# Properties

 Label 8100.2 Level 8100 Weight 2 Dimension 740936 Nonzero newspaces 48 Sturm bound 6998400

## Defining parameters

 Level: $$N$$ = $$8100 = 2^{2} \cdot 3^{4} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$6998400$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8100))$$.

Total New Old
Modular forms 1764720 745528 1019192
Cusp forms 1734481 740936 993545
Eisenstein series 30239 4592 25647

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8100))$$

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
8100.2.a $$\chi_{8100}(1, \cdot)$$ 8100.2.a.a 1 1
8100.2.a.b 1
8100.2.a.c 1
8100.2.a.d 1
8100.2.a.e 1
8100.2.a.f 1
8100.2.a.g 1
8100.2.a.h 1
8100.2.a.i 1
8100.2.a.j 1
8100.2.a.k 1
8100.2.a.l 1
8100.2.a.m 1
8100.2.a.n 1
8100.2.a.o 2
8100.2.a.p 2
8100.2.a.q 2
8100.2.a.r 2
8100.2.a.s 2
8100.2.a.t 2
8100.2.a.u 3
8100.2.a.v 3
8100.2.a.w 4
8100.2.a.x 4
8100.2.a.y 4
8100.2.a.z 4
8100.2.a.ba 4
8100.2.a.bb 4
8100.2.a.bc 6
8100.2.a.bd 6
8100.2.a.be 8
8100.2.d $$\chi_{8100}(649, \cdot)$$ 8100.2.d.a 2 1
8100.2.d.b 2
8100.2.d.c 2
8100.2.d.d 2
8100.2.d.e 2
8100.2.d.f 2
8100.2.d.g 2
8100.2.d.h 2
8100.2.d.i 2
8100.2.d.j 2
8100.2.d.k 4
8100.2.d.l 4
8100.2.d.m 4
8100.2.d.n 4
8100.2.d.o 6
8100.2.d.p 6
8100.2.d.q 8
8100.2.d.r 8
8100.2.d.s 8
8100.2.e $$\chi_{8100}(7451, \cdot)$$ n/a 444 1
8100.2.h $$\chi_{8100}(8099, \cdot)$$ n/a 424 1
8100.2.i $$\chi_{8100}(2701, \cdot)$$ n/a 152 2
8100.2.j $$\chi_{8100}(1457, \cdot)$$ n/a 144 2
8100.2.k $$\chi_{8100}(2107, \cdot)$$ n/a 848 2
8100.2.n $$\chi_{8100}(1621, \cdot)$$ n/a 480 4
8100.2.o $$\chi_{8100}(2699, \cdot)$$ n/a 856 2
8100.2.r $$\chi_{8100}(2051, \cdot)$$ n/a 900 2
8100.2.s $$\chi_{8100}(3349, \cdot)$$ n/a 144 2
8100.2.v $$\chi_{8100}(901, \cdot)$$ n/a 342 6
8100.2.w $$\chi_{8100}(971, \cdot)$$ n/a 2848 4
8100.2.x $$\chi_{8100}(2269, \cdot)$$ n/a 480 4
8100.2.ba $$\chi_{8100}(1619, \cdot)$$ n/a 2848 4
8100.2.bf $$\chi_{8100}(593, \cdot)$$ n/a 288 4
8100.2.bg $$\chi_{8100}(1243, \cdot)$$ n/a 1712 4
8100.2.bh $$\chi_{8100}(541, \cdot)$$ n/a 960 8
8100.2.bk $$\chi_{8100}(899, \cdot)$$ n/a 1920 6
8100.2.bm $$\chi_{8100}(1549, \cdot)$$ n/a 324 6
8100.2.bn $$\chi_{8100}(251, \cdot)$$ n/a 2016 6
8100.2.br $$\chi_{8100}(163, \cdot)$$ n/a 5696 8
8100.2.bs $$\chi_{8100}(1133, \cdot)$$ n/a 960 8
8100.2.bt $$\chi_{8100}(301, \cdot)$$ n/a 3078 18
8100.2.bw $$\chi_{8100}(539, \cdot)$$ n/a 5728 8
8100.2.bz $$\chi_{8100}(109, \cdot)$$ n/a 960 8
8100.2.ca $$\chi_{8100}(431, \cdot)$$ n/a 5728 8
8100.2.cc $$\chi_{8100}(307, \cdot)$$ n/a 3840 12
8100.2.ce $$\chi_{8100}(557, \cdot)$$ n/a 648 12
8100.2.cf $$\chi_{8100}(181, \cdot)$$ n/a 2160 24
8100.2.ch $$\chi_{8100}(299, \cdot)$$ n/a 17424 18
8100.2.cj $$\chi_{8100}(551, \cdot)$$ n/a 18360 18
8100.2.cm $$\chi_{8100}(49, \cdot)$$ n/a 2916 18
8100.2.cn $$\chi_{8100}(703, \cdot)$$ n/a 11456 16
8100.2.co $$\chi_{8100}(53, \cdot)$$ n/a 1920 16
8100.2.cs $$\chi_{8100}(71, \cdot)$$ n/a 12864 24
8100.2.ct $$\chi_{8100}(289, \cdot)$$ n/a 2160 24
8100.2.cv $$\chi_{8100}(179, \cdot)$$ n/a 12864 24
8100.2.cy $$\chi_{8100}(257, \cdot)$$ n/a 5832 36
8100.2.db $$\chi_{8100}(7, \cdot)$$ n/a 34848 36
8100.2.dc $$\chi_{8100}(61, \cdot)$$ n/a 19440 72
8100.2.dd $$\chi_{8100}(17, \cdot)$$ n/a 4320 48
8100.2.df $$\chi_{8100}(127, \cdot)$$ n/a 25728 48
8100.2.di $$\chi_{8100}(11, \cdot)$$ n/a 116352 72
8100.2.dj $$\chi_{8100}(169, \cdot)$$ n/a 19440 72
8100.2.dn $$\chi_{8100}(59, \cdot)$$ n/a 116352 72
8100.2.do $$\chi_{8100}(67, \cdot)$$ n/a 232704 144
8100.2.dr $$\chi_{8100}(77, \cdot)$$ n/a 38880 144

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8100))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8100)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(300))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(405))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(450))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(675))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(810))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(900))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1350))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1620))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2025))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2700))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4050))$$$$^{\oplus 2}$$