# Properties

 Label 8092.2 Level 8092 Weight 2 Dimension 1105296 Nonzero newspaces 40 Sturm bound 7990272

## Defining parameters

 Level: $$N$$ = $$8092 = 2^{2} \cdot 7 \cdot 17^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$7990272$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8092))$$.

Total New Old
Modular forms 2009568 1112668 896900
Cusp forms 1985569 1105296 880273
Eisenstein series 23999 7372 16627

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8092))$$

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
8092.2.a $$\chi_{8092}(1, \cdot)$$ 8092.2.a.a 1 1
8092.2.a.b 1
8092.2.a.c 1
8092.2.a.d 1
8092.2.a.e 1
8092.2.a.f 1
8092.2.a.g 1
8092.2.a.h 1
8092.2.a.i 1
8092.2.a.j 1
8092.2.a.k 2
8092.2.a.l 2
8092.2.a.m 2
8092.2.a.n 2
8092.2.a.o 3
8092.2.a.p 3
8092.2.a.q 4
8092.2.a.r 4
8092.2.a.s 8
8092.2.a.t 8
8092.2.a.u 12
8092.2.a.v 12
8092.2.a.w 12
8092.2.a.x 12
8092.2.a.y 20
8092.2.a.z 20
8092.2.b $$\chi_{8092}(6357, \cdot)$$ n/a 136 1
8092.2.e $$\chi_{8092}(8091, \cdot)$$ n/a 1052 1
8092.2.f $$\chi_{8092}(1735, \cdot)$$ n/a 1054 1
8092.2.i $$\chi_{8092}(1157, \cdot)$$ n/a 362 2
8092.2.k $$\chi_{8092}(251, \cdot)$$ n/a 2104 2
8092.2.l $$\chi_{8092}(6609, \cdot)$$ n/a 272 2
8092.2.p $$\chi_{8092}(579, \cdot)$$ n/a 2108 2
8092.2.q $$\chi_{8092}(4623, \cdot)$$ n/a 2104 2
8092.2.t $$\chi_{8092}(1733, \cdot)$$ n/a 360 2
8092.2.u $$\chi_{8092}(757, \cdot)$$ n/a 536 4
8092.2.w $$\chi_{8092}(2491, \cdot)$$ n/a 4208 4
8092.2.z $$\chi_{8092}(327, \cdot)$$ n/a 4208 4
8092.2.ba $$\chi_{8092}(905, \cdot)$$ n/a 720 4
8092.2.bd $$\chi_{8092}(827, \cdot)$$ n/a 6480 8
8092.2.be $$\chi_{8092}(2561, \cdot)$$ n/a 1440 8
8092.2.bg $$\chi_{8092}(477, \cdot)$$ n/a 2432 16
8092.2.bi $$\chi_{8092}(977, \cdot)$$ n/a 1440 8
8092.2.bk $$\chi_{8092}(423, \cdot)$$ n/a 8416 8
8092.2.bn $$\chi_{8092}(307, \cdot)$$ n/a 19520 16
8092.2.bo $$\chi_{8092}(475, \cdot)$$ n/a 19520 16
8092.2.br $$\chi_{8092}(169, \cdot)$$ n/a 2432 16
8092.2.bt $$\chi_{8092}(1025, \cdot)$$ n/a 2880 16
8092.2.bu $$\chi_{8092}(907, \cdot)$$ n/a 16832 16
8092.2.bw $$\chi_{8092}(137, \cdot)$$ n/a 6528 32
8092.2.by $$\chi_{8092}(225, \cdot)$$ n/a 4864 32
8092.2.bz $$\chi_{8092}(55, \cdot)$$ n/a 39040 32
8092.2.cb $$\chi_{8092}(305, \cdot)$$ n/a 6528 32
8092.2.ce $$\chi_{8092}(271, \cdot)$$ n/a 39040 32
8092.2.cf $$\chi_{8092}(103, \cdot)$$ n/a 39040 32
8092.2.cj $$\chi_{8092}(83, \cdot)$$ n/a 78080 64
8092.2.cl $$\chi_{8092}(253, \cdot)$$ n/a 9856 64
8092.2.cn $$\chi_{8092}(81, \cdot)$$ n/a 13056 64
8092.2.co $$\chi_{8092}(47, \cdot)$$ n/a 78080 64
8092.2.cr $$\chi_{8092}(41, \cdot)$$ n/a 26112 128
8092.2.cs $$\chi_{8092}(71, \cdot)$$ n/a 117504 128
8092.2.cu $$\chi_{8092}(19, \cdot)$$ n/a 156160 128
8092.2.cw $$\chi_{8092}(9, \cdot)$$ n/a 26112 128
8092.2.cz $$\chi_{8092}(11, \cdot)$$ n/a 312320 256
8092.2.da $$\chi_{8092}(5, \cdot)$$ n/a 52224 256

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8092))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8092)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(289))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(476))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(578))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1156))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2023))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4046))$$$$^{\oplus 2}$$