# Properties

 Label 8035.2 Level 8035 Weight 2 Dimension 2.36242e+06 Nonzero newspaces 12 Sturm bound 1.03298e+07

## Defining parameters

 Level: $$N$$ = $$8035 = 5 \cdot 1607$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Sturm bound: $$10329792$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8035))$$.

Total New Old
Modular forms 2588872 2372057 216815
Cusp forms 2576025 2362425 213600
Eisenstein series 12847 9632 3215

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8035))$$

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
8035.2.a $$\chi_{8035}(1, \cdot)$$ 8035.2.a.a 1 1
8035.2.a.b 114
8035.2.a.c 127
8035.2.a.d 140
8035.2.a.e 153
8035.2.b $$\chi_{8035}(6429, \cdot)$$ n/a 802 1
8035.2.e $$\chi_{8035}(3213, \cdot)$$ n/a 1604 2
8035.2.g $$\chi_{8035}(1046, \cdot)$$ n/a 5360 10
8035.2.j $$\chi_{8035}(444, \cdot)$$ n/a 8020 10
8035.2.l $$\chi_{8035}(1163, \cdot)$$ n/a 16040 20
8035.2.m $$\chi_{8035}(96, \cdot)$$ n/a 38592 72
8035.2.p $$\chi_{8035}(34, \cdot)$$ n/a 57744 72
8035.2.r $$\chi_{8035}(38, \cdot)$$ n/a 115488 144
8035.2.s $$\chi_{8035}(6, \cdot)$$ n/a 385920 720
8035.2.t $$\chi_{8035}(4, \cdot)$$ n/a 577440 720
8035.2.w $$\chi_{8035}(7, \cdot)$$ n/a 1154880 1440

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8035))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8035)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1607))$$$$^{\oplus 2}$$