# Properties

 Label 8550.2 Level 8550 Weight 2 Dimension 470189 Nonzero newspaces 96 Sturm bound 7776000

## Defining parameters

 Level: $$N$$ = $$8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$7776000$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8550))$$.

Total New Old
Modular forms 1960128 470189 1489939
Cusp forms 1927873 470189 1457684
Eisenstein series 32255 0 32255

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8550))$$

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
8550.2.a $$\chi_{8550}(1, \cdot)$$ 8550.2.a.a 1 1
8550.2.a.b 1
8550.2.a.c 1
8550.2.a.d 1
8550.2.a.e 1
8550.2.a.f 1
8550.2.a.g 1
8550.2.a.h 1
8550.2.a.i 1
8550.2.a.j 1
8550.2.a.k 1
8550.2.a.l 1
8550.2.a.m 1
8550.2.a.n 1
8550.2.a.o 1
8550.2.a.p 1
8550.2.a.q 1
8550.2.a.r 1
8550.2.a.s 1
8550.2.a.t 1
8550.2.a.u 1
8550.2.a.v 1
8550.2.a.w 1
8550.2.a.x 1
8550.2.a.y 1
8550.2.a.z 1
8550.2.a.ba 1
8550.2.a.bb 1
8550.2.a.bc 1
8550.2.a.bd 1
8550.2.a.be 1
8550.2.a.bf 1
8550.2.a.bg 1
8550.2.a.bh 1
8550.2.a.bi 1
8550.2.a.bj 1
8550.2.a.bk 1
8550.2.a.bl 1
8550.2.a.bm 1
8550.2.a.bn 2
8550.2.a.bo 2
8550.2.a.bp 2
8550.2.a.bq 2
8550.2.a.br 2
8550.2.a.bs 2
8550.2.a.bt 2
8550.2.a.bu 2
8550.2.a.bv 2
8550.2.a.bw 2
8550.2.a.bx 2
8550.2.a.by 2
8550.2.a.bz 2
8550.2.a.ca 2
8550.2.a.cb 2
8550.2.a.cc 3
8550.2.a.cd 3
8550.2.a.ce 3
8550.2.a.cf 3
8550.2.a.cg 3
8550.2.a.ch 3
8550.2.a.ci 3
8550.2.a.cj 3
8550.2.a.ck 3
8550.2.a.cl 3
8550.2.a.cm 3
8550.2.a.cn 3
8550.2.a.co 3
8550.2.a.cp 3
8550.2.a.cq 3
8550.2.a.cr 3
8550.2.a.cs 3
8550.2.a.ct 3
8550.2.a.cu 4
8550.2.a.cv 4
8550.2.a.cw 6
8550.2.a.cx 6
8550.2.c $$\chi_{8550}(8549, \cdot)$$ n/a 120 1
8550.2.d $$\chi_{8550}(6499, \cdot)$$ n/a 134 1
8550.2.f $$\chi_{8550}(2051, \cdot)$$ n/a 124 1
8550.2.i $$\chi_{8550}(5251, \cdot)$$ n/a 760 2
8550.2.j $$\chi_{8550}(2851, \cdot)$$ n/a 684 2
8550.2.k $$\chi_{8550}(2101, \cdot)$$ n/a 760 2
8550.2.l $$\chi_{8550}(4951, \cdot)$$ n/a 314 2
8550.2.n $$\chi_{8550}(2357, \cdot)$$ n/a 216 2
8550.2.p $$\chi_{8550}(3457, \cdot)$$ n/a 300 2
8550.2.q $$\chi_{8550}(1711, \cdot)$$ n/a 896 4
8550.2.r $$\chi_{8550}(449, \cdot)$$ n/a 240 2
8550.2.u $$\chi_{8550}(2899, \cdot)$$ n/a 300 2
8550.2.y $$\chi_{8550}(8201, \cdot)$$ n/a 760 2
8550.2.bb $$\chi_{8550}(4901, \cdot)$$ n/a 760 2
8550.2.bc $$\chi_{8550}(2801, \cdot)$$ n/a 760 2
8550.2.be $$\chi_{8550}(49, \cdot)$$ n/a 720 2
