# Properties

 Label 6044.2 Level 6044 Weight 2 Dimension 664400 Nonzero newspaces 8 Sturm bound 4.56624e+06

## Defining parameters

 Level: $$N$$ = $$6044\( 6044 = 2^{2} \cdot 1511$$ \) Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$4566240$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6044))$$.

Total New Old
Modular forms 1145335 667420 477915
Cusp forms 1137786 664400 473386
Eisenstein series 7549 3020 4529

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6044))$$

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
6044.2.a $$\chi_{6044}(1, \cdot)$$ 6044.2.a.a 63 1
6044.2.a.b 63
6044.2.c $$\chi_{6044}(6043, \cdot)$$ n/a 754 1
6044.2.e $$\chi_{6044}(2045, \cdot)$$ n/a 504 4
6044.2.f $$\chi_{6044}(423, \cdot)$$ n/a 3016 4
6044.2.i $$\chi_{6044}(9, \cdot)$$ n/a 18900 150
6044.2.k $$\chi_{6044}(55, \cdot)$$ n/a 113100 150
6044.2.m $$\chi_{6044}(5, \cdot)$$ n/a 75600 600
6044.2.p $$\chi_{6044}(11, \cdot)$$ n/a 452400 600

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6044))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6044)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1511))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3022))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database