# Properties

 Label 8042.2 Level 8042 Weight 2 Dimension 673684 Nonzero newspaces 16 Sturm bound 8.08422e+06

## Defining parameters

 Level: $$N$$ = $$8042 = 2 \cdot 4021$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$8084220$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8042))$$.

Total New Old
Modular forms 2025075 673684 1351391
Cusp forms 2017036 673684 1343352
Eisenstein series 8039 0 8039

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8042))$$

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
8042.2.a $$\chi_{8042}(1, \cdot)$$ 8042.2.a.a 67 1
8042.2.a.b 82
8042.2.a.c 86
8042.2.a.d 101
8042.2.b $$\chi_{8042}(8041, \cdot)$$ n/a 336 1
8042.2.c $$\chi_{8042}(5833, \cdot)$$ n/a 670 2
8042.2.e $$\chi_{8042}(2401, \cdot)$$ n/a 1348 4
8042.2.f $$\chi_{8042}(1813, \cdot)$$ n/a 668 2
8042.2.g $$\chi_{8042}(49, \cdot)$$ n/a 1344 4
8042.2.i $$\chi_{8042}(37, \cdot)$$ n/a 2680 8
8042.2.k $$\chi_{8042}(329, \cdot)$$ n/a 2672 8
8042.2.m $$\chi_{8042}(67, \cdot)$$ n/a 22242 66
8042.2.n $$\chi_{8042}(13, \cdot)$$ n/a 22176 66
8042.2.o $$\chi_{8042}(77, \cdot)$$ n/a 44220 132
8042.2.q $$\chi_{8042}(27, \cdot)$$ n/a 88968 264
8042.2.r $$\chi_{8042}(53, \cdot)$$ n/a 44088 132
8042.2.s $$\chi_{8042}(17, \cdot)$$ n/a 88704 264
8042.2.u $$\chi_{8042}(3, \cdot)$$ n/a 176880 528
8042.2.w $$\chi_{8042}(39, \cdot)$$ n/a 176352 528

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8042))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8042)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(4021))$$$$^{\oplus 2}$$