## Defining parameters

 Level: $$N$$ = $$6041 = 7 \cdot 863$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$5958144$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6041))$$.

Total New Old
Modular forms 1494708 1431773 62935
Cusp forms 1484365 1423161 61204
Eisenstein series 10343 8612 1731

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6041))$$

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
6041.2.a $$\chi_{6041}(1, \cdot)$$ 6041.2.a.a 1 1
6041.2.a.b 2
6041.2.a.c 83
6041.2.a.d 101
6041.2.a.e 112
6041.2.a.f 132
6041.2.c $$\chi_{6041}(6040, \cdot)$$ n/a 574 1
6041.2.e $$\chi_{6041}(3453, \cdot)$$ n/a 1148 2
6041.2.g $$\chi_{6041}(1725, \cdot)$$ n/a 1148 2
6041.2.i $$\chi_{6041}(8, \cdot)$$ n/a 185760 430
6041.2.k $$\chi_{6041}(13, \cdot)$$ n/a 246820 430
6041.2.m $$\chi_{6041}(2, \cdot)$$ n/a 493640 860
6041.2.o $$\chi_{6041}(5, \cdot)$$ n/a 493640 860

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6041))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6041)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(863))$$$$^{\oplus 2}$$