# Properties

 Label 8026.2 Level 8026 Weight 2 Dimension 671006 Nonzero newspaces 8 Sturm bound 8.05208e+06

## Defining parameters

 Level: $$N$$ = $$8026 = 2 \cdot 4013$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$8052084$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8026))$$.

Total New Old
Modular forms 2017033 671006 1346027
Cusp forms 2009010 671006 1338004
Eisenstein series 8023 0 8023

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8026))$$

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
8026.2.a $$\chi_{8026}(1, \cdot)$$ 8026.2.a.a 71 1
8026.2.a.b 81
8026.2.a.c 86
8026.2.a.d 96
8026.2.b $$\chi_{8026}(8025, \cdot)$$ n/a 334 1
8026.2.d $$\chi_{8026}(53, \cdot)$$ n/a 5360 16
8026.2.e $$\chi_{8026}(831, \cdot)$$ n/a 5344 16
8026.2.f $$\chi_{8026}(263, \cdot)$$ n/a 19430 58
8026.2.h $$\chi_{8026}(119, \cdot)$$ n/a 19372 58
8026.2.j $$\chi_{8026}(7, \cdot)$$ n/a 310880 928
8026.2.k $$\chi_{8026}(9, \cdot)$$ n/a 309952 928

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8026))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8026)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(4013))$$$$^{\oplus 2}$$