# Properties

 Label 6900.2 Level 6900 Weight 2 Dimension 507316 Nonzero newspaces 48 Sturm bound 5068800

## Defining parameters

 Level: $$N$$ = $$6900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$5068800$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6900))$$.

Total New Old
Modular forms 1279520 510756 768764
Cusp forms 1254881 507316 747565
Eisenstein series 24639 3440 21199

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6900))$$

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
6900.2.a $$\chi_{6900}(1, \cdot)$$ 6900.2.a.a 1 1
6900.2.a.b 1
6900.2.a.c 1
6900.2.a.d 1
6900.2.a.e 1
6900.2.a.f 1
6900.2.a.g 1
6900.2.a.h 1
6900.2.a.i 1
6900.2.a.j 2
6900.2.a.k 2
6900.2.a.l 2
6900.2.a.m 2
6900.2.a.n 2
6900.2.a.o 2
6900.2.a.p 2
6900.2.a.q 2
6900.2.a.r 2
6900.2.a.s 2
6900.2.a.t 2
6900.2.a.u 2
6900.2.a.v 2
6900.2.a.w 2
6900.2.a.x 3
6900.2.a.y 3
6900.2.a.z 3
6900.2.a.ba 4
6900.2.a.bb 4
6900.2.a.bc 7
6900.2.a.bd 7
6900.2.f $$\chi_{6900}(6349, \cdot)$$ 6900.2.f.a 2 1
6900.2.f.b 2
6900.2.f.c 2
6900.2.f.d 2
6900.2.f.e 2
6900.2.f.f 2
6900.2.f.g 2
6900.2.f.h 4
6900.2.f.i 4
6900.2.f.j 4
6900.2.f.k 4
6900.2.f.l 4
6900.2.f.m 4
6900.2.f.n 4
6900.2.f.o 4
6900.2.f.p 4
6900.2.f.q 4
6900.2.f.r 6
6900.2.f.s 8
6900.2.g $$\chi_{6900}(2299, \cdot)$$ n/a 432 1
6900.2.h $$\chi_{6900}(1151, \cdot)$$ n/a 836 1
6900.2.i $$\chi_{6900}(4001, \cdot)$$ n/a 152 1
6900.2.n $$\chi_{6900}(3449, \cdot)$$ n/a 144 1
6900.2.o $$\chi_{6900}(599, \cdot)$$ n/a 792 1
6900.2.p $$\chi_{6900}(2851, \cdot)$$ n/a 456 1
6900.2.q $$\chi_{6900}(2207, \cdot)$$ n/a 1712 2
6900.2.r $$\chi_{6900}(2393, \cdot)$$ n/a 264 2
6900.2.s $$\chi_{6900}(1243, \cdot)$$ n/a 792 2
6900.2.t $$\chi_{6900}(1057, \cdot)$$ n/a 144 2
6900.2.y $$\chi_{6900}(1381, \cdot)$$ n/a 448 4
6900.2.z $$\chi_{6900}(1241, \cdot)$$ n/a 960 4
6900.2.ba $$\chi_{6900}(2531, \cdot)$$ n/a 5280 4
6900.2.bb $$\chi_{6900}(919, \cdot)$$ n/a 2880 4
6900.2.bc $$\chi_{6900}(829, \cdot)$$ n/a 432 4
6900.2.bh $$\chi_{6900}(91, \cdot)$$ n/a 2880 4
6900.2.bi $$\chi_{6900}(1979, \cdot)$$ n/a 5280 4
6900.2.bj $$\chi_{6900}(689, \cdot)$$ n/a 960 4
6900.2.bo $$\chi_{6900}(301, \cdot)$$ n/a 760 10
6900.2.bt $$\chi_{6900}(1333, \cdot)$$ n/a 960 8
6900.2.bu $$\chi_{6900}(967, \cdot)$$ n/a 5280 8
6900.2.bv $$\chi_{6900}(737, \cdot)$$ n/a 1760 8
6900.2.bw $$\chi_{6900}(827, \cdot)$$ n/a 11456 8
6900.2.bx $$\chi_{6900}(451, \cdot)$$ n/a 4560 10
6900.2.by $$\chi_{6900}(899, \cdot)$$ n/a 8560 10
6900.2.bz $$\chi_{6900}(149, \cdot)$$ n/a 1440 10
6900.2.ce $$\chi_{6900}(401, \cdot)$$ n/a 1520 10
6900.2.cf $$\chi_{6900}(1451, \cdot)$$ n/a 9000 10
6900.2.cg $$\chi_{6900}(199, \cdot)$$ n/a 4320 10
6900.2.ch $$\chi_{6900}(49, \cdot)$$ n/a 720 10
6900.2.cq $$\chi_{6900}(157, \cdot)$$ n/a 1440 20
6900.2.cr $$\chi_{6900}(307, \cdot)$$ n/a 8640 20
6900.2.cs $$\chi_{6900}(257, \cdot)$$ n/a 2880 20
6900.2.ct $$\chi_{6900}(107, \cdot)$$ n/a 17120 20
6900.2.cu $$\chi_{6900}(121, \cdot)$$ n/a 4800 40
6900.2.cz $$\chi_{6900}(89, \cdot)$$ n/a 9600 40
6900.2.da $$\chi_{6900}(59, \cdot)$$ n/a 57280 40
6900.2.db $$\chi_{6900}(511, \cdot)$$ n/a 28800 40
6900.2.dg $$\chi_{6900}(169, \cdot)$$ n/a 4800 40
6900.2.dh $$\chi_{6900}(19, \cdot)$$ n/a 28800 40
6900.2.di $$\chi_{6900}(71, \cdot)$$ n/a 57280 40
6900.2.dj $$\chi_{6900}(221, \cdot)$$ n/a 9600 40
6900.2.dk $$\chi_{6900}(83, \cdot)$$ n/a 114560 80
6900.2.dl $$\chi_{6900}(77, \cdot)$$ n/a 19200 80
6900.2.dm $$\chi_{6900}(127, \cdot)$$ n/a 57600 80
6900.2.dn $$\chi_{6900}(37, \cdot)$$ n/a 9600 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6900))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6900)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(138))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(276))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(300))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(345))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(575))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(690))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1380))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1725))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2300))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3450))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6900))$$$$^{\oplus 1}$$