/a 4256 4
9075.2.bi \(\chi_{9075}(1976, \cdot)\) n/a 2640 4
9075.2.bj \(\chi_{9075}(941, \cdot)\) n/a 4256 4
9075.2.bl \(\chi_{9075}(364, \cdot)\) n/a 2176 4
9075.2.bo \(\chi_{9075}(959, \cdot)\) n/a 4256 4
9075.2.br \(\chi_{9075}(3869, \cdot)\) n/a 4256 4
9075.2.bs \(\chi_{9075}(524, \cdot)\) n/a 2528 4
9075.2.bu \(\chi_{9075}(239, \cdot)\) n/a 4256 4
9075.2.bv \(\chi_{9075}(1939, \cdot)\) n/a 2160 4
9075.2.bx \(\chi_{9075}(124, \cdot)\) n/a 1296 4
9075.2.by \(\chi_{9075}(1654, \cdot)\) n/a 2160 4
9075.2.cb \(\chi_{9075}(2689, \cdot)\) n/a 2160 4
9075.2.ce \(\chi_{9075}(1814, \cdot)\) n/a 4256 4
9075.2.cg \(\chi_{9075}(161, \cdot)\) n/a 4256 4
9075.2.ci \(\chi_{9075}(826, \cdot)\) n/a 4180 10
9075.2.cj \(\chi_{9075}(323, \cdot)\) n/a 8512 8
9075.2.cm \(\chi_{9075}(2272, \cdot)\) n/a 4320 8
9075.2.cn \(\chi_{9075}(112, \cdot)\) n/a 4320 8
9075.2.ct \(\chi_{9075}(122, \cdot)\) n/a 8576 8
9075.2.cu \(\chi_{9075}(632, \cdot)\) n/a 5056 8
9075.2.cv \(\chi_{9075}(1358, \cdot)\) n/a 8512 8
9075.2.cw \(\chi_{9075}(608, \cdot)\) n/a 8512 8
9075.2.cx \(\chi_{9075}(118, \cdot)\) n/a 2592 8
9075.2.cy \(\chi_{9075}(1183, \cdot)\) n/a 4320 8
9075.2.cz \(\chi_{9075}(403, \cdot)\) n/a 4320 8
9075.2.da \(\chi_{9075}(967, \cdot)\) n/a 4320 8
9075.2.dg \(\chi_{9075}(1697, \cdot)\) n/a 8512 8
9075.2.dj \(\chi_{9075}(626, \cdot)\) n/a 8300 10
9075.2.dl \(\chi_{9075}(824, \cdot)\) n/a 7880 10
9075.2.dm \(\chi_{9075}(199, \cdot)\) n/a 3960 10
9075.2.dp \(\chi_{9075}(518, \cdot)\) n/a 15760 20
9075.2.dq \(\chi_{9075}(43, \cdot)\) n/a 7920 20
9075.2.ds \(\chi_{9075}(31, \cdot)\) n/a 26400 40
9075.2.dt \(\chi_{9075}(166, \cdot)\) n/a 26400 40
9075.2.du \(\chi_{9075}(181, \cdot)\) n/a 26400 40
9075.2.dv \(\chi_{9075}(421, \cdot)\) n/a 26400 40
9075.2.dw \(\chi_{9075}(301, \cdot)\) n/a 16720 40
9075.2.dx \(\chi_{9075}(16, \cdot)\) n/a 26400 40
9075.2.dz \(\chi_{9075}(41, \cdot)\) n/a 52640 40
9075.2.eb \(\chi_{9075}(164, \cdot)\) n/a 52640 40
9075.2.ee \(\chi_{9075}(169, \cdot)\) n/a 26400 40
9075.2.eh \(\chi_{9075}(4, \cdot)\) n/a 26400 40
9075.2.ei \(\chi_{9075}(49, \cdot)\) n/a 15840 40
9075.2.ek \(\chi_{9075}(229, \cdot)\) n/a 26400 40
9075.2.el \(\chi_{9075}(359, \cdot)\) n/a 52640 40
9075.2.en \(\chi_{9075}(74, \cdot)\) n/a 31520 40
9075.2.eo \(\chi_{9075}(29, \cdot)\) n/a 52640 40
9075.2.er \(\chi_{9075}(134, \cdot)\) n/a 52640 40
9075.2.eu \(\chi_{9075}(34, \cdot)\) n/a 26400 40
9075.2.ew \(\chi_{9075}(116, \cdot)\) n/a 52640 40
9075.2.ex \(\chi_{9075}(101, \cdot)\) n/a 33200 40
9075.2.fa \(\chi_{9075}(266, \cdot)\) n/a 52640 40
9075.2.fc \(\chi_{9075}(281, \cdot)\) n/a 52640 40
9075.2.fi \(\chi_{9075}(131, \cdot)\) n/a 52640 40
9075.2.fk \(\chi_{9075}(379, \cdot)\) n/a 26400 40
9075.2.fn \(\chi_{9075}(479, \cdot)\) n/a 52640 40
9075.2.fo \(\chi_{9075}(47, \cdot)\) n/a 105280 80
9075.2.fu \(\chi_{9075}(142, \cdot)\) n/a 52800 80
9075.2.fv \(\chi_{9075}(172, \cdot)\) n/a 52800 80
9075.2.fw \(\chi_{9075}(52, \cdot)\) n/a 52800 80
9075.2.fx \(\chi_{9075}(7, \cdot)\) n/a 31680 80
9075.2.fy \(\chi_{9075}(38, \cdot)\) n/a 105280 80
9075.2.fz \(\chi_{9075}(53, \cdot)\) n/a 105280 80
9075.2.ga \(\chi_{9075}(218, \cdot)\) n/a 63040 80
9075.2.gb \(\chi_{9075}(23, \cdot)\) n/a 105280 80
9075.2.gh \(\chi_{9075}(13, \cdot)\) n/a 52800 80
9075.2.gi \(\chi_{9075}(28, \cdot)\) n/a 52800 80
9075.2.gl \(\chi_{9075}(113, \cdot)\) n/a 105280 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9075))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(825))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1815))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3025))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9075))\)\(^{\oplus 1}\)