# Properties

 Label 4021.2 Level 4021 Weight 2 Dimension 671676 Nonzero newspaces 16 Sturm bound 2.69474e+06

## Defining parameters

 Level: $$N$$ = $$4021$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$2694740$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4021))$$.

Total New Old
Modular forms 675695 675695 0
Cusp forms 671676 671676 0
Eisenstein series 4019 4019 0

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4021))$$

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
4021.2.a $$\chi_{4021}(1, \cdot)$$ 4021.2.a.a 1 1
4021.2.a.b 151
4021.2.a.c 182
4021.2.b $$\chi_{4021}(4020, \cdot)$$ n/a 334 1
4021.2.c $$\chi_{4021}(1812, \cdot)$$ n/a 668 2
4021.2.e $$\chi_{4021}(2401, \cdot)$$ n/a 1332 4
4021.2.f $$\chi_{4021}(1813, \cdot)$$ n/a 670 2
4021.2.g $$\chi_{4021}(49, \cdot)$$ n/a 1336 4
4021.2.i $$\chi_{4021}(37, \cdot)$$ n/a 2672 8
4021.2.k $$\chi_{4021}(110, \cdot)$$ n/a 2680 8
4021.2.m $$\chi_{4021}(67, \cdot)$$ n/a 21978 66
4021.2.n $$\chi_{4021}(13, \cdot)$$ n/a 22044 66
4021.2.o $$\chi_{4021}(77, \cdot)$$ n/a 44088 132
4021.2.q $$\chi_{4021}(27, \cdot)$$ n/a 87912 264
4021.2.r $$\chi_{4021}(53, \cdot)$$ n/a 44220 132
4021.2.s $$\chi_{4021}(17, \cdot)$$ n/a 88176 264
4021.2.u $$\chi_{4021}(3, \cdot)$$ n/a 176352 528
4021.2.w $$\chi_{4021}(4, \cdot)$$ n/a 176880 528

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