# Properties

 Label 4013.2 Level 4013 Weight 2 Dimension 669002 Nonzero newspaces 8 Sturm bound 2.68403e+06

## Defining parameters

 Level: $$N$$ = $$4013$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$2684028$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4013))$$.

Total New Old
Modular forms 673013 673013 0
Cusp forms 669002 669002 0
Eisenstein series 4011 4011 0

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4013))$$

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
4013.2.a $$\chi_{4013}(1, \cdot)$$ 4013.2.a.a 1 1
4013.2.a.b 157
4013.2.a.c 176
4013.2.b $$\chi_{4013}(4012, \cdot)$$ n/a 334 1
4013.2.d $$\chi_{4013}(53, \cdot)$$ n/a 5328 16
4013.2.e $$\chi_{4013}(10, \cdot)$$ n/a 5344 16
4013.2.f $$\chi_{4013}(40, \cdot)$$ n/a 19314 58
4013.2.h $$\chi_{4013}(114, \cdot)$$ n/a 19372 58
4013.2.j $$\chi_{4013}(7, \cdot)$$ n/a 309024 928
4013.2.k $$\chi_{4013}(4, \cdot)$$ n/a 309952 928

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