# Properties

 Label 4003.2 Level 4003 Weight 2 Dimension 665667 Nonzero newspaces 8 Sturm bound 2.67067e+06

## Defining parameters

 Level: $$N$$ = $$4003$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$2670668$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4003))$$.

Total New Old
Modular forms 669668 669668 0
Cusp forms 665667 665667 0
Eisenstein series 4001 4001 0

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4003))$$

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
4003.2.a $$\chi_{4003}(1, \cdot)$$ 4003.2.a.a 2 1
4003.2.a.b 152
4003.2.a.c 179
4003.2.c $$\chi_{4003}(822, \cdot)$$ n/a 666 2
4003.2.e $$\chi_{4003}(551, \cdot)$$ n/a 7304 22
4003.2.f $$\chi_{4003}(102, \cdot)$$ n/a 9296 28
4003.2.i $$\chi_{4003}(129, \cdot)$$ n/a 14652 44
4003.2.j $$\chi_{4003}(10, \cdot)$$ n/a 18648 56
4003.2.m $$\chi_{4003}(6, \cdot)$$ n/a 204512 616
4003.2.o $$\chi_{4003}(4, \cdot)$$ n/a 410256 1232

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