# Properties

 Label 8043.2 Level 8043 Weight 2 Dimension 1.68308e+06 Nonzero newspaces 16 Sturm bound 9.38803e+06

## Defining parameters

 Level: $$N$$ = $$8043 = 3 \cdot 7 \cdot 383$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$9388032$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8043))$$.

Total New Old
Modular forms 2356176 1690699 665477
Cusp forms 2337841 1683083 654758
Eisenstein series 18335 7616 10719

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8043))$$

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
8043.2.a $$\chi_{8043}(1, \cdot)$$ 8043.2.a.a 1 1
8043.2.a.b 1
8043.2.a.c 1
8043.2.a.d 1
8043.2.a.e 1
8043.2.a.f 1
8043.2.a.g 1
8043.2.a.h 1
8043.2.a.i 1
8043.2.a.j 1
8043.2.a.k 1
8043.2.a.l 2
8043.2.a.m 3
8043.2.a.n 40
8043.2.a.o 41
8043.2.a.p 41
8043.2.a.q 44
8043.2.a.r 46
8043.2.a.s 50
8043.2.a.t 52
8043.2.a.u 53
8043.2.d $$\chi_{8043}(3065, \cdot)$$ n/a 1020 1
8043.2.e $$\chi_{8043}(2297, \cdot)$$ n/a 768 1
8043.2.h $$\chi_{8043}(2680, \cdot)$$ n/a 512 1
8043.2.i $$\chi_{8043}(1150, \cdot)$$ n/a 1020 2
8043.2.j $$\chi_{8043}(1531, \cdot)$$ n/a 1024 2
8043.2.m $$\chi_{8043}(3446, \cdot)$$ n/a 2040 2
8043.2.n $$\chi_{8043}(1916, \cdot)$$ n/a 2036 2
8043.2.q $$\chi_{8043}(43, \cdot)$$ n/a 72960 190
8043.2.r $$\chi_{8043}(13, \cdot)$$ n/a 97280 190
8043.2.u $$\chi_{8043}(155, \cdot)$$ n/a 145920 190
8043.2.v $$\chi_{8043}(62, \cdot)$$ n/a 193800 190
8043.2.y $$\chi_{8043}(4, \cdot)$$ n/a 194560 380
8043.2.bb $$\chi_{8043}(17, \cdot)$$ n/a 387600 380
8043.2.bc $$\chi_{8043}(11, \cdot)$$ n/a 387600 380
8043.2.bf $$\chi_{8043}(10, \cdot)$$ n/a 194560 380

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8043))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8043)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(383))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1149))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2681))$$$$^{\oplus 2}$$