8550.2.bh $$\chi_{8550}(799, \cdot)$$ n/a 648 2
8550.2.bi $$\chi_{8550}(3199, \cdot)$$ n/a 720 2
8550.2.bl $$\chi_{8550}(749, \cdot)$$ n/a 720 2
8550.2.bm $$\chi_{8550}(2849, \cdot)$$ n/a 720 2
8550.2.bp $$\chi_{8550}(6149, \cdot)$$ n/a 720 2
8550.2.br $$\chi_{8550}(2501, \cdot)$$ n/a 248 2
8550.2.bt $$\chi_{8550}(2251, \cdot)$$ n/a 954 6
8550.2.bu $$\chi_{8550}(301, \cdot)$$ n/a 2280 6
8550.2.bv $$\chi_{8550}(1201, \cdot)$$ n/a 2280 6
8550.2.bx $$\chi_{8550}(1369, \cdot)$$ n/a 904 4
8550.2.by $$\chi_{8550}(1709, \cdot)$$ n/a 800 4
8550.2.cc $$\chi_{8550}(341, \cdot)$$ n/a 800 4
8550.2.cd $$\chi_{8550}(1493, \cdot)$$ n/a 480 4
8550.2.cg $$\chi_{8550}(493, \cdot)$$ n/a 1440 4
8550.2.ch $$\chi_{8550}(943, \cdot)$$ n/a 1440 4
8550.2.ck $$\chi_{8550}(1057, \cdot)$$ n/a 1440 4
8550.2.cm $$\chi_{8550}(2243, \cdot)$$ n/a 1296 4
8550.2.cn $$\chi_{8550}(1607, \cdot)$$ n/a 1440 4
8550.2.cq $$\chi_{8550}(4457, \cdot)$$ n/a 1440 4
8550.2.cr $$\chi_{8550}(1243, \cdot)$$ n/a 600 4
8550.2.ct $$\chi_{8550}(391, \cdot)$$ n/a 4800 8
8550.2.cu $$\chi_{8550}(571, \cdot)$$ n/a 4320 8
8550.2.cv $$\chi_{8550}(121, \cdot)$$ n/a 4800 8
8550.2.cw $$\chi_{8550}(1261, \cdot)$$ n/a 2000 8
8550.2.cx $$\chi_{8550}(1849, \cdot)$$ n/a 2160 6
8550.2.da $$\chi_{8550}(299, \cdot)$$ n/a 2160 6
8550.2.db $$\chi_{8550}(401, \cdot)$$ n/a 2280 6
8550.2.df $$\chi_{8550}(3851, \cdot)$$ n/a 768 6
8550.2.dh $$\chi_{8550}(1649, \cdot)$$ n/a 2160 6
8550.2.dj $$\chi_{8550}(199, \cdot)$$ n/a 900 6
8550.2.dm $$\chi_{8550}(1799, \cdot)$$ n/a 720 6
8550.2.do $$\chi_{8550}(499, \cdot)$$ n/a 2160 6
8550.2.dr $$\chi_{8550}(851, \cdot)$$ n/a 2280 6
8550.2.ds $$\chi_{8550}(37, \cdot)$$ n/a 2000 8
8550.2.du $$\chi_{8550}(647, \cdot)$$ n/a 1440 8
8550.2.dw $$\chi_{8550}(919, \cdot)$$ n/a 2000 8
8550.2.dz $$\chi_{8550}(179, \cdot)$$ n/a 1600 8
8550.2.eb $$\chi_{8550}(221, \cdot)$$ n/a 4800 8
8550.2.ec $$\chi_{8550}(911, \cdot)$$ n/a 4800 8
8550.2.ef $$\chi_{8550}(1361, \cdot)$$ n/a 4800 8
8550.2.ej $$\chi_{8550}(1019, \cdot)$$ n/a 4800 8
8550.2.em $$\chi_{8550}(569, \cdot)$$ n/a 4800 8
8550.2.en $$\chi_{8550}(1589, \cdot)$$ n/a 4800 8
8550.2.eq $$\chi_{8550}(619, \cdot)$$ n/a 4800 8
8550.2.er $$\chi_{8550}(229, \cdot)$$ n/a 4320 8
8550.2.eu $$\chi_{8550}(1759, \cdot)$$ n/a 4800 8
8550.2.ew $$\chi_{8550}(521, \cdot)$$ n/a 1600 8
8550.2.ez $$\chi_{8550}(443, \cdot)$$ n/a 4320 12
