# Properties

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

## 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 the 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

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