## Defining parameters

 Level: $$N$$ = $$799 = 17 \cdot 47$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$8$$ Sturm bound: $$52992$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(799))$$.

Total New Old
Modular forms 781 715 66
Cusp forms 45 41 4
Eisenstein series 736 674 62

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 41 0 0 0

## Trace form

 $$41q - 3q^{4} + q^{9} + O(q^{10})$$ $$41q - 3q^{4} + q^{9} - 10q^{12} - 10q^{14} - 7q^{16} - 2q^{17} - 10q^{18} - 10q^{24} + q^{25} - 10q^{32} - 3q^{36} - 10q^{42} - 7q^{47} + 30q^{48} + q^{49} - 8q^{50} - 5q^{51} - 4q^{53} + 30q^{54} - 4q^{55} + 30q^{56} - 10q^{63} - 11q^{64} - 11q^{68} - 10q^{72} + q^{81} - 14q^{83} + 70q^{84} - 4q^{89} - 10q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(799))$$

We only show spaces with odd 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
799.1.c $$\chi_{799}(798, \cdot)$$ 799.1.c.a 1 1
799.1.c.b 2
799.1.c.c 4
799.1.c.d 4
799.1.d $$\chi_{799}(375, \cdot)$$ None 0 1
799.1.e $$\chi_{799}(140, \cdot)$$ 799.1.e.a 2 2
799.1.e.b 8
799.1.h $$\chi_{799}(93, \cdot)$$ 799.1.h.a 4 4
799.1.h.b 16
799.1.i $$\chi_{799}(48, \cdot)$$ None 0 8
799.1.l $$\chi_{799}(35, \cdot)$$ None 0 22
799.1.m $$\chi_{799}(33, \cdot)$$ None 0 22
799.1.p $$\chi_{799}(13, \cdot)$$ None 0 44
799.1.q $$\chi_{799}(15, \cdot)$$ None 0 88
799.1.t $$\chi_{799}(3, \cdot)$$ None 0 176

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(799))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(799)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(47))$$$$^{\oplus 2}$$