8550.2.fc $$\chi_{8550}(907, \cdot)$$ n/a 4320 12
8550.2.fd $$\chi_{8550}(307, \cdot)$$ n/a 1800 12
8550.2.fe $$\chi_{8550}(707, \cdot)$$ n/a 4320 12
8550.2.ff $$\chi_{8550}(557, \cdot)$$ n/a 1440 12
8550.2.fi $$\chi_{8550}(193, \cdot)$$ n/a 4320 12
8550.2.fk $$\chi_{8550}(61, \cdot)$$ n/a 14400 24
8550.2.fl $$\chi_{8550}(271, \cdot)$$ n/a 6000 24
8550.2.fm $$\chi_{8550}(481, \cdot)$$ n/a 14400 24
8550.2.fo $$\chi_{8550}(217, \cdot)$$ n/a 4000 16
8550.2.fp $$\chi_{8550}(353, \cdot)$$ n/a 9600 16
8550.2.fs $$\chi_{8550}(83, \cdot)$$ n/a 9600 16
8550.2.ft $$\chi_{8550}(77, \cdot)$$ n/a 8640 16
8550.2.fv $$\chi_{8550}(373, \cdot)$$ n/a 9600 16
8550.2.fy $$\chi_{8550}(103, \cdot)$$ n/a 9600 16
8550.2.fz $$\chi_{8550}(1177, \cdot)$$ n/a 9600 16
8550.2.gc $$\chi_{8550}(197, \cdot)$$ n/a 3200 16
8550.2.gd $$\chi_{8550}(509, \cdot)$$ n/a 14400 24
8550.2.gg $$\chi_{8550}(139, \cdot)$$ n/a 14400 24
8550.2.gi $$\chi_{8550}(71, \cdot)$$ n/a 4800 24
8550.2.gm $$\chi_{8550}(41, \cdot)$$ n/a 14400 24
8550.2.gn $$\chi_{8550}(709, \cdot)$$ n/a 14400 24
8550.2.gp $$\chi_{8550}(89, \cdot)$$ n/a 4800 24
8550.2.gs $$\chi_{8550}(289, \cdot)$$ n/a 6000 24
8550.2.gu $$\chi_{8550}(29, \cdot)$$ n/a 14400 24
8550.2.gv $$\chi_{8550}(641, \cdot)$$ n/a 14400 24
8550.2.gz $$\chi_{8550}(337, \cdot)$$ n/a 28800 48
8550.2.hc $$\chi_{8550}(23, \cdot)$$ n/a 28800 48
8550.2.hd $$\chi_{8550}(17, \cdot)$$ n/a 9600 48
8550.2.he $$\chi_{8550}(13, \cdot)$$ n/a 28800 48
8550.2.hf $$\chi_{8550}(127, \cdot)$$ n/a 12000 48
8550.2.hi $$\chi_{8550}(47, \cdot)$$ n/a 28800 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8550))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8550)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(171))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(342))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(450))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(475))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(570))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(855))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(950))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1425))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1710))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2850))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4275))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8550))$$$$^{\oplus 1}$$