# Properties

 Label 1575.2.di Level 1575 Weight 2 Character orbit di Rep. character $$\chi_{1575}(169,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 1440 Sturm bound 480

# Related objects

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1575.di (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$225$$ Character field: $$\Q(\zeta_{30})$$ Sturm bound: $$480$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1575, [\chi])$$.

Total New Old
Modular forms 1952 1440 512
Cusp forms 1888 1440 448
Eisenstein series 64 0 64

## Trace form

 $$1440q - 180q^{4} - 8q^{5} + 4q^{9} + O(q^{10})$$ $$1440q - 180q^{4} - 8q^{5} + 4q^{9} - 16q^{11} + 40q^{12} + 8q^{14} - 20q^{15} + 180q^{16} + 6q^{20} + 28q^{24} + 24q^{25} + 24q^{29} - 20q^{30} + 12q^{31} + 62q^{36} + 140q^{38} - 12q^{39} + 100q^{42} - 80q^{44} - 138q^{45} - 50q^{47} - 330q^{48} + 720q^{49} + 50q^{50} - 20q^{51} - 126q^{54} + 12q^{55} - 24q^{56} + 6q^{59} + 178q^{60} - 20q^{63} + 360q^{64} - 80q^{65} - 180q^{66} - 30q^{67} + 70q^{69} + 152q^{71} - 140q^{72} - 188q^{74} - 60q^{75} - 300q^{78} - 384q^{80} - 52q^{81} + 24q^{85} - 20q^{86} - 250q^{87} + 80q^{89} + 16q^{90} - 140q^{92} - 72q^{94} - 20q^{95} + 8q^{96} - 84q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1575, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(1575, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(225, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database