# Properties

 Label 8013.2 Level 8013 Weight 2 Dimension 1.78089e+06 Nonzero newspaces 16 Sturm bound 9.51232e+06

## Defining parameters

 Level: $$N$$ = $$8013 = 3 \cdot 2671$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$9512320$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8013))$$.

Total New Old
Modular forms 2383420 1786229 597191
Cusp forms 2372741 1780889 591852
Eisenstein series 10679 5340 5339

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8013))$$

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
8013.2.a $$\chi_{8013}(1, \cdot)$$ 8013.2.a.a 94 1
8013.2.a.b 106
8013.2.a.c 116
8013.2.a.d 129
8013.2.b $$\chi_{8013}(8012, \cdot)$$ n/a 888 1
8013.2.e $$\chi_{8013}(544, \cdot)$$ n/a 890 2
8013.2.f $$\chi_{8013}(2575, \cdot)$$ n/a 1784 4
8013.2.h $$\chi_{8013}(545, \cdot)$$ n/a 1778 2
8013.2.l $$\chi_{8013}(473, \cdot)$$ n/a 3552 4
8013.2.m $$\chi_{8013}(37, \cdot)$$ n/a 3560 8
8013.2.o $$\chi_{8013}(881, \cdot)$$ n/a 7112 8
8013.2.q $$\chi_{8013}(490, \cdot)$$ n/a 39248 88
8013.2.t $$\chi_{8013}(104, \cdot)$$ n/a 78144 88
8013.2.u $$\chi_{8013}(40, \cdot)$$ n/a 78320 176
8013.2.v $$\chi_{8013}(4, \cdot)$$ n/a 156992 352
8013.2.x $$\chi_{8013}(62, \cdot)$$ n/a 156464 176
8013.2.z $$\chi_{8013}(11, \cdot)$$ n/a 312576 352
8013.2.bc $$\chi_{8013}(10, \cdot)$$ n/a 313280 704
8013.2.be $$\chi_{8013}(14, \cdot)$$ n/a 625856 704

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8013))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8013)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(2671))$